-------
"•6 DAILY CLEANING OF TEST CHAMBERS
or
- -a
fl'tted
. 7
TEST SOLUTION RENEWAL
a
have proven suitablefor effi,«?
on-site toxicity studies no more thin 24
of the effluent and use in a t°M{y t'i?
t.,t is stored ,„ an
nta'ers Such as 8-20
and storage. For
^
one solution is aerted the u OXysfn co"ce"t^tion
aerated. Aerate the test solution 'in ?h- tl,50nh8nJrations must be
larvae are not disturbed. the test Cambers gently, so that
H.8 ROUTINE CHEMICAL AND PHYSICAL ANALYSIS
(Figure 7*):' •?ni""' the f«"^"9 -asuren,ents are made and recorded
137
-------
11.8.1.1 DO is measured at the beginning and end of each 24-h exposure
period in one test chamber at all test concentrations and in the control.
11.8.1.2 Temperature, pH, and salinity are measured at the end of each 24-h
exposure period in one test chamber at all test concentrations and in the
control- The pH is measured in the effluent sample each day.
11.9 OBSERVATIONS DURING THE TEST
11.9.1 The number of live larvae in each test chamber are recorded daily
(Figure 7), and the dead larvae are discarded.
11.9.2 Daily test observations, solution renewals, and removal of dead
larvae, should be carried out carefully to protect the larvae from
unnecessary disturbance during the test. Care should be taken to see that
the larvae remain immersed at all times during the performance of the above
operations.
11.10 TERMINATION OF THE TEST
11.10.1 The test is terminated after seven days of exposure. At
termination, the number of surviving larvae in each test chamber are counted
and as a group are immediately prepared for drying and weighing, or are
preserved in 4% formalin or 70% ethanol for drying and weighing at a later
date. For immediate drying and weighing, siphon or pour live larvae onto a
500 urn mesh screen in a large beaker to retain the larvae and allow Artemia
to be rinsed away. Rinse the larvae with cold deionized water to remove
salts that might contribute to the dry weight. Sacrifice the larvae in an
ice bath of deionized water. Small aluminum weighing boats can be used to
dry and weigh larvae. An appropriate number of aluminum weigh boats (one
per replicate) are marked for identification and weighed to 0.01 mg, and the
weights are recorded (Figure 8) on the data sheets.
11.10.2 Immediately before drying, the preserved larvae are rinsed in
distilled water. The rinsed larvae from each test chamber are transferred,
using forceps, to a tared weighing boat and dried at 6QQC for 24 h, or at
105°C for a minimum of 6 h. Immediately upon removal from the drying
oven, the weighing boats are placed in a desiccator to cool and to prevent
the adsorption of moisture from the air until weighed. Weigh all weighing
boats containing the dried larvae to 0.01 mg, subtract the tare weight to
determine dry weight of larvae in each replicate, and record (Figure 8) of
data sheets). Divide the dry weight by the number of larvae per replicate
to determine the average dry weight, and record (Figures 8 and 9) of the
data sheets. Complete the summary data sheet (Figure 9) after calculating
the average measurements and statistically analyzing the dry weights and per
cent survival for the entire test.
138
-------
12. ACCEPTABILITY OF TEST RESULTS
12.1 Test results are acceptable if (1) the average survival of control
larvae is equal to or greater than 80#, and (2) where the test starts with
7-day old larvae, the average dry weight of the control larvae, when dried
immediately after test termination, is equal to or greater than 0.50 mg, or
the average dry weight of the control larvae preserved in 4% formalin or 70%
ethanol is equal to or greater than 0.43 mg.
13. SUMMARY OF TEST CONDITIONS
13.1 A summary of test conditions is listed in Table 2. %
14. DATA ANALYSIS
14.1 General
14.1.1 Tabulate and summarize the data.
14.1.2 The end points of toxicity tests using the inland silverside are
based on the adverse effects on survival and growth. Point estimates* such
as LCI, LC5, LC10 and LC50, are calculated using Probit Analysis (Finney,
1971). LOEC and NOEC values, for survival and growth, are obtained using a
hypothesis test approach such as Dunnett's Procedure (Dunnett, 1955) or
Steel's Many-one Rank Test (Steel, 1959; Miller, 1981). See the Appendix
for examples of the manual computations, program listings, and examples of
data input and program output.
14.1.3 The statistical tests described here must be used with a knowledge
of the assumptions upon which the tests are contingent. The assistance of a
statistician is recommended for analysts who are not proficient in
statistics.
14.2 EXAMPLE OF ANALYSIS OF MENIDIA SURVIVAL DATA
14.2.1 Formal statistical analysis of the survival data is outlined in
Fiqure 2. The response used in the analysis is the proportion of animals
surviving in each test or control chamber. Separate analyses are performed
for the estimation of the NOEC and LOEC end points and for the estimation of
the LCI, LC5, LC10 and LC50 end points. Concentrations at which there is no
survival in any of the test chambers are excluded from statistical analysis
of the NOEC and LOEC, but included in the estimation of the LC end points.
14.2.2 For the case of equal numbers of replicates across all
concentrations and the control, the evaluation of the NOEC and LOEC end
points is made via a parametric test, Dunnett's Procedure, or a
nonparametric test, Steel's Many-one Rank Test, on the arcsin transformed
data. Underlying assumptions of Dunnett's Procedure, normality and
homogeneity of variance, are formally tested. The test for normality is the
Shapiro-Wilks Test, and Bartlett's Test is used to determine the homogeneity
of variance. If either of these tests fail, the nonparametric test, Steel's
Many-one Rank Test, is used to determine the NOEC and LOEC end points. If
the assumptions of Dunnett's Procedure are met, the end points are estimated
by the parametric procedure.
139
-------
TABLE 2. SUMMARY OF RECOMMENDED TEST CONDITIONS FOR THE INLAND STI VFpqrnr
(MENIDIA BERYLLINA) LARVAL SURVIVAL AND GROWTH TEST SILVERSIDE
1. Test type:
2. Salinity:
3. Temperature:
4. Light quality:
5. Light intensity:
6. Photoperiod:
7. Test chamber size:
8. Test solution volume:
9. Renewal of test
concentrations:
10. Age of test organisms:
11. Larvae/test chamber
and control:
12. Replicate
chambers/concentration
13. Source of food:
14. Feeding regime:
15. Cleaning:
16. Aeration:
Static-renewal
5 o/oo to 32 o/oo (+ 2 o/oo of
the selected test salinity)
.25 + 20C
Ambient laboratory illumination
10-20 uE/m2/s (50-100 ft-c) (ambient
laboratory, levels)
14 h light, 10 h darkness
300 mL - 1 L containers
250-750 mL/replicate (loading and
DO restrictions must be met)
daily
7-11 days post hatch
15 (minimum of 10)
4 (minimum of 3)
Newly hatched Artemia nauplii
Feed 0.10 g wet weight Artemia
nauplii per replicate orTdays 0-2;
Feed 0.15 g wet weight Artemia
nauplii per replicate on~dayT"3-6
Siphon daily, immediately before test
solution renewal and feeding
None* unless DO concentration falls
below 60% of saturation, then
aerate all chambers. Rate should be
less than 100 bubbles/min.
-------
H»i iiril HMIiiii nil t«tl iiiiit'ifirillna-l
TABLE 2. SUMMARY OF RECOMMENDED TEST CONDITIONS FOR THE INLAND SILVERSTDF
BERYLLINA) LARVAL SURVIVAL AND GROWTH TEST (CONTINUED)
17. Dilution water:
18. Effluent concentrations
19. Dilution factor:
20. Test duration:
21. Effects measured:
Uncontaminated source of sea
water or deionized water mixed
with hypersaline brine.
At least 5 and a control
Approximately 0.3 or 0.5
7 days
Survival and growth (weight)
141
-------
14-2.4 Probit Analysis (Finnev 10711 -
TABLE 3. INLAND SILVERSIDE SURVIVAL
DATA
RAW
0.80
0.87
0.93
0.73
0.80
0.87
0.80
0.33
0.60
0.40
0.53
0.07
0.0
0.0
0.0
0.0
0.0
0.0
ARC SINE
TRANS-
FORMED
1.107
1.202
1.303
.024
1.107
1.202
0-612
0.886
0.685
0.815
0.268
MEAN (7,-
S-,-2
1.204
0.010
1
1.111
0,008
2
0-868 0.589
0-061 0.082
3 4
14.2.6 Test for Normality
observations by sub trying the ^ oT.l?^"* 1s t0 cente' the
concentration from each observation in till °bservatio^ within a
observat7ons are summarized in Tab?e 4 * concent™tion. The centered
142
-------
SURVIVAL
SURVIVAL DATA
PROPORTION SURVIVING
„ ARCSIN
TRANSFORMATION
LC1PL°C5.TLCE10TILMCA5T0E
DISTRIBUTION
NORMAL DISTRIBUTION
BARTLETT'S TEST
HETEROGENEOUS
VARIANCE
HOMOGENEOUS VARIANCE
EQUAL NUMBER OF
REPLICATES?
EQUAL NUMBER OF
REPLICATES?
T-TEST WITH
BONFERRONI
STEEL'S MANY-ONE
WILCOXON RANK SUM
TEST WITH
BONFERRONI ADJUSTMENT
ADJUSTMENT
"gun, 2. How chart for statistical analysis of Menida survival data.
-------
XH-
— UJU.
*-coo<
*~- uioru.
O(/)0.—
iO
o 6
NOlldOdOdd
T
d
T
q
d
144
-------
TABLE 4. CENTERED OBSERVATIONS FOR SHAPRIO-WILKS EXAMPLE
Effluent Concentration (%} ,^:>:>'
Replicate
A
B
C
Control
-0.097
-0.002
0.099
1.0
-0.087
-0.004
0.091
3.2
0.239
-0.256
0.018
10.0
0.096
0.226
-0.321
14.2.6.2 Calculate the denominator, D9 of the statistic:
n
D -
X)2
Where: Xj = the ith centered observation
X = the overall mean of the centered observations
n = the total number of centered observations
14.2.6.3 For this set of data, n =.12
t? . i
(0.002) = 0.0002
12
D = 0.3214
14.2.6.4 Order the centered observations from smallest to largest
where x(i) denotes the ith ordered observation. The ordered
observations for this example are listed in Table 5.
TABLE 5. ORDERED CENTERED OBSERVATIONS FOR SHAPIRO-WILKS EXAMPLE
i
1
2
3
4
5
6
xd>
-0.321
-0.256
-0.097
-0.087
-0.004
-0.002
i
7
8
9
10
11
12
xtD
0.018
0.091
0.096
0.099
0.226
0.239
145
-------
14.2.6.5 From Table 4, Appendix B, for the number of observations, n,
obtain the coefficients ai, 32, ... a^ where k is approximately
n/2. For the data in this example, n = 12 and k = 6. The a-,- values are
listed in Table 6.
: 14.2.6.6 Compute the test statistic, W, as follows:
i
k
w s
D
The differences
in this example,
W =
- Xti)) ]2
- x(i) are listed in Table 6. For the data
= °-945
TABLE 6. COEFFICIENTS AND DIFFERENCES FOR SHAPIRO-WILKS EXAMPLE
a
xtn-i+1) -
1
2
3
4
5
6
0.5475
0.3325
0.2347
0.1586
0.0922 .
0.0303
0.560
0.482
0.196
0.183
0.095
0.020
XH2) - Xd)
x\ 1 1 ) - x'^ )
X(10) - X(3)
x(9) - x^4)
x(8) - x(5)
XC7) . X 6
14.2.6.7 The decision rule for this test is to compare W as calculated
in 14.2.6.6 to a critical value found in Table 6, Appendix B. If the
computed W is less than the critical value, conclude that the data are
not normally distributed. For the data in this example, the critical
value at a significance level of 0.01 and n - 12 observations is 0.805.
Since W = 0.945 is greater than the critical value, conclude that the
data are normally distributed*
14.2.7 Test for Homogeneity of Variance
14.2.7.1 The test used to examine whether the variation in survival is
the same across all effluent concentrations including the control, is
Bartlett's Test (Snedecor and Cochran, 1980). The test statistic is as
follows:
P
[ ( I
1=1
In S2 - t YJ In
1=1
146
-------
Where
P =
degrees of freedom for each effluent concen^
tration and control, Vi = (nj - 1)
number of levels of effluent concentration
including the control
t.E,Vi Si2j
P P
C = 1 + [ 3(p-l)]-l [ I 1/Vi - ( t
In = loge
i -1,2, ..., p where p is the number of concentrations
including the control
nj = the number of replicates for concentration i.
14.2.7,2 For the data in this example, (See Table 3) all effluent
concentrations including the control have the same number of replicates
{ni - 3 for all i). Thus, Vi - 2 for all i.
14.2.7.3 Bartlett's statistic is therefore:
B - [(8)ln(0.0402) - 2 I ln(S?j/1.2083
i = l 1
= [8(-3.2139) - 2(-14.73T)J/1.2083
- 3.7508/1.2083
=. 3.104
14.2.7.4 B is approximately distributed as chi-square with p - 1 degrees
of freedom, when the variances are in fact the same. Therefore, the
appropriate critical value for this test, at a significance level of 0.01
with three degrees of freedom, is 11.345. Since B = 3.104 is less than
the critical value of 11.345, conclude that the variances are not
different.
147
-------
14.2.8 Dunnett's Procedure
14.2.8.1 To obtain an estimate of the pooled variance for the Dunnett's
Procedure, construct an ANOVA table as described in Table 7.
TABLE 7. ANOVA TABLE
Source
Between
Within
Total
Where:
df
P - 1
N - p
N - 1
p = number
N = total
n-j = number
Sum of Squares Mean Square(MS)
(SS) CSS/df)
2
SSB SB ^ 5SB/(p-l)
2
ssw ' SW - SSW/(N-p)
SST
of effluent concentrations including the contn
number of observations n] + p? ..* +np
of observations in concentration i
SSB - I Tj2/ni - G2/N
Between Sum of Squares
SST «
Total Sum of Squares
SSW = SST - SSB
Within Sum of Squares
r
G = the grand total of all sample observations, G = I T-j
T-j = the total of the replicate measurements for
concentration "i"
(ii = the jth observation for concentration "i" (represents
the proportion surviving for effluent concentration
i in test chamber j)
148
-------
14.2.8.2 For the data in this example
__ ^ __ _ __ -•*
ri 1 — no — no ~ n/i — ^
N = 12
T] = YH + Yi2 + Y]3 = 3.612
T2 = Y2i + Y22 + Y23 « 3.333
^3 = Y31 + Y32 + Y33 - 2.605
T4 = Y41 + Y42 + Y43 - 1.768
G = T] + T2 + T3 + T4 = 11.318
p
SSB = £ T-j2/ni - Q2/N
- (11.318)2 s
n-i
SST =
- (11.318)2
12
.002
SSW = SST - SSB - 1.002 - 0.681 - 0.321
SB2 - SSB/p-1 - 0.681/4-1 - 0.227
SW2 = SSW/N-p = 0.321/12-4 - 0.040
14.2.8.3 Summarize these calculations in the ANUVA table (Table 8)
TABLE 8. ANOVA TABLE FOR DUNNETTS PROCEDURE EXAMPLE
Source
Between
Within
df
3
8
Sum of Squares
(SS)
0.681
0.321
Mean Square(MS)
(SS/df)
0.227
0.040
Total
11
.002
149.
-------
14.2.8.4 To perform the individual comparisons, calculate the t
statistic for each concentration, and control combination as follows:
Where Yi
ni
SWV HAii) + (1/ni)
* mean proportion surviving for effluent concentration i
= mean proportion surviving for the control
= square root of within mean sqaure
= number of replicates for control
= number of replicates for concentration i.
14.2,8.5 Table 9 includes the calculated t values for each
concentration and control combination. In this example, comparing the
concentration with the control the calculation is as follows:
1.
( 1.204 - 1.111 )
[ 0.20 v/ 1173'} + (1/3) ]
= 0.570
TABLE 9. CALCULATED T-VALUES
Effluent Concentration^)
1.0
3.2
10.0
2
3
4
0.570
2.058
3.766
14.2.8.6 Since the purpose of this test is to detect a significant
reduction in survival, a (one-sided) test is appropriate. The critical
value for this one-sided test is found in Table 5, Appendix C. For an
overall alpha level of 0.05, eight degrees of freedom for error and three
concentrations (excluding the control) the critical value is 2.42. The
mean proportion surviving for concentration "i" is considered
significantly less than the mean proportion surviving for the control if
ti is greater than the critical value. Therefore, only the 10.0%
concentration has a significantly lower mean proportion surviving than
the control. Hence the NOEC is 3.2% and the LOEC is 10.0%.
-------
14.2.8.7 To quantify the sensitivity of the test, the minimum significant
difference (MSD) that can be detected statistically may be calculated.
MSD = d SWV (1/ni) + (1/n)
Where d = the critical value for the Dunnett's procedure
SK = the square root of the within mean square
n = the common number of replicates at each concentration
(this assumes equal replication at each concentration
n-f = the number of replicates in the control.
14.2.8.8 In this example:
- ;,- MSD - 2.42 (0.20) /TT/S) + (1/3F
= 2.42 (0.20H0.817)
= 0.395
14.2.8.9 The MSD (0.395) is in transformed units. To determine the MSD in
terms of percent survival, carry out the following conversion.
1. Subtract the MSD from the transformed control mean*
1.204 - 0.395 = 0.809
2. Obtain the untransformed values for the control mean and the
difference calculated in 4.10.1.
[Sine (1.204) ]2 * 0.871
[Sine (0.809) ]2 = 0.524
3. The untransformed MSD (MSDU) is determined by subtracting the
untransformed values from 4.10*2.
MSDU'= 0.871 - 0.524 = 0.347
14.2.8.10 Therefore, for this set of data, the minimum difference in mean
proportion surviving between the control and any effluent concentration that
can be detected as statistically significant is 0.347.
14.2.8.11 This represents a 40% decrease in survival from the control.
151
-------
:;;;;;
14.2.9 Probit Analysis ,J
dff* use?.r°r the probit analysis is summarized in
r,re,r^a«^s "s
«-
i:
TABLE 10. DATA FOR PROBIT ANALYSIS
Number Dead
Number Exposed
6
45
9
45
.Effluent Concentration (%)
Control 1.0 3,2 10.0 32.0 100.0
19
45
30
45
45
45
45
45
152
-------
TABLE 11. OUTPUT FROM EPA PROBIT ANALYSIS PROGRAM. Version 1.3
USED FOR CALCULATING EC VALUES
Probit Analysis of Inland Silverside Larval Survival Data
Cone.
control
1.0000
3.2000
10.0000
32.0000
100.0000
Number
Exposed
45
45
45
45
45
45
Number
Resp.
6
9
19
30
45
45
Proportion
Responding
0.1333
0.2000
0.4222
0.6667
1.0000
1.0000
Adjusted
Proportion
Responding
0,0000
0.0483
0.3126
0.6034
1.0000
1.0000
Predicted
Proportion
Responding
0.1594
0.0262
0.2479
0.7094
0.9649
0.9988
Chi - Square Heterogeneity =
4.026
Mu
Sigma
Parainet er
I nt erirept
Slope
Spoutaneous
Response Rate
0.778527
0.401388
Estimate
std. Err.
95% confidence Limits
3.060416
2.491352
0.159420
0.445523
0.449330
0.044587
( 2.187191,
{ 1.610665,
( 0.072030,
3.933641)
3. 372039)
0.246810)
Estimated F.c Values and Confidence Limits
Poi nt
Cone.
0.6995
1.3131
1.8370
2.3042
6.0052
15.6504
19.6312
27.4644
51,5557
Lower Upper
Confidence Limits
1.4644
2.3671
3.0701
3.6688
8.2460
24.5887
33.5876
54.3685
138.5833
0. J575
0.4109
0.6825
0.9587
3.8086
11.4046
14.0149
18.6517
30.8662
153
-------
PLOT OF ADJUSTED PROBITS AND PREDICTED REGRESSION LINE
Probit
10+
9 +
7 +
6 +
5 +
4 +
3 +
2 +
+
EC01
EC10
EC25
EC50 EC75 EC90
EC99
figure 4. Plot of adjusted probits and predicted regression line,
154
-------
14.3 ANALYSIS OF GROWTH DATA
14.3.1 Formal statistical analysis of the growth data is outlined in
Figure 5. The response used in the statistical analysis is mean weight per
replicate. Concentrations above the NOEC for survival are excluded from the
growth analysis.
14.3.2 The statistical analysis consists of a parametric test, Dunnett's
Procedure, and a non-parametric test. Steel's Many-one Rank Test. The
underlying assumptions of the Dunnett's Procedure, normality and homogeneity
of variance, are formally tested. The test for normality is the
Shapiro-Wilks Test and Bartlett's Test is used to test for homogeneity of
variance. If either of these tests fail, the non-parametric test, Steel's
Many-one Rank Test, is used to determine the NOEC and LOEC end points. If
the assumptions of Dunnett's Procedure are met, the end points are
determined by the parametric test,
14.3.3 Additionally, if unequal numbers of replicates occur among the
concentration levels tested there are parametric and non-parametric
alternative analyses. The parametric analysis is the Bonferroni t-test. The
Wilcoxon Rank Sum Test with the Bonferroni adjustment is the non-parametric
alternative. For detailed information on the Bonferroni adjustment, see the
Appendix.
14.3.4 The data, mean and standard deviation of the growth observations at
each concentration including the control are listed in Table 12. A plot of
the data in Table 12 is provided in Figure 6. Since there was no survival
in the 32% and 100% concentrations, these are not considered in the growth
analysis. Additionally, since there is significant mortality in the 10%
effluent concentration, its effect on growth is not considered.
TABLE 12. INLAND SILVERSIDE GROWTH DATA
Replicate Control
Effluent Concentration (%)
1.0
3.2
10.0 32.0 100.0
A
B
C
Mean (7,-)
Si2
i
0.939
0.976
0.975
0.963
0.0004
1
0.996
1.152
1.066
1.071
0.006
2
0.903
0.864
1.197
0.988
0.033
3
0.491 -
0.589 -
1.131 -
0.737 -
0.119 -
4 5
_
-
."
-
-
6
155
-------
STATISTICAL ANALYSIS OF INLAND SILVERSIDE LARVAL
SURVIVAL AND GROWTH TEST
GROWTH DATA
(EXCLUDING CONCENTRATIONS" ABOVE NOEC FOR SURVIVAL)
DISTRIBUTION
NORMAL DISTRIBUTION
HETEROGENEOUS
VARIANCE
BARTLE.TT'S TEST
HOMOGENEOUS VARIANCE
EQUAL NUMBER OF
REPLICATES?
EQUAL NUMBER OF
REPLICATES?
WILCOXON RANK SUM
TEST WITH
BONFERRONI ADJUSTMENT
STEEL'S MANY-ONE
ENDPOINT ESTIMATES
NOEC, LOEC
Figure 5. Flow chart for statistical analysis of Menldia growth data.
156
-------
i
ttJ
0>
s-
o
.«'. 1* ....,.,,.
ddddddddddoddddddddd
(OH) 1HOGM NV3W
O
d
157
-------
14.3.5 Test for Normality
a
ation from each observation ,'n that ™ observations within a
observations are summarized in Table ?3 conce^ration. The centered
TABLE 13. CENTERED OBSERVATIONS FOR SHAPIRO-
WILKS EXAMPLE
0.024
0.013
0.012
0.075
0.08T
0.005
-0.085
-0.124
0.209
H.3.5.2 Calculate the denominator, D, of the test Stat1st1c
D = Z (Xf - x)2
7=1
Where X7- = the ith centered observation
5 == ffi ss^is s
For this set of data:
n B g
1(0.002) = 0.000
D - 0.0794
'4.3.5.3 Order th. centered observations fro, s.allest to ,.P9est.
- ... .X(n)
ob""«*"'"- Th.,e ordered observations
{„'
158
-------
TABLE 14.
ORDERED CENTERED OBSERVATIONS FOR SHAPIRO-UILKS EXAMPLE
-0.124
-0.085
-0.075
-0.024
-0.005
6
7
8
9
0.012
0.013
0.081
0.209
' *
n/2. For the d^th
listed in Table 15.
n,
are
14.3.5.5 Compute the test statistic, W, as follows:
k
- xd'Jj ]2
W = 1 [,r ai-
The differences x(n-i+l) _ x(j)
of data:
are H t d .
nstea in Table 15. For this set
0.0794
.2707)2 = n
*t/u/; u-
TABLE 15. COEFFICIENTS AND DIFFERENCES FOR SHAPRIO-WILKS EXAMPLE
x(n-i+1) - x(i)
' ' —
X(9) -
1
2
3
4
0.5888
0.3244
0.1976
0.0947
0.333
0.166
0.088
0.036
X<7)
X(6)
X(3)
X(4)
the
159
-------
14.3.6 Test for Homogeneity of Variance
14.3.6.1 The test used to examine whether the variation in mean dry
weight is the same across all effluent concentrations including the
control, is Bartlett's Test {Snedecor and Cochran, 1980). The test
statistic is as follows:
R —
[ ( I Vi) In 52 - I Vi In
Where V-j = degrees of freedom for each effluent concen-
tration and control, V, = (nj - 1)
number of levels of effluent concentration
including the control
C = 1 + ( 3{p-l))-l [ X 1/V-i - ( I v-j)-l ]
1*1 i=l
In = loge
i = 1, 2, ..., p where p is the number of concentrations
including the control
n-j = the number of replicates for concentration i.
14,3.6.2 For the data in this example, (See Table 12) all effluent
concentrations including the control have the same number of replicates
(rif = 3 for all i). Thus, V, = 2 for all i.
14.3.6.3 Bartlett's statistic is therefore:
B = [{6)ln(0.0132) - 2 I ln(S1)2]/i.25
1-1
- [6(-4.3275) - 2(ln(0.0004)+ln{0.0061)+ln(0.0331))]/1.25
- t-25.965 - {-32.664)J/1.25
« 5.359
160
-------
appropriate critical value for this test
with 2 degrees of freedom, is sfz '
cnt,c.T..v.,u. of 9.270. concede
14.3.7 Dunnett's Procedure
B -
- 1 "9"",
- .The)"efore, the
7eVe] °f °'0]
Source
Total
TABLE 16. ANOVA TABLE
N - 1
Sum of Squares
(SS)
Between
Within
P - 1
N - p
SSB
SSW
SST
Mean Square(MS)
(SS/dfJ
SB = SSB/(p-l)
2
SSW/{N-p)
Where:
nf = number of observations in concentraion*! P
* I T7-2/ni - Q2/N
Between Sum of Squares
SST » z zt 2 . G2/N
i=l j=1
SSW = SST - SSB
Total Sum of Squares
Within Sum of Squares
the grand total of all sample observations, G = j TI-
for
iJ
hP mpL°HServation for Concentration »i» (represents
the mean dry weight of the fish for effuent
concentration f in test chamber jj 6TTIuent
161
-------
14.3.7.2 For the data in this
example:
T3 -
G =
SSB =
tf f Y]3 = 0.939 + 0.
Y22 + Y23 - C
= 2.890
- 0.903 + 0.864 +i:?97==23;92644
T2 + T3 = 9.068
1_(27.467) -
ii-068)2
9
0.019
n.
= 9-235 - (9^68)2 , ^
- SST - SSB » 0.098 - 0.0)9 = 0.079
SB2 - SSB/p-1 , 0.019/3-1 . 0.009
SW2 = SSW/N-p = 0.079/9-3 = 0.013
'4-3.7.3 s«.rfze these calculations in the ANOVA fbl. (Table ,7)
TABLE 17. ANOVA TABLE FOR DUNNETT'S PROCEDURE EXAMPLE
Source
df
Sum of Squares
(SS)
Mean Square(MS)
(SS/df)
Between 2
Within
-------
"ere f;
W
< Yl - Yl )
— —
Sh/N/TlA)]) + (]/nf
g
- square root of within mean sqaure
- number of replicates for control
- number of replicates for' concentration i
1.0* concentration
t =
TABLE 18. CALCULATED T-VALUES
•••
Effluent Concentration
.- t, .»".„*
ca value for this one-sided test it fn , ?PProPrlate. The
For an overall alpha level of 0 05 six rf« "d ^ Iable 5» APPe"dix C
two concentrations (excluding the wntrol)9th^Sr0-/re?doni for error
The mean weight for concentration •?" is rnnS?rff "J10?1 Value fs 2'34-
than mean weight for the control if \ • conside''ed significantly less
value. Therefore, all efS concelltMt?n«t-r ^an the Criti"l
have significantly lower mean weights than V^f '" Jhl? example do not
and the LOEC for growth can not bf calculated °U He"Ce the NOEC
calculated,
statistically may be
163
-------
Where d =
n =
m =
14.3.7.8 In this example:
can be'
= 2.34 (0.114) VTT73TTT
"2.34 (O.T14H0.8T65
- 0.218
1S represe"ts
reduction fn niean .eight fro, the
15- PRECISION AND
15.1 PRECISION
an^ S S°r'*°E
sulfate as reference^oxicants
Tables 19 and 20. in the '
of the inland ,
and sodful"
are ™1d in
' the
15.2 ACCURACY
15-2.1 The accuracy of toxicity tests cannot be determined.
164
-------
TABLE 19. SINGLE LABORATORY PRECISION OF THE INLAND SILVERSIOE
(MENIDIA BERYLLINA) SURVIVAL AND GROWTH TEST PERFORMED IN
=1L *™™:. ™ rAE FROM FISH ^«YN
SEAWATER, AND COPPER AS /
Survival
Test
NOEC
(ug/LJ
63
125
135
125
125
Growth
LOEC
(ug/L)
125
250
250
250
250
NOEC
(ug/L)
••"— • r- • i
125
125
63
125
31
LOEC
(ug/L)
— - i i — I,,
SE
SE
125
SE
63
Most
Sensitive
End Point
S
G
G
'Tests performed by George Morrison and Elise Torello
were: 31, 63, 125, 250,and 500 ug/u
3Adults collected in the field.
co"ce"trations
5SE = Survival effects. Growth data at these
'
165
-------
™LE
Test
™
SKATER. USING LARVAE FROM
luryjvaj
NOEC L0£c
(mg/L)
Growth
NOEC
(mg/L)
Most
Sensitive
End Point
*t = Survival Effprtc r
concentrations were disreaaTL/?*' at these ^^'cant
reduction in sUrviVa?.Sre9arded because there was a significant
166
-------
o o
s- •«-
c
O
t/i c:
13
S_ Jfl gj
oj >
03 —
Q. 03
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S- 0
o
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s_
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cn
(D -^
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W T
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o
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-^ "*
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si:
i ^
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t—
LLJ
5
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aj
OJ 00
IET (Tl
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a>
nj
-------
-o
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•- ^z
n *•-
a. =
t-
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a.
hU
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t.
a
u
1-
<
t
C
L
z
o
cc
t-
UJ
O
z
•0 O
*•
tt
Effluent 1
r*
(O
^
^
m
«
-
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r-
(D
if)
1
tN
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to
I »
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to
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5 «
u
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UJ —
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fjumnvs I
i 0
0
o
m
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i —
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3B
*-
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_
^
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h
•
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-^ 3 1
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il
li
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is
Ul
< >
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?'
il
*s
h
c
I/
t- +
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0 '
ul
ff!
z
—
—
. t-
LX
. z
UJ
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o
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t „!
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1 -
TEMP
m
SALINITY
2
Q
X -^
s ?
i!
5*
* a
Is
« a
o
«
i- •
i
15 5*
Ji
si
-------
Figure 8. Data forms for inland silverside larval survival
and growth test. Dry weights of larvaeJ
[Test Dates:
Species:
Pan
#
Cone,
&
Rep.
Initial
Wt.
Final
Wt.
(mg)
Diff.
(mg)
#
Larvae
Av. Wt./
Larvae
(mg)
'Adapted from: M. A. Heber, M. M. Hughes, S. C. Schimmel, and
D. Bengtson, 1987
169
-------
Tost Dates:
Figure 9. Data forms for inland silverside larval
survival and growth test. Summary of test
results. '
Species:
Effluent Tested:
TREATMENT
# LIVE
LARVAE
SURVIVAL
{%)
MEAN DRY WT./
LARVAE fmg)
±S.D.
SIGNIF. DIFF.
FROM CONTROL
(o)
MEAN
TEMPERATURE
(oC)
+ S.D.
MEAN SALINITY
000
±S.D.
AV. DISSOLVED
OXYGEN
(mg.t) +S.D
••MM^M^H
COMMENTS;
^Adapted from: Heber, M.
and D. Bengston, 1987.
A., M. M. Hughes, S. C. Sctiimnel,
70
-------
SECTION 14
TEST METHOD1'2
MYSID (MYSIDOPSIS BAHl/\) SURVIVAL, GROWTH, AND FECUNDITY TEST
METHOD 1007
1. SCOPE AND APPLICATION
1.1 This method estimates the chronic toxicity of effluents and receiving
waters to the estuarine mysid, Mysidopsis bahia, during a seven-day, <
static-renewal exposure. The effects include the synergistic, antagonistic,
and additive effects of all the chemical, physical, and additive components
which adversely affect the physiological and biochemical functions of the test
organisms.
1,2 Detection limits of the toxicity of an effluent or pure substance are
organism dependent.
1 3 Single or multiple excursions in toxicity may not be detected using 24-h
composite samples. Also, because of the long sample collection period
involved in composite sampling and because the test chambers are not sealed,
highly volatile and highly degradable toxicants in the source may not be
detected in the test.
1.4 This method should be restricted to use by, or under the supervision^of,
professionals experienced in aquatic toxicity testing. Specialized training
is required to determine the sex of the maturing mysids and the presence of
eggs in the oviducts of the females.
2. SUMMARY OF METHOD
2 1 This rapid-chronic test consists of an exposure of 7-day old Mysidopsis
bahia juveniles to different concentrations of effluent, or to receiving water
Tna static system, during the period of egg development. The test end points
are survival, growth (measured as dry weight), and fecundity {measured as the
percentage of females with eggs in the oviduct and/or brood pouch).
3. DEFINITIONS
(Reserved for addition of terms at a later date).
4. INTERFERENCES
4.1 Toxic substances may be introduced by contaminants in dilution water,
glassware, sample hardware, and testing equipment (see Section 5, Facilities
and Equipment).
^The format used for this method was taken from Kopp, 1983.
2This method was adapted from Lussier, Kuhn, and Sewall. 1987, Environmental ,
Research Laboratory, U. S. Environmental Protection Agency, Narragansett,
Rhode Island. r;
-------
4.2 Improper effluent sampling and handling may adversely affect test
results (see Section 8, Effluent and Receiving Water Sampling and Sample
Handling).
4.3 The test results can be confounded by (1) the presence of pathogenic
and/or predatory organisms in the dilution water and effluent, (2) the
condition of the brood stock from which the test animals were taken, (3) the
amount and type of natural food in the effluent or dilution water, (4)
nutritional value of the Artemia nauplii fed during the test, and (5) the
quantity of Artemia nauplii or other food added during the test, which may
sequester metals and other toxic substances, and lower the DO.
5. SAFETY
5.1 See Section 3, Health and Safety.
6. APPARATUS AND EQUIPMENT
6.1 Facilities for holding and acclimating test organisms.
6.2 Brine shrimp culture unit -- see paragraph 7.12 below.
6.3 Mysid culture unit — see Paragraph 7 below. This test requires a
minimum of 240 7-day old {juvenile} mysids. It is preferable to obtain the
test organisms from an inhouse culture unit. If it is not feasible to
culture mysids inhouse, juveniles can be obtained from other sources, if
shipped in well oxygenated saline water in insulated containers.
6.4 Samplers -- automatic sampler, preferrably with sample cooling
capability, that can collect a 24-h composite sample of 5 L.
6.5 Environmental chamber or equivalent facility with temperature control
(26 + IOC).
6.6 Water purification system -- Millipore Super-Q, deionized water or
equivalent.
6.7 Balance — capable of accurately weighing to 0.000001 g.
6.8 Reference weights, Class S — for checking performance of balance.
Reference weights should bracket the expected weights of the weighing boats
and weighing boats plus organisms.
6.9 Drying oven -- 105°C, for drying organisms.
6.10 Desiccator -- for holding dried organisms.
6.11 Air pump — for supplying air.
6.12 Air lines, and air stones -- for aerating cultures, brood chambers, -,'
and holding tanks, and supplying air to test solutions with low DO.
172
-------
6.13 pH and DO meters -- for routine physical and chemical measurements.
Unless the test is being conducted to specifically measure the effect of one
of the above parameters, a portable, field-grade instrument is acceptable.
6.14 Tray -- for test vessels; approximately 90 X 48 cm to hold 56 vessels.
6.15 Standard or micro-Winkler apparatus -- for determining DO and checking
DO meters
6.16 Dissecting microscope (350-400X magnification) -- for examining
organisms in the test vessels to determine their sex and to check for the
presence of eggs in the oviducts of the females.
6.17 Light box -- for illuminating organisms during examination.
6.18 Refractometer or other method-- for determining salinity.
6.19 Thermometers, glass or electronic, laboratory grade -- for measuring
water temperatures.
6.20 Thermometers, bulb-thermograph or electronic-chart type -- for
continuously recording temperature.
6.21 Thermometer, National Bureau of Standards Certified (see USEPA METHOD
170.1, USEPA, 1979} -- to calibrate laboratory thermometers.
6.22 Test vessels -- 200 mi borosilicate glass beakers or 8 oz disposable
plastic cups (manufactured by Falcon Division of Becton, Dickinson Co., 1950
Williams Dr., Oxnard, CA 93030} or other similar containers. Cups must be
rinsed thorougnly in distilled or deionized water and then pre-soaked
(conditioned) overnight in dilution water before use. Forty-eight (48) test
vessels are required for each test (eight replicates at each of five
effluent concentrations and a control).
6.23 Beakers or flasks -- six, borosilicate glass or non-toxic plasticware,
2000 ml for making test solutions.
6.24 Wash bottles -- for deionized water, for washing organisms from
containers and for rinsing small glassware and instrument electrodes and
probes.
6.25 Volumetric flasks and graduated cylinders -- Class A, borosilicate
glass or non-toxic plastic labware, 50-2000 ml for making test solutions.
6.26 Separatory funnels, 2-1 -- Two-four for culturing Artemia.
6.27 Pipets, volumetric — Class A, 1-100 nt.
6.28 Pipets, automatic -- adjustable, 1-100 ml.
6.29 Pipets, serological -- 1-10 ml, graduated.
173
-------
6.30 Pipet bulbs and fillers — PROPIPETR, or equivalent.
6.31 Droppers, and glass tubing with fire polished edges, 4mm ID — for
transferring organisms.
6.32 Forceps — for transferring organisms to weighing boats.
6.33 NITEXR mesh sieves {150 urn and 1000 urn) — for concentrating
organisms.
6.34 Depression glass slides or depression spot plates -- two, for
observing organisms.
7. REAGENTS AND CONSUMABLE MATERIALS
7.1 Sample containers -- for sample shipment and storage (see Section 8,
Effluent and Receiving Water Sampling and Sample Handling).
7.2 Data sheets {one set per test) — for data recording {Figures 14, 15,
and 16).
7.3 Tape, colored and markers, water-proof — for labelling and marking
test chambers, containers, etc.
7.4 Weighing boats, aluminum — to determine the dry weight of organisms.
7.5 Buffers, pH 4, 7, and 10 (or as per instructions of instrument
manufacturer) -- for standards and calibration check (see USEPA Method
150.1, USEPA, 1979).
7.6 Membranes and filling solutions for dissolved oxygen probe (see USEPA
Method 360.1, USEPA, 1979), or reagents for modified Winkler analysis.
7.7. Laboratory quality assurance samples and standards for the above
methods.
7.8 Reference toxicant solutions (see Section 4» Quality Assurance).
7.9 Reagent water -- defined as distilled or deionized water that does not
contain substances which are toxic to the test organisms {see paragraph 6.6
above).
7.10 Effluent, surface water, and dilution water — see Section 7, Dilution
Water, and Section 8, Effluent and Surface Water Sampling and Sample
Handling. Dilution water containing organisms that might prey upon or
otherwise interfere with the test organisms should be filtered through a
fine mesh net {with 150 urn or smaller openings).
7.10.1 Saline test and dilution water — The salinity of the test water
must be in the range of 20 %o to 30 o/oo. The salinity should vary by
174
-------
no more than + 2 °/oo among the chambers on a given day. If effluent and
receiving water tests are conducted concurrently, the salinities of these
tests should be similar.
7.10.1.1 The overwhelming majority of industrial and sewage treatment
effluents entering marine and estuarine systems contain little or no
measurable salts. Exposure of mysids to these effluents will require
adjustments in the salinity of the test solutions. It is important to
maintain a constant salinity across all treatments. In addition, it may be
desirable to match the test salinity with that of the receiving water.
Although artificial sea salts have been shown to be acceptable for
life-cycle toxicity tests with mysids (Home, et al, 1983; ASTM, 1986), the
use of artificial sea salts in this test is not recommended at this time.
Hypersaline brine derived from natural seawater should be used to adjust
salinities. However, it should be noted that with (100 °/oo) hypersaline
brine, the maximum concentration of effluent that can be tested is 80%
effluent at 20 °/oo salinity and 70% effluent at 70 °/oo salinity.
7.10.1.2 Hypersaline brine -(HSB) has several advantages that make it
desirable for use in toxicity testing. It can be made from any high
quality, filtered seawater by evaporation, and can be added to the effluent
or to deionized water to increase the salinity. Brine derived from natural
seawater contains the necessary trace metals, biogenic colloids, and some of
the microbial components necessary for adequate growth, survival, and/or
reproduction of marine and estuarine organisms, and may be stored for
prolonged periods without any apparent degradation.
7,10.1.3 The Ideal container for making brine from natural seawater is one
that (1) has a high surface to volume ratio, (2) is made of a non-corrosive
material, and (3) is easily cleaned (fiberglass containers are ideal).
Special care should be used to prevent any toxic materials from coming in
contact with the seawater being used to generate the brine. If a heater is
immersed directly into the seawater, ensure that the heater materials do not
corrode or leach any substances that would contaminate the brine. One
successful method used is a thermostatically controlled heat exchanger made
from fiberglass. For aeration, use only oil-free air compressors to prevent
contamination.
7.10.1.4 Before adding seawater to the brine generator, thoroughly clean
the generator, aeration supply tube, heater, and any other materials that
will be in direct contact with the brine. A good quality biodegradable
detergent should be used, followed by several thorough deionized water
rinses. High quality (and preferably high salinity) seawater should be
filtered to at least 10 urn before placing into the brine generator. Water
should be collected on an incoming tide to minimize the possibility of
contamination.
7.10.1.5 The temperature of the seawater is increased slowly to 40°C.
The water should be aerated to prevent temperature stratification and to
increase water evaporation. The brine should be checked daily (depending on
the volume being generated) to ensure that the salinity does not exceed
175
-------
100 °/oo and that the temperature does not exceed 4Q°C, Additional
seawater may be added to the brine to obtain the volume of brine required.
7.10,1.6 After the required salinity is attained, the HSB should be
filtered a second time through a 10 urn filter and poured directly into
portable containers (20-L cubitainers or polycarbonate water cooler jugs are
suitable). The containers should be capped and labelled with the date the
brine was generated and its salinity. Containers of HSB should be stored in
the dark and maintained under room temperature until used.
7.10.1.7 If a source of HSB is available, test solutions can be made by
following the directions below:
7.10.1.8 Thoroughly mix together the deionized water and brine before
mixing in the effluent. Divide the salinity of the HSB by the expected test
salinity to determine the proportion of deionized water to brine. For
example, if the salinity of the brine is 100 /oo salinity from a HSB of
100 o/oo, 200 ml of brine and 800 ml of deionized water are required.
7.10.1.9 Table 1 illustrates the composition of 3-L test solutions at 20
o/oo if they are made by combining effluent (0 °/oo), deionized water
and HSB of 100 o/oo (only). The volume (ml) of brine required is
determined by using the amount calculated above. In this case, 200 ml of
brine is required for 1 L; therefore, 600 ml would be required for 3 L of
solution. The volumes of HSB required are constant. The volumes of
deionized water are determined by subtracting the volumes of effluent and
brine from the total volume of solution: 3000 ml - ml effluent - ml brine =
ml deionized water.
7.12 .BRINE SHRIMP (ARTEMIA) NAUPLII {see Peltier and Weber, 1985).
7.12.1 Newly hatched Artemia nauplii are used for food for the stock
cultures and test organisms. Although there are many commercial sources of
brine shrimp cysts, the Brazilian or Colombian strains are preferred because
the supplies examined have had low concentrations of chemical residues and
produce nauplii of suitably small size. (One source that has been found to
be acceptable is Aquarium Products, 180L Penrod Ct., Glen Burnie, Maryland
21061). Each new batch of Artemia cysts must be evaluated for size
(Vanhaecke and Sorgeloos, 1980, and Vanhaecke et al., 1980) and nutritional
suitability (see Leger et al., 1985, 1986) against known suitable reference
cysts by performing a side-by-side larval growth test using the "new" and
"reference" cysts. The "reference" cysts used in the suitability test may
be a previously tested and acceptable batch of cysts, or may be obtained
from the Quality Assurance Branch, Environmental Monitoring and Support
Laboratory, Cincinnati, Ohio. A sample of newly-hatched Artemia nauplii
from each new batch of cysts should be chemically analyzed.If the,
concentration of total organic chlorine exceeds 0.15 ug/g wet weight, or the
176
-------
TABLE 1. QUANTITIES OF EFFLUENT, DEIONIZED WATER, AND HYPERSALINE BRINE
(100 o/oo) NEEDED TO PREPARE 1800 ML VOLUMES OF TEST SOLUTION
WITH A SALINITY OF 20 o/oo.
Effluent
Concentration
'(*)
33
10
3.3
1.0
0.33
Control
Volume of
Effluent
(0 o/oo)
(iML)
600
200
67
22
7.3
—
Volume of
Deionized
Water
(mL)
840
1240
1373
1418
1433
1440
Volume of
Hypersaline
Brine
(mL) j.
360
360
360
360
360
360
Total
896
7744
2160
177
-------
total concentration of organochlorine pesticides plus PCBs exceeds 0.3 ug/g
wet weight, the Arternla cysts should not be used (For analytical method see
EPA, 1982).
7.1?. 2 Artemia nauplii are obtained as follows:
1. Add 1 L of seawater, or an aqueous uniodized salt (NaCl) solution
prepared with 35 g salt or artificial sea salts per liter, to a 2-L
separatory funnel, or equivalent.
2. Add 10 ml Artemia cysts to the separatory funnel and aerate for 24 h
at 27°C, Hatching time varies with incubation temperature and the
geographic strain of Artemia used. See Peltier and Weber (1985),
for details on Artemia culture and quality control.
3. After 24 h, cufoTTTFe air supply in the separatory funnel.
Artemia nauplii are phototactic, and will concentrate at the bottom
of the "funnel if it is covered for 5-10 min with a dark cloth or
paper towel. Caution: if the concentrated nauplii are left on the
bottom much longer than 10 min without aeration, excessive mortality
will result.
4. Drain the nauplii into a funnel fitted with a 150 urn Nitex screen,
and rinse with seawater or equivalent before use.
5. Resuspend the nauplii on the funnel in a small amount of water for
feeding.
7.12.3 Testing the acceptability of Arteinia, nauplii as food for mysids.
7.12.3.1 The primary criteria for acceptability of each new supply of brine
shrimp 'cysts is adequate survival, growth, and reproduction of the mysids.
The tnysids used to evaluate the acceptability of the brine shrimp nauplii
must be of the same geographical origin and stage of development (7 days
old) as those used routinely in the toxicity tests. Two 7-day chrome tests
are performed side-by-side, each consisting of eight replicate test vessels
containing five juveniles (40 organisms per test, total of BO organisms).
The juveniles in one set of test chambers is fed reference (acceptable)
nauplii and the other set is fed nauplii from the "new" source of Artemia
cysts.
7.12.3.2 The feeding rate and frequency, test vessels, volume of control
water, duration of the test, and age of the nauplii at the start of the
should be the same as used for the routine toxicity tests.
test,
are only
The
7.12.3.3 Results of the brine shrimp nutrition assay, where there
two treatments, can be evaluated statistically by use of a t-test.
"new" food is acceptable if there are no statistically significant
differences in the survival, growth, and reproduction of the mysids fed the
two sources of nauplii.
7.13 MYSIDS
(See Rodgers, et al., 1986, and
information on inysid ecology)
Peltier and Weber, 1985, for
7.13.1 Brood Stock
7.13.1.1
cultures
To provide an adequate supply of juveniles for a test, mysid
should be started at least four weeks before the test animals
are
178
-------
needed. At least 200 mysids should be placed in each culture tank to ensure
that 1500 to 2000 animals will be available by the time preparations for a
test are initiated.
7.13,1.2 Mysids may be shipped or otherwise transported in polyethylene
bottles or CUBITAINERSR. Place 50 animals in 700 ml of seawater in a 1-L
shipping container. To control bacterial growth and prevent DO depletion
during shipment, do not add food. Before closing the shipping container,
oxygenate the water for 10 min. The mysids will starve if not fed within
36 h, therefore, they should be shipped so that they are not in transit more
than 24 h.
7.13.1.3 The identification of. the stock culture should be verified using
the key from Heard, Price and Stuck, 1987. Records of the verification
should be retained along with a few of the preserved specimens.
7.13.1.4 Glass aquaria {120- to 200-L) are recommended for cultures. Other
types of culture chambers may also be convenient. Three or more separate
cultures should be maintained to protect against loss of the entire culture
stock in case of accident, low DO, or high nitrite levels, and to provide
sufficient numbers of juvenile mysids for toxicity tests. Fill the aquaria
about three-fourths full of seawater. A flow-through system is recommended
if sufficient natural seawater is available, but a closed, recirciflating or
static renewal system may be used if proper water conditioning is provided
and care is exercised to keep the pH above 7,8 and nitrite levels below
0.05 mg/L.
7.13.1.5 Standard aquarium undergravel filters should be used with either
the flow-through or recirculating system to provide aeration and a current
conducive to feeding (Gentile et al.» 1983). The undergravel filter is
covered with a prewashed, coarse T^-5 mm) dolomite substrate, 2.5 cm deep
for flow-through cultures or 10 cm deep for recirculating cultures.
7.13.1.6 The recirculating culture system is conditioned as follows:
1. After the dolomite has been added, the filter is attached to the air
supply and operated for 24 h.
2. Approximately. 4 L of seed water obtained from a successfully
operating culture is added to the culture chamber.
3. The nitrite level is checked daily with an aquarium test kit or with
EPA Method 354.1. (USEPA, 1979b).
4. Add about 30 ml of concentrated Artemia nauplii every other day until
the nitrite level reaches at least 2.0 mg/L. The nitrite will
continue to rise for several days without adding more Artemia and
will then slowly decrease to less than 0.05 mg/L.
5. After the nitrite level falls below 0.05 mg/L, add another 30 mL of
Artemia nauplii concentrate and check the nitrite concentration every
day,
6. Continue this cycle until the addition of Artemia nauplii does not
cause a rise in the nitrite concentration. The culture chamber is
then conditioned and is ready to receive mysids.
7. Add only a few (5-20) mysids at first, to determine if conditions are
favorable. If these mysids are still doing well after a week, several
hundred more can be added.
179 ;;•
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7.13.1.7 It is important to add enough food to keep the adult animals from
cannibalizing the young, but not so much that the DO is depleted or that
there is a build up of toxic concentrations of ammonia and nitrite. Just
enough newly-hatched Artemia nauplii are fed twice a day so that each
feeding is consumed before the next feeding.
7.13.1.8 Natural sea water is recommended as the culture medium, but HSB
may be used to make up the culture water if natural sea water is not
available.
7.13.1.9 Mysidopsis bahla should be cultured at a temperature of
25 + 2°C. No water temperature control equipment is needed if the ambient
laboratory temperature remains in the recommended range, and if there are no
frequent, rapid, large temperature excursions in the culture room.
7.13.1.10 The salinity should be maintained at 30 +_ 2 °/oo, or at a lower
salinity (but not less than 20 °/oo) if most of the tests will be
conducted at a lower salinity.
7.13.1.11 Day/night cycles prevailing in most laboratories will provide
adequate illumination for normal growth and reproduction. A 16-h/8-h
day/night cycle in which the light is gradually increased and decreased to
simulate dawn and dusk conditions, is recommended.
7.13.1.12 Mysids cannot survive DOs below 5 mg/L for extended periods. The
airlift used in most undergravel filters will usually .provide sufficient
DO. If the DO drops below 60% saturation (4.8 mg/L at 25°C and 30 ppt
salinity; see Section 8), additional aeration should be provided. Measure
the DO in the cultures daily during the first week and then at least weekly
thereafter.
7.13.1.13 Suspend a clear glass or plastic panel over the cultures, or use
some other means of excluding dust and dirt, but leave enough space between
the covers and culture tanks to allow circulation of air over the cultures.
7.13.1.14 If hydroids or worms appear in the cultures, remove the mysids
and clean the chambers thoroughly, using soap and hot water. Rinse once
with acid (10% HC1) and three times with distilled or deionized water.
Mysids with attached hydroids should be discarded. Those without hydroids
should be transferred by hand pipeting into three changes of clean seawater
before returning them to the cleaned culture chamber. To guard against
predators, natural sea water should be filtered through a net with 30 urn
mesh openings before entering the culture vessels.
7.13.1.15 Mysidopsis bahia are very sensitive to low pH and sudden changes
in temperature. Care should be taken to maintain the pH at 8.0 + 0.3, and
to limit rapid changes in water temperature to less than 3°C.
180
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7.13.1.16 Mysids should be handled carefully and as little as possible so
that they are not unnecessarily stressed or injured. They should be
transferred between culture chambers with long handled cups with netted
bottoms. Animals should be transferred to the test vessels with a large
bore pipette (4-mm), taking care to release the animals under the surface of
the water. Discard any mysids that are injured during handling,
7.13.1.17 Culture Maintenance
7.13.1.17.1 Cultures in closed, recirculating systems are fed twice a day.
If no nauplii are present in the culture chamber after four hours, the
amount of food should be increased slightly. In flow-through systems, ;
excess food can be a problem by promoting bacterial growth and low dissolved
oxygen.
7.13.1.17.2 Careful culture maintenance is essential. The organisms should
not be allowed to become too crowded. The cultures should be cropped as
often as necessary to maintain a density of about 20 mysids per liter. At
this density, at least 70% of the females should have eggs in their brood
pouch. If they do not, the cultures are probably under stress, and the
cause should be found and corrected. If the cause cannot be found, it may
be necessary to re-start the cultures with a clean culture chamber, a new
batch of culture water, and clean gravel.
7.13.1.17.3 In closed, recirculating systems, about one third of the
culture water should be replaced with newly prepared seawater every week.
Before siphoning the old media from the culture, it is recommended that the
sides of the vessel be scraped and the gravel carefully turned over to
prevent excessive build up of algal growth. Twice a year the mysids should
be removed from the recirculating cultures, the gravel rinsed in clean
seawater, the sides of the chamber washed with clean seawater, and the
gravel and animals returned to the culture vessel with newly conditioned
seawater. No detergent should be used, and care should be taken not to rinse
all the bacteria from the gravel.
7.13.2 Test Organisms
7.13.2.1 The test is begun with 7-day old juveniles. To have the test
animals available and acclimated to test conditions at the start of the
test, they must be obtained from the stock culture eight days in advance of
the test. Whenever possible, brood stock should be obtained from cultures
having similar salinity, temperature, light regime, etc., as are to be used
in the toxicity test.
7.13.2.2 Eight days before the test is to start, sufficient gravid females
are placed in brood chambers. Assuming that 240 juveniles are needed for
each test, approximately half this number (120) of gravid females should be
transferred to brood chambers. The mysids are removed from the culture tank
with a net or netted cup and placed in 20-cm diameter finger bowls. The
gravid females are transferred from the finger bowls to the brood chambers
with a large-bore pipette or, alternatively, are transferred by pouring the
contents of the finger bowls into the water in the brood chambers.
181
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7.13.2.3 The mysid juveniles may be collected for the toxicity tests by .,
transferring gravid females from the stock cultures to netted {1000 urn)
flow-through containers (Figure 1} held within 4-L glass, wide-mouth
separatory funnels. Newly released juveniles can pass through the netting,
whereas the females are retained. The gravid females are fed newly hatched
Artemia nauplii, and are held overnight to permit the release of young. The
juvenile mysids are collected by opening the stopcock on the funnel and
collecting them in another container from which they are transferred to
holding tanks using a wide bore {4 mm ID) pipette. The brood chambers
usually require aeration to maintain sufficient DO and to keep the food in
suspension.
7.13.2.4 The temperature in the brood chamber should be maintained at the
upper acceptable culture limit (26 - 27°C), or 1°C higher than the
cultures, to encourage faster brood release. At this temperature,
sufficient juveniles should be produced for the test.
7.13.2.5 The newly released juveniles (age = 0 days) are transferred to
20-L glass aquaria (holding vessels) which are gently aerated. Smaller
holding vessels may be used, but the density of organisms should not exceed
20 mysids per liter. The test animals are held in the holding vessel for
six days prior to initiation of the test. The holding medium is renewed
every other day.
7.13.2.6 During the holding period, the mysids are acclimated to the
salinity at which the test will be conducted, unless already at that
salinity. The salinity should be changed no more than 2 °/oo per 24 h to
minimize stress on the juveniles.
7.13.2.7 The temperature during the holding period is critical to mysid
development, and must be maintained at 26 - 27°C. If the temperature
cannot be maintained in this range, it is advisable to hold the juveniles an
additional day before beginning the test.
7.13.2.8 During the holding period, just enough newly-hatched Artemia
nauplii are fed twice a day (a total of at least 150 nauplii per mysid per
day) so that some food is constantly present.
7.13.2.9 If the test is to be performed in the field, the juvenile mysids
should be gently siphoned into 1-L polyethylene wide-mouth jars with
screw-cap lids filled two-thirds full with clean seawater from the holding
tank. The water in these jars is aerated for 10 min, and the jars are
capped and packed in insulated boxes for shipment to the test site. Food
should not be added to the jars to prevent the development of excessive
bacterial growth and a reduction in DO.
182
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INFLOW
OUTFLOW
.NETTED
CHAMBER
.SEPARATORY
.FUNNEL £
NETTED
CHAMBER
Figure 1. Apparatus (brood chamber) for collection of
juvenile mysids. From Lussier, Kuhn, and
Sewall, 1987.
183
-------
7.13.2.10 Upon arrival at the test site (in less than 24 h) the mysids are
gently poured from the jars into 20-cm diameter glass culture dishes. The
jars are rinsed with salt water to dislodge any mysids that may adhere to
the sides. If the water appears milky, siphon off half of it with a netted
funnel {to avoid siphoning the mysids} and replace with clean salt water of
the same salinity and temperature. If no Artemia nauplii are present in the
dishes, feed about 150 nauplii per mysid.
8. SAMPLE COLLECTION, PRESERVATION AND HANDLING
8.1 See Section 8, Effluent and Receiving Water Sampling and Sample
Handling.
!9. CALIBRATION
t -i i i •! '
9.1 See Section 4, Quality Assurance.
10. QUALITY CONTROL
10.1 See Section 4, Quality Assurance.
10.2 The reference toxicant recommended for use with the mysid 7-day test
is copper sulfate.
11. TEST PROCEDURE
11.1 TEST DESIGN .;
11.1.1 The test consists of at least five effluent concentrations plus a
site water control and a reference water treatment (natural seawater or
seawater made up from hypersaline brine).
11.1.2 Effluent concentrations are expressed in percent effluent.
11.1.3 Eight replicate test vessels, each containing five 7-day old
animals, are used per effluent concentration and control.
11.2 TEST SOLUTIONS
11,2.1 Surface waters
11.2.1.1 Surface water toxicity is determined with samples used directly as
collected.
11.2.2 Effluents
11.2.2.1 The selection of the effluent test concentrations should be based
on the objectives of the study. One of two dilution factors, approximately
0.3 or 0.5, is commonly used. A dilution factor of approximately 0.3 allows
testing between 100% and 1% effluent using only five effluent concentrations
184
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000%, 30%, 10%, 3%, and UK This series of dilutions minimizes the level
If effort, but because of the wide interval between test concentrations
rovides poor test precision. A dilution factor of 0.5 provides
Greater precision, but requires several additional dilutions^ span the
;ame range of effluent concentrations. Improvements in precision decline
•apidly as the dilution factor is increased beyond 0.5.
1222 If the effluent is known or suspected to be highly toxic, a lower
•ange of effluent concentrations should be used (such as 10%, 3%, 1%, 0.3%,
,nd 0.1%). If high mortality is observed during the first 1 or 2 h of the
•est, additional concentrations can be added.
-i 2 2 3 The volume of effluent required for daily renewal of eight
Implicates per concentration, each containing 150 mL of test solution, is
Spproximately 1200 mL. Prepare enough test solution (approximately 1600 mL)
it each effluent concentration to provide 400 mL additional volume for
:hemical analyses.
1224 The test should begin as soon as possible, preferably within 24 h
fafter sample collection. In no case should the test be started more than
72 h after sample collection. Oust, prior to testing, the temperature of the
fsample should be adjusted to the test temperature (26 - 27°C) and
laintained at that temperature while the dilutions are being made.
Ill 2.2.5 Effluent dilutions should be prepared for all replicates in each
treatment in one flask to ensure low variability among the replicates. The
Kelt chambers (cups) are labelled with the test concentration and replicate
[number Dispense 150 mL of the appropriate effluent dilution to each cup.
!n.3 START OF THE TEST
[11.3.1 Begin the test by randomly placing five animals (one at a time) in
each test cup of each treatment using a large bore (4 mm ID) pipette. It is
!eas er fo ca ture the animals if the volume of water in the dish is reduced
[and the dish is placed on a light table. It is recommended that the
!??ansflr pipette be rinsed frequently because mysids tend to adhere to the
inside surface.
11.4 LIGHT, PHOTOPERIOD, DO, AND TEMPERATURE
HI.4.1 The light quality and intensity under ambient laboratory conditions
are generally adequate. Light intensity of 10-20 uE/mZ/s, or 50 to 00
foot candles (ft c), with a 16 h light and 8 h dark cycle and a 30 mm
fphase- n out per od is recommended. It is critical that the test water
temperature be maintained at 26 - 27<>C. It is recommended that the test
fwater temperature be continuously recorded.
11 4 1 1 If a water bath is used to maintain the test temperature, the
water depth surrounding the test cups should be at least 2.5 cm deep.
185
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11.4.1.2 Rooms or incubators with high volume ventilation should be used
with caution because the volatilization of the test solutions and
evaporation of dilution water may cause wide fluctuations in salinity.
Covering the test cups with clear polyethylene plastic may help prevent
volatilization and evaporation of the test solutions.
11.4.2 Low DOs may be a problem when conducting effluent toxicity tests.
However, test cups should not be aerated unless the DO falls below 60% of
saturation. The higher concentrations of some effluents will require
aeration to maintain adequate DO concentrations. If one solution is aerated
then all the treatments and the controls must also be gently aerated.
11.5 FEEDING
11.5.1 During the test, the mysids in each test chamber should be fed
Arteima nauplii, which are less than 24-h old, at the rate of 150 nauplii
per mysid per day. Adding the entire daily ration at a single feeding
immediately after test solution renewal may result in a significant DO
depression. Therefore, it is preferable to feed half of the daily ration
immediately after test solution renewal, and the second half 8 - 12 h
later. Increase the feeding if the nauplii are consumed in less than 4 h.
It is important that the nauplii be washed before introduction to the test
vessels.
11.6 TEST SOLUTION RENEWAL
11.6.1 Test solutions are renewed daily. Slowly pour off all but 10 cm of
the old test medium into a 20 cm diameter culture dish on a light table. Be
sure to check for animals that may have adhered to the sides of the test
,vessel. Rinse them back into the test cups. Add 150 mL of new test
solution slowly to each cup. Check the culture dish for animals that may
have been poured out with the old media, and return them to the test
vessel.
11.7 ROUTINE CHEMICAL AND PHYSICAL DETERMINATIONS
11.7.1 At a minimum, the following measurements should be made in at least
one replicate in the control and the high and low test concentrations at the
beginning of the test: temperature, dissolved oxygen, pH, and salinity (see
Figure 14).
11.7.2 DO should be measured in at least one replicate in the control and
the high and low test concentrations before renewing the test medium and
after the medium is renewed each day. In addition to the daily
calibrations, the DO meter should be checked at least once a week against a
standard Winkler titration. - ;
11,7.3 pH, temperature, and salinity should be measured in at least one
replicate for each treatment at the beginning of each 24-h exposure period.
11.7.4 It may be advisable to measure the ammonia and nitrite in the
controls before each renewal to be certain that toxicity from these sources
is not confounding the test results.
186
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11.8 OBSERVATIONS DURING THE TEST
11.8.1 The number of live mysids are counted and recorded each day when the
test solutions are renewed (see Figure 15). Dead animals and excess food
should be removed with a pipette before the test solutions are renewed.
11.9 TERMINATION OF THE TEST
11.9.1 After measuring the DO, pH, temperature, and salinity and recording
survival, terminate the test by pouring off the test solution in all the
cups to a one-cm depth and refilling the cups with clean seawater. This
will keep the animals alive, but not exposed to the toxicant, while waiting
to be examined for sex and the presence of eggs.
11.9.2 The live animals must be examined for eggs and the sexes determined
within 12 h of the termination of the test. If the test was conducted in
the field, and the animals cannot be examined on site, the live animals
should be shipped back to the laboratory for processing. Pour each
replicate into a labelled 100 ml plastic screw-capped jar, and send to the
laboratory immediately.
11.9.3 If the test was conducted in the laboratory, or when the test
animals arrive in the laboratory from the field test site, the test
organisms must be processed immediately while still alive as follows:
11.9.3.1 Examine each replicate under a stereomicroscope (240X) to
determine the number of immature animals, the sex of the mature animals, and
the presence or absence of eggs in the oviducts or brood sacs of the females
(see Figures 2-5). This must be done while the mysids are alive because they
turn opaque upon dying. This step should not be attempted by a person who
has not had specialized training in the determination of sex and presence of
eggs in the oviduct.
11.9.3.2 Record the number of immatures, males, females with eggs and
females without eggs on data sheets.
11.9.3.3 Rinse the mysids by pipetting them into a small netted cup and
dipping the cup into a dish containing deionized water. Using forceps,
place the mysids from each replicate cup on tared weighing boats and dry at
60°C for 24 h or at 105<>C for at least 6 h.
11.9.3.3.1 Pieces of aluminum foil (1-cm square) or small aluminum weighing
boats can be used for dry weight analyses. The weighing pans or boats
should not exceed 10 mg in weight.
11.9.3.3.2 Number each pan with a waterproof pen with the treatment
concentration and replicate number. Forty-eight (48) weighing pans are
required per test if all the organisms survive.
187
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MATURE FEMALE,EGGS IN OVIDUCTS
eyestalk
antennule
antenna
carapace
[\* V* Ttm^ -^wstotocyst
* developing ^x%Sg^ . .
broad \T ^^^-telson
sac P^opods
'developing brood sac
oviducts with developing ova
Figure 2. Mature female M. bah la with eggs in oviducts,
From Lussier, Kuhn, and Sewall, 1987.
188
-------
MATURE FEMALE, EGGS IN BROOD SAC
eyestolk
:antennule
ontenno
coropace
brood sac with
developing embryos
siotocyst
telson
uropod'
brood soc with
developing embryos
oviducts with developing ovo
Figure 3. Mature female M. bahia with eggs in oviducts and developing
embryos in the brood sac. Above: lateral view. Below: dorsal
view. From Lussier, Kuhn, and Sewall, 1987.
189
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MATURE MALE
eyestotk
carapace
antennule
statocyst
lelson
gonad
oil globules
Figure 4. Mature male M. bahia. From Lussier, Kuhn,
and Sewall, 1987.
190
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IMMATURE
ontennule
antenna
eyestolk
corapoce
slotocyst
telson
uropod'
Figure 5. Immature M. bahia, (A) lateral view, (B) dorsal view.
From LussTerT^ufrn, and Sewall, 1987.
191
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11..9.3.3.3 Remove the pans from the oven and transfer immediately to a
dessicator. After cooling for 1 h, weigh to the nearest microgram.
12. ACCEPTABILITY OF TEST RESULTS
12.1 The minimum requirements for an acceptable test are 80% survival and
an average weight of at least 0.20 mg/mysid in the controls. If fecundity
in the controls is adequate (egg production by 50% of females), fecundity
should be used as a criterion of effect in addition to survival and growth.
13. SUMMARY OF TEST CONDITIONS
13.1 A summary of test conditions is listed in Table 2.
14. DATA ANALYSIS
14.1 GENERAL
14.1.1 Tabulate and summarize the data.
survival, growth, and fecundity data.
Table 3 presents a sample set of
14.T.2 The end points of the mysid 7-day rapid-chronic test are based on
the adverse effects on survival, growth, and egg development. Point
estimates, such as LCI, LC5, LC10 and LC50, are calculated using Probit
Analysis (Finney, 1971). LOEC and NOEC values, for survival, growth, and
reproduction are obtained using a hypothesis test approach such as Dunnett's
Procedure (Dunnett, 1955) or Steel's Many-one Rank Test (Steel, 1959;
Miller, 1981). See the Appendix for examples of the manual computations,
program listings, and examples of data input and program output.
14.1.3 The statistical tests described here must be used with a knowledge
of the assumptions upon which the tests are contingent. The assistance of a
statistician is recommended for analysts who are not proficient in
statistics.
14.2 EXAMPLE OF ANALYSIS OF MYSID SURVIVAL DATA
14,2.1 Formal statistical analysis of the survival data is outlined in
Fiqure 6. The response used in the analysis is the proportion of animals
surviving in each test or control chamber. Separate analyses are performed
,for the estimation of the NOEC and LOEC end points and for the estimation of
the LCI, LC5, LC10 and LC50 end points. Concentrations at which there is no
survival in any of the test chambers are excluded from statistical analysis
of the NOEC and LOEC, but included in the estimation of the LC end points.
14.2.2 For the case of equal numbers of replicates across all
concentrations and the control, the evaluation of the NOEC and LOEC end
points is made via a parametric test, Dunnett's Procedure, or a
nonparametric test, Steel's Many-one Rank Test, on the arcsin transformed
data. Underlying assumptions of Dunnett's Procedure, normality and
homogeneity of variance, are formally tested. The test for normality is the
Shapiro-Wilks Test, and Bartlett's Test is used to determine the homogeneity
192
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TABLE 2. SUMMARY OF RECOMMENDED TEST CONDITIONS FOR MVSIDOPSIS BAH IA
SEVEN DAY SURVIVAL, GROWTH, AND FECUNDITY TEST
1. Test type:
2. Salinity:
3. Temperature:
4. Photoperiod:
5. Light intensity:
6. Test chamber:
7. Test solution volume:
8. Renewal of test solutions:
9. Age of test organisms:
10. Number of treatments per study:
11. Number of organisms per test
chamber:
12. Number of replicate chambers
per treatment:
13. Source of food:
14. Feeding regime:
15. Aeration:
16. Dilution water:
17. Test duration:
18. Dilution factor:
19. Effects measured:
20. Cleaning:
Static renewal
20 o/oo to 30 °/oo + 2 "Voo
26 - 27°C
16 h light, 8 h dark, with phase
in/out period
10-20 uE/m2/s (50-100 ft,c,)
8 oz plastic disposable cups, or
400 mL glass beakers
150 ml per replicate cup
Daily , ;^;
7 days
Minimum of 5 treatments a-nd a
control
8
Artemia nauplii
Feed 150 24-h old nauplii per mysid
daily, half after test solution
renewal and half after 8 - 12 h.
None unless DO falls below 60%
saturation, then gently in all cups
Natural sea water or hypersaline brine
7 days
Approximately 0.3 or 0.5
Survival, growth, and egg development
Pipette excess food from cups daily
193
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TABLE 3. DATA FOR MYSID SHRIMP 7-DAY SURVIVAL, GROWTH, AND FECUNDITY TEST
Treatment Replicate
Chamber
-- — ~ — — —
1
i
2
£_
3
v
Control 4
5
•j
6
\f
7
1
8
1
i
2
£»
3
*j
50 ppb 4
6
w
7
/
8
1
i
2
L»
3
^
100 ppb 4
g
U
7
/
8
1
i
~
210 ppb 4
A
u
7
/
8
1
i
2
3
-------
of variance. If either of these tests fail, the nonparametric test, Steel's
Many-one Rank Test, is used to determine the NOEC and LOEC end points. If
the assumptions of Dunnett's Procedure are met, the end points are estimated
by the parametric procedure.
14.2.3 If unequal numbers of replicates occur among the concentration
levels tested, there are parametric and nonparametric alternative analyses.
The parametric analysis is the Bonferroni t-test. The Wilcoxon Rank Sum Test
with the Bonferroni adjustment is the nonparametric alternative. For
detailed information on the Bonferroni adjustment see the Appendix.
14.2.4 Probit Analysis (Finney, 1971) is used to estimate the concentration
that causes a specified percent decrease in survival from the control. In
this analysis, the total mortality data from all test replicates at a given
concentration are combined {total number dead at concentration level i
divided by total number exposed at concentration level i),
14.2.5 The proportion of survival in each replicate must first be
transformed by the arcsin transformation procedure decribed in the Appendix.
The raw and transformed data, means and standard deviation of the transformed
observations at each concentration including the control are listed in
Table 4, A plot of the mean survival is provided in Figure 7.
TABLE 4. MYSIDOPSIS BAHIA SURVIVAL DATA
Concentration
Replicate Control
50.0
100.0
210.0
450.0
Raw
Arcsin
Trans
formed
Mean(Yi)
Si2
i
i
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
0.80
0.80
1.00
1.00
1.00
1.00
1.00
0,80
1.107
1.107
1.345
1,345
1.345
1.345
1.345
1.107
1.256
0.015
1
0.80
1.00
0.80
0.80
1.00
1.00
0.80
1.00
1.107
1.345
1.107
1,107
1.345
1.345
1.107
1.345
1.226
0.016
2
0.60
1.00
1.00
1.00
1.00
0.60
0.80
0.80
0.886
1.345
1.345
1.345
1,345
0.886
1.107
1.107
1.171
0.042
.3
1.00
0.80
0.20
0.80
0.60
0.80
0.80
0.80
1.345
. 1,107
0.464
1.107
0,886
1.107
1.107
1.107
1.029
0.067
4
0.00
0.20
0.00
0.20
0.00
0.00
0.00
0.40
0.225
0.464
0.225
0.464
0.225
0.225
0.225
0.685
0.342
0.031
5
195
-------
1
I
•
STATIST
SURV]
*
PROBIT
ANALYSIS
1
ENDPOINT ESTIMATE
LCI, LC5, LC10.LC50
NORMAL
HOMOGENEOUS VARIANCE
™ EQUAL
REF
ICAL ANALYSIS OF MYSIDOPSIS BAHIA
•VAL. GROWTH AND FECUNDITY TEST
SURVIVAL
SURVIVAL DATA
PROPORTION SURVIVING
1
f
ARCSIN
TRANSFORMATION
I NUN-NUHM
DISTRIBUTION!
' i Hfc
BARTLETT S TEST » •**
1 i
i t
. NUMBER OF EQUAL NUMBER OF
1ICATES? REPLICATES?
YES I ' I YES
T-TEST WITH n...
BONFERRONI UUP
ADJUSTMENT
1 \ \ WTI rr
JNETT'S1 STEEL'S MANY-ONE ' "^^
TEST j RANK TEST | BONFERT
AL DISTRIBUTION
TEROGENEOUS
VARIANCE
NO
v
XON RANK SUM
EST WITH
ONI ADJUSTMENT
•'"-• i
ENDPOINT ESTIMATES
NOEC, LOEC t
Figure 6. Flow chart for analysis of mysid survival data
••?•>• 196
-------
z
o
o
o
o
a:
o
U4
UJ
X
o
o
o
C
O)
E
-M
(O
0)
O
fTJ
O)
-o
1.
3
V)
o
0.
cu
i-
NOIiaOdOMd
197
-------
|4.2.6 Test for Normality <-^ .,
114.2.6.1 The first step of the test for normality is to center the
Observations by subtracting the mean of all observations within a
:oncentration from each observation in that concentration . The centered
^observations are listed in Table 5.
TABLE 5. CENTERED OBSERVATIONS FOR SHAPIRO-WILKS EXAMPLE
El' 1 flLJ L~ L* sJ* ^t^JllL«iM«LJ \JLJOL.l\Vr1FlWH*J 1 UP\ *J J L/il 1 IV W H .1 L* T\ *J L- r\r\\ n L. L.
1
1 Concentration
1
I Replicate
1
2
3
4
5
6
7
8
Control
{Site Water)
-0.149
-0.149
0.089
0.089
0.089
0.089
0.089
-0.149
50.0
-0.119
0.119
-0.119
-0.119
0.119
0.119
-0.119
0.119
100.0
-0.285
0.174
0.174
0.174
0.174
-0.285
-0.064
-0.064
210.0
0.316
0.078
-0.565
0.078
-0.142
0.078
0.078
0.078
450.0
-0.117
0.121
-0.117
0.121
-0.117
-0.117
-0.117
0.342
14.2.6.2 Calculate the denominator, D, of the test statistic:
n
D = t (Xi - X)2
Where Xj = the ith centered observation
x = tne overall mean of the centered observations
n = the total number of centered observations.
For this set of data,
n = 40
1 (-0.006) = 0.0
W
D = 1.197 ? -
14.2.6.3 Order the centered observations from smallest to largest:
x(l) . x<2) - ... - x(n)
Where %d} is the ith ordered observation. These ordered observations
are listed in Table 6.
198
-------
TABLE 6. ORDERED CENTERED OBSERVATIONS FOR SHAPIRO-WILKS EXAMPLE
x(D
1
2
3
4
• ?,. 5
•;;i 6
7
8
9
10
n
12
13
14
15
16
17
18
19
20
-0.565
-0.285
-0.285
-0.149
-0.149
-0.149
-0.143
-0.119
-0.119
-0.119
-0.119
-0.117
-0.117
-0.117
-0.117
-0.117
-0.064
-0.064
0.078
0.078
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
0.078
0.078
0.078
0.089
0.089
0.089
0.089
0.089
0.119
0.119
0.119
0.119
0.121
0.121
0.174
0.174
0.174
0.174
0.316
0.342
14.2.6.4 From Table 4, Appendix B, for the number of observations, n,
obtain the coefficients a], a2»..--> aR where k is approximately
n/2. For the data in this example, n = 40 and k = 20. The a-,* values
are listed in Table 7.
14.2.6.5 Compute the test statistic, W, as follows:
1 k
D 1 = l'
. X(D) ]2
The differences X
-------
14.2.6.6 The decision rule for this test is to compare W with the
critical value found in Table 6, Appendix B. If the computed W is less
than the critical value, conclude that the data are not normally
distributed.
For this set of data, the critical value at a significance level of 0.01
and n = 40 observations is 0.919. Since W = 0.9167 is less than the
critical value, the conclusion of the test is that it is reasonable to
assume the data are not normally distributed.
14.2.6.7 Since the data do not meet the assumption of normality, Steel's
[Many-One Rank Test will be used to analyze the survival data.
TABLE 7. COEFFICIENTS AND DIFFERENCES FOR SHAPIRO-WILKS EXAMPLE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0.3964
0.2737
0.2368
0.2098
0.1878
0.1691
0.1526
0.1376
0.1237
0.1108
0.0986
0.0870
0.0759
0.0651
0.0546
0.0444
0.0343
0.0244
0.0146
0.0049
0.907
0.601
0.459
0.323
0.323
0.323
0.264
0,240
0.238
0.238
0.238
0.236
0.206
0.206
0.206
0.206
0.153
0.142
0.0
0.0
X(40)
X(39)
X<38)
X(37)
X 36)
X 35
X(34)
X(33)
x(32)
x(31 }
X<30)
X(29)
x(28)
X(27)
X<26)
X(Z5)
X(24)
X<23)
X(22)
X(21)
- x(D
- x 2>
- X(3)
- * 4!
- X<5)
- x(6)
- x(7)
- X<8)
- X<9)
- xdo)
- xdi)
- X(12)
- X(13)
- X(14)
- X(15)
- X<16)
- xH7)
- X(18)
- X(19)
- X(20)
200
-------
14.2.7 Steel's Many-One Rank Test
14.2.7.1 For each control and concentration combination, combine the
data and arrange the observations in order of size from smallest to t^.
largest. Assign the ranks (1,2, ... ,40) to the ordered observations"
with a rank of 1 assigned to the smallest observation, rank of 2 assigned
to the next larger observation, etc. If ties occur when ranking, assign
the average rank to each tied observation.
14.2.7.2 An example pf assigning ranks to the combined data for the
control and 50.0 ppb concentration is given in Table 8. This ranking
procedure is repeated for each control/concentration combination. The
complete set of rankings is summarized in Table 9. The ranks are next
summed for each concentration level, as shown in Table 10.
1.4.2.7.3 For this example, we want to determine if the survival in any
of the concentrations is significantly lower than the survival in the
control. If this occurs, the rank sum at that concentration would be
significantly lower than the rank sum of the control. Thus we are only
concerned with comparing the rank sums for the survival at each of the
various concentration levels with some "minimum" or critical rank sum,
at or below which the survival would be considered significantly lower
than the control. At a significance level of 0.05, the minimum rank sum
in a test with four concentrations (excluding the control) and eight
replicates is 47 (See Table 5, Appendix E).
14.2.7.4 Since the rank sum for the 450 ppb concentration level is less
than the critical value, the proportion surviving in that concentration
is considered significantly less than that in the control. Since no
other rank sums are less than or equal to the critical value, no other
concentrations have a significantly lower proportion surviving than the ,
control. Hence, the NOEC and the LOEC are assumed to be 210.0 ppb and /
450.0 ppb, respectively. t
201
-------
TABLE 8. ASSIGNING RANKS TO THE CONTROL AND 502 CONCENTRATION LEVEL
FOR STEEL'S MANY-ONE RANK TEST
Rank
Transformed Proportion
of Total Mortality
Concentration
4
4
4
4
4
4
4
12 :
12
12
12
12
12
12
12
12
1.107
1.107
1.107
1.107
1.107
1.107
1.107
1.571
1.571
1.571
1.571
1.571
1.571
1.571
1.571
1.571
Control
Control
Control
50%
50%
50%
50%
Control
Control
Control
Control
Control
50%
50%
50%
50%
TABLE 9. TABLE OF RANKS^
MRepl
i- . Control
50
100
210
450
n cate
HuR
1 ?
11 i
i
IB 6
1 8
1.107(4,5,6
1.107(4,5,6
1.345(12,12
1.345(12,12
1.345(12,12
1.345(12,12
1.345(12,12
1.107(4,5,6
.5,10)
.5,10)
,13.5,14)
,13.5,14)
,13.5,14)
,13.5,14)
,13.5,14)
.5,10)
1.107(4)
1.345(12)
1.107(4)
1.107(4)
1.345(12)
1.345(12)
1.107(4)
1.345(12)
0.886(1.5)
1.345(12)
1.345(12)
1,345(12)
1.345(12)
0,886(1.5)
1.107(5)
1.107(5)
1.345(13.5)
1.107(6.5)
0.464(1)
1,107(6.5)
0.886(2)
1.107(6,5)
1.107(6.5)
1.107(6.5)
0.225(3)
0.464(6.5)
0.225(3)
0.464(6.5)
0.225(3)
0.225(3)
0.225(3)
0.685(8)
^Control ranks are given in the order of the concentration with which
they were ranked.
202
-------
TABLE 10. RANK SUMS
Concentration
50
100
210
450
Rank Sum
64
61
49
36
14.2.8 Probit Analysis
14.2.8.1
Table 11.
Program.
Figure 8.
The data used for the probit analysis is summarized in
To perform the probit analysis, run the EPA Probit Analysis
An example of the program output is provided in Table 12 and
14.2,8.2 For this example, the chi-square test for heterogeneity was not
significant. Thus probit analysis appears to be appropriate for this set
of data.
TABLE 11. DATA FOR PROBIT ANALYSIS
No. Dead
No. Exposed
Control
3
40
50.0
4
40
Concentration
100.0 210.0
6
40
11
40
450.0
36
40
203
-------
TABLE 12. OUTPUT FROM EPA PROBIT ANALYSIS PROGRAM, VERSION 1.3,
USED FOR CALCULATING EC VALUES
Prpbit Analysis of Hysidopsis Bah
Con c ,
y Control
50.0000
f 100.0000
' 210 . 0000
450 . 0000
Chi ~ Square
Mu
Sigma
Parameter
Intercept
Elope '
Number Number
Exposed Resp.
40 4
40 4
40 6
40 1 1
40 , 36
Heterogeneity = 0
2 . 4641 1 7
0 . 156802
Estimate Std.
-10.714873 3.194
6.377486 1.274
ia Survival
Observed
Proportion
Respond ing
0 . 1000
0 . 1000
0 . 1500
0 2750
0. 9000
. 51 7
Err
243 ( - 1
491 (
Data
Adjusted
Pr opor t i on
Responding
0. 0000
- . 0179
0 . 0387
0.1801
0. 8869
•
95 % Con f i den ce
6 91 5550 , -4
3879483. 8
Predicted
Proportion
Re s pond ing
0.1158
0 . 0000
0 . 001 5
0.1827
0 . 8861
Limits
454156)
875488)
Spontaneous 0.115787
Response Rate
0.029555
0.057859,
0.173715)
Estimated EC Values and Confidence Limits
Point
Cone
L ower U~ppe r
95% Confidence Limits
EC 1
EC 5 ,
EC1 0 .
EC15 .
EC50.
EC85.
EC90 .
EC95 .
EC99 .
00
. 00
00
00
00
00
00
00
00
">;'' 125
160
183
200 .
291 .
423
462 .
527 .
674 .
7042
7661
2992
2664
1 503
2791
4602
2789
3496
66 .
98
1 21
139
240.
361
391 .
436 .
528 .
2441
3363
0638
0534
4525
8588
0961
0173
6572
169
203
225
242
338
545.
621 .
760 .
1121.
1 21 1
7259
' 5930
0966
8918
0946
6678
1 824
1 471
204
-------
PLOT OP ADJUSTED PROBITE AND PREDICTED REGRESSION LINE
Probit
10*
7*
EC 01
EC10 EC25 EC50 EC75 EC90
EC99
Figure 8. Plot of adjusted probits and predicted regression line.
205
-------
14.3 EXAMPLE OF ANALYSIS OF MYSID GROWTH DATA
14.3.1 Formal statistical analysis of the growth data Is outlined in
Figure 9. The response used in the statistical analysis is mean weight of
males and females combined per replicate. Concentrations above the NOEC for
survival are excluded from the growth analysis.
14.3.2 The statistical analysis consists of a parametric test, Dunnett's
Procedure, and a non-parametric test, Steel's Many-one Rank Test. The
underlying assumptions of the Dunnett's Procedure, normality and homogeneity
of variance, are formally tested. The test for normality is the
Shapiro-Wilks Test and Bartlett's Test is used to test for homogeneity of
variance. If either of these tests fail, the non-parametric test, Steel's
Many-one Rank Test, is used to determine the NOEC and LOEC end points. If
the assumptions of Dunnett's Procedure are met, the end points are
determined by the parametric test, - '
14.3.3 Additionally, if unequal numbers of replicates occur among the
concentration levels tested there are parametric and non-parametric
alternative analyses. The parametric analysis is the Bonferroni t-test. The
Wilcoxon Rank Sum Test with the Bonferroni adjustment is the non-parametric
alternative. For detailed information on the Bonferroni adjustment, see the
Appendix.
14.3,4 The data, mean and standard deviation of the observations at each
concentration including the control for this example are listed in
Table 13. A plot of the data is provided in Figure 10. Since there is
significant mortality in the 450 ppb concentration, its effect on growth is
not considered,
TABLE 13, MYSID GROWTH DATA
Replicate Control
Concentration (ppb)
50.0
100.0
210.0
450.0
Mean(Yi)
Si2
i
1
2
3
4
5
6
7
8
0.183
0.148
0.216
0.199
0.176
0.243
0.213
0.180
0.195
0.0008
1
0.192
0.193
0,237
0.237
0.256
0,191
0.152
0.177
0.204
0.0012
2
0.190
0.172
0.160
0.199
0.165
0.241
0.259
0.186
0.197
0.0013
3
0.153
0.117
0.085
0.153
0.086
.'• 0.193
•='• 0.137
0.129
0.132
0.0013
4
_
0.060
-
0.009
-
_
-
0.203
-
5
206
-------
STATISTICAL ANALYSIS OF MYSIDOPSIS BAHIA
SURVIVAL. GROWTH AND FECUNDITY TEST
GROWTH
, • GROWTH DATA
MEAN WEIGHT
(EXCLUDING CONCENTRATIONS ABOVE NOEC FOR SURV
bnArlHU nILIso ILof
NORMAL DISTRIBUTION 1
. ^ HE1
BARTLETT S TEST • -^*
HOMOGENEOUS VARIANCE
£5 EQUAL NUMBER OF EQUAL NUMBER OF
REPLICATES? REPLICATES?
VPQ YF9
V , j |
T-TEST WITH ni|NKIFTT.s STEEL'S MANY-ONE WILCD>
BONFERRONI DUNTN|STTT S RANK TEST TE
ADJUSTMENT TfcS' HA . BONFERRC
" 1
ENDPOINT ESTIMATES
NOEC, LOEC
IVAL}
L DISTRIBUTION
FEROGENEOUS
VARIANCE
NO
v
ON RANK SUM
.ST WITH
)NI ADJUSTMENT
Figure 9. Flow chart for statistical analysis of mysid growth data
207
-------
(/I
ZUJ
Ol-
t-tn
O
O:
LUZ-JI—
Z3OO
OOSO
O
CJU.— lt-
< <_
UJLU>3
3 O
U_>X
>
UJ—J Z
-JOOQ;
— 00 U.
ZQS —
LU X
3bJO>-
x —_*
LUI—LUh-
:z
•<
I— LULU U.
OV13 —
LULU
ZO.Z —
OLU<(/»
O
s~
Ol
O
**-
ui
•r-
U.
208
-------
14.3.5 Test for Normality
JI4.3.5.1 The first step of the test for normality is to center the J
Sobservations by subtracting the mean of all observations within a
fconcentration from each observation in that concentration. The centered
Sobservations are listed in Table 14.
TABLE 14. CENTERED OBSERVATIONS FOR SHAPIRO-WILKS EXAMPLE
||H Concentration
mm
K Replicate
^fflp
• 1 •
8B» %
H 3
• 4
• 5
H 6
H 7
H 8
RHP . .... .,_
Control
-0.012
-0.047
0.021
0,004
-0.019
0.048
0.018
-0.015
50.0
-0.012
-0.011
0,033
0.033
0.052
-0.013
-0.052
-0.027
100.0
-0.006
-0,024
-0.036
0.002
-0.032
0.044
0.062
-0.010
(ppb)
210.0
0.021
-0.015
-0.047
0.021
-0.046
0.061
0.005
-0.003
;14.3.5.2 Calculate the denominator, D, of the statistic:
n _
D = I (Xi - X)2
i=l
= the ith centered observation
= tne overall mean of the centered observations
Where
n = the total number of centered observations
[14.3.5.3 For this set of data: n = 32
X = - (-0.000) = 0.000
D = 0.0329
14.3.5.4 Order the centered observations from smallest to largest
X(l) - X(2) - ... - X(n)
/here x(i) denotes the ith ordered observation. The ordered
Pobservations for this example are listed in Table 15.
209
-------
TABLE 15
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
ORDERED CENTERED OBSERVATIONS FOR SHAPIRO-WIUS EXAMPLE
-0.052
-0.047
-0.047
-0.046
-0.036
-0.032
-0.027
-0.024
-0.019
-0.015
-0.015
-0.013
-0.012
-0.012
-0.011
-0.010
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
-0.006
-0.003
0,002
0.004
0.005
0.018
0,021
0.021
0.021
0.033
0.033
0.044
0.048
0.052
0.061
0.062
|14.3.5.6 Compute the test statistic, W, as follows:
1 k
" ~ — L Z a -i (x(n~7+l) vM ) \ to
D 1 — 1 ' A*'')JC.
\
The differences x(n-i + l) . y(i) avio ,. . . .
in this examolP. X are llsted m Table 16.
example,
For the data
0.0329
= 0.9469
210
-------
TABLE 16. COEFFICIENTS AND DIFFERENCES FOR SHAPIRO-WILKS EXAMPLE
J .— . — M.^ — . — .^ .^.- .«-_ | ,|
1 0.4188
[ 2 0.2898
1 3 0.2462
4 0.2141
1 5 0.1878
1 6 0.1651
1 7 0.1449
8 0.1265
1 9 0.1093
: . 10 0.0931
11 0.0777
12 0.0629
13 0.0485
14 0.0344
15 0.0206
16 0.0068
0.114
0.108
0.099
0.094
0.080
0.065
0.060
0.045
0.040
0.036
0.033
0.018
0.016
0.014
0.008
0.004
X(32)
X(3D
X(30)
X<29)
X(28)
X(27)
X(26)
X(25)
X(24)
X(23)
X(22)
x(21 )
X(20)
X<19)
x(18)
Xd7)
- xd)
- X<2)
- X(3)
- X(5)
- X<6)
- X(7)
- X(8)
- xdo)
- x(12)
- Xd3)
- xHs)
- X(16)
14.3.5.7 The decision rule for this test is to compare W as calculated
in 14.3.5,6 to a critical value found in Table 6, Appendix B. If the
computed W is less than the critical value, conclude that the data are
not normally distributed. For this set of data, the critical value at a
signficance level of 0.01 and n = 32 observations is 0.904. Since W =
0.9496 is greater than the critical value, it is reasonable to assume
that the data are normally distributed.
14.3.6 Test for Homogeneity of Variance
14.3.6.1 The test used to examine whether the variation in mean weight of
the mysids is the same across all concentration levels including the
.control, is Bartlett's Test {Snedecor and Cochran, 1980). The test
'statistic is as follows: ;-
B =
[
P
{ I Vj
1=1
} In $2
C
P
-2V-
1=1
j In S-j2 ]
Where V-j = degrees of freedom for each copper concen-
tration and control, V-j = (nf - 1)
p = number of concentration levels including
the control
211
-------
C » 1 + ( 3(p-l)H [ z i/Vl - {
>: In = loge
1 ~ 1, 2, ..., p where p is the number of concentrations
including the control
ni = the number of replicates for concentration 1.
14.3.6.2 For the data in this example (See Table 13), all concentrations
including the control have the same number of replicates (ni = 8 for
all i). Thus, Vi = 7 for all i. 1
14,3.6.3 Bartlett's statistic is therefore:
B = [(28)ln(0.0012) - 71 ln{Sj)2]/l.06
= [28(-6.7254) - 7'(-27.1471)]/] .06
= [-188.3112 - (-190.0297)3/1,06
= 1.621
14.3.6.4 B is approximately distributed as chi-square with p - 1 degrees
of freedom, when the variances are in fact the same. Therefore, the
appropriate critical value for this test, at a significance level of 0.01
with three degrees of freedom, is 9.210. Since B = 1.621 is less than
the critical value of 9.210, conclude that the variances are not
different.
14.3.7 Dunnett's Procedure
i
114.3.7.1 To obtain an estimate of the pooled variance for the Dunnett's
(Procedure, construct an ANOVA table as described in Table 17.
212
-------
TABLE 17, ANOVA TABLE
m
mg Source
B Between
KtSS
m
•H Within
•
H Totdl
m
B
Kfhere p
H N
df
P - 1
N - p
N - 1
= number
= total
Sum of Squares
(SS)
SSB
SSW
SST
of concentration levels
number of observations ni
Mean Square(MS)
(SS/df)
2
SB = SSB/(p-l)
2
SW = SSW/(N-p)
including the control
I + n? ... +nn
= number of observations in concentration i
SSB = Z T12/n1 - Q2/N
Between Sum of Squares
P I'M
SST = I I YH
1=1 j=l
SSW = SST - SSB
- Q2/N
Total Sum of Squares
Within Sum of Squares
4.3.7.2
nl =
T2 =
T3 =
T4 =
G = the grand total of all sample observations, G = z T-j
1 = 1
T-j = the total of the replicate measurements for
concentration "i"
Yfj = the jth observation for concentration "i" (represents
the mean dry weight of the mysids for concentration
i in test chamber j)
For the data in this example:
n2 = n3 = n4 = 8
32
YII + Yi2 + ... + Y]8 = 1.558
+ Y22 + ... + Y28 = 1-635
+ Y32 + ... + Y38 = 1.572
+ Y42 + ... + Y48 = 1.053
G = TI + T2 + T3 + T4 = 5.818
213
-------
SSB * I Tj2/ni - G2/N
i = l
= JJ 8.680} - (5.818)2 = 0.027
8 32
SST = E I
1=1 =
- Q2/N
= 1.118 - (5.818)2 = o.060
32 :
SSW = SST - SSB = 0.060 - 0.027 = 0.033
SB2 = SSB/p=1 = 0.027/4-1 = 0.009
SW2 = SSW/N-p = 0.033/32-4 = 0.001
14.3.7.3 Summarize these calculations in the ANOVA table (Table 18
TABLE 18. ANOVA TABLE FOR DUNNETT'S PROCEDURE EXAMPLE
•
• Source
!8i
H Between
H
W Within
IB
H Total
H
df
3
28
31
Sum of Squares
(SS)
0.027
0.033
0.060
Mean Square(MS)
(SS/df)
0,009
0.001
,14.3.7.4 To perform the individual comparisons, calculate the t
Statistic for each concentration, and control combination as follows
Sw/
+ (I/nil
Where Yj = mean dry weight for concentration i
= mean dry weight for the control
= square root of within mean sqaure
= number of replicates for control
= number of replicates for concentration i.
214
Sw
"1
"1
-------
f. -a
f _ *
.3.7.5 I.ble 19 include. ».
the
follows:
( 0.195 - 0.204 )
[ 0.032 /(I/a) +
TABLE 19. CALCULATED T-VALUES
Concentration (ppb)
50.0
100.0
210.0
,4.3.7.6 Since the purpose of this test ^^
reduction in mean weight, a (o e-sided) t est
!
-0.562
-0.125
3,938
significant
s
calculated.
MSD = d SW >/ (1/ni) + U/n)
Where: d
S
n
= the critical value for the Dunnett's procedure
= Sssaa
, the number of replicates in the control.
14.3.7.8 In this example:
MSD = 2.15 (0-032) >/"
= 2.15 (0.032M0.5)
= 0.034
* , i? At reduction in mean weight from the
14.3.7.10 This represents a 17.4% reduction
control.
215
-------
14.4 EXAMPLE OF ANALYSIS OF MYSID FECUNDITY DATA
14.4.1 Formal statistical analysis of the fecundity data is outlined in
[Figure 11. The response used in the analysis is the proportion of females
fwith eggs in each test or control chamber. If no females were present in a
Ireplicate, a response of zero should not be used. Instead there are no data
[available for that replicate and the number of replicates for that level of
[concentration or the control should be reduced by one. Separate analyses
[are performed for the estimation of the NOEC and LOEC end points and for the
istimation of the EC1, ECS, EC10 and EC50 end points. The data for a
;oncentration are excluded from the statistical analysis of the NOEC and
•C if there no eggs were produced in all of the replicates in which
•emales existed. However, all data are included in the estimation of the EC
*nd points,
[4.4,2 For the case of equal numbers of replicates across all
:oncentrations and the control, the evaluation of the NOEC and LOEC end
)oints is made via a parametric test, Dunnett's Procedure, or a
lonparametric test, Steel's Many-one Rank Test, on the arcsin transformed
Hata. Underlying assumptions of Dunnett's Procedure, normality and
homogeneity of variance, are formally tested. The test for normality is the
IShapiro-Wilks Test, and Bartlett's Test is used to determine the homogeneity
Ipf variance. If either of these tests fail, the nonparametric test, Steel's
ilany-one Rank Test, is used to determine the NOEC and LOEC end points. If
ithe assumptions of Dunnett's Procedure are met, the end points are estimated
)y the parametric procedure.
114.4.3 If unequal numbers of replicates occur among the concentration
levels tested, there are parametric and nonparametric alternative analyses.
"he parametric analysis is the Bonferroni t-test. The Wilcoxon Rank Sum
"est with the Bonferroni adjustment is the nonparametric alternative. For
letailed information on the Bonferroni adjustment see Appendix D.
t
14.4.4 Probit Analysis (Finney, 1971) is used to estimate the concentration
lausing a specified reduction in fecundity measured by the proportion of
'emales without eggs. As in survival data, the fecundity data from all test
'eplicates at a given concentration are combined, total number of females
n'thout eggs at concentration i divided by the total number of females at
;oncentration i, to yield the proportion for that concentration. Since the
variable of interest is the proportion of females producing no eggs, the
proportion of females without eggs as a natural occurrence should be allowed
-or in the analysis. The natural infertility is estimated from the
proportion of females without eggs in the control. With an added adjustment
Ifor spontaneous infertility rate, the Probit Analysis is carried out as for
Ithe survival data. A discussion of the Probit Analysis with adjustment for
fspontaneous response in the controls is included in Section 9 (Data
{Analysis).
216
-------
,14.4.5 In this example, the proportion of female mysids with eggs in each
^replicate is first transformed by the arcsin transformation procedure
(described in Appendix B. Since the denominator of the proportion of females
!with eggs varies with the number of females occurring in that replicate, the
'adjustment of the arcsin transformation for 0% and 100% is not used for this
'data. The raw and transformed data, means and standard deviations of the
: transformed observations at each test concentration including the control
'are listed in Table 20. Since there is significant mortality in the 450 ppb
^concentration, its effect on reproduction is not considered. Additionally,
^since no eggs were produced by females in any of the replicates for the 210
b concentration, it is not included in this statistical analysis and is
(considered a qualitative reproductive effect.
TABLE 20. MYSID FECUNDITY DATA: PERCENT FEMALES WITH EGGS
Replicate Control
Test Concentration (ppb)
50.0 100,0 210.0
1
• RAW
1
i
IARC SINE
1 TRANS-
• FORMED
i
i
1 Meant Yi)
i$i2
li
,
2
3
4
5
6
7
8
1
2
3
4
5
5
7
8
1.00
1.00
0.67
1.00
1.00
0.80
1.00
1.00
1.57
1.57
0.96
1.57
1.57
1.12
1.57
1.57
1.44
0.064
1
0.50
0.33
0.67
-
0.40
0.50
0.25
0.33
0.78
0.61
' 0.96
-
0.68
0.78
0.52
0.61
0.71
0.021
2
0.33
0.50
0.00
0.50
0.67
0.00
0.25
~
0.61
0.78
0.00
0.78
0.96
0.00
0.52
0.52
0.147
3
0.0
0.0
0,0
0.0
0.0
0.0 ;
0.0 ^
0.0
_
-
.-:;:
':. :•'•''
"'.'•
••' ""
-
-
-
4
217
-------
STATISTICAL
SURVIVAL.
ANALYSIS OF MYSIDOPSIS BAHIA
GROWTH AND FECUNDITY TEST
FECUNDITY
FECUNDITY DATA
PROPORTION OF FEMALES WITH EGGS
(EXCLUDING CONCENTRATIONS ABOVE NOEC FOR SI
1
PROBIT
ANALYSIS
1
ENDPOINT ESTIMATE s
EC1 EC5 EC10 EC50
+
ARCSIN
TRANSFORMATION
* NON-NORM
f
NORMAL DISTRIBUTION!
HOMOGENEOUS VARIANCE
V
BARTLETT'S TEST *4 HE
•^ EQUAL NUMBER OF EQUAL NUMBER OF
REPLICATES? REPLICATES?
^- YES 1
T-TEST WITH niJNNFTT'£
BONFERRONI UUNTNFtclT fc
An.HIRTMFNT ' co J
1 YES
3 STEEL'S MANY-ONE WILC?
RANK TEST RONFERR
*
ENDPOINT ESTIMATES
NOEC, LOEC
RVIVAL)
AL DISTRIBUTION
TEROGENEOUS
VARIANCE
NO
_ — . — -
V
XON RANK SUM
EST WITH
ONI ADJUSTMENT
Figure 11. Flow chart for statistical analysis of mysid fecundity data.
218 .-:vr;;:V' . ^^
-------
a;
JC
t/j
-a
(0
O)
c:
o
S-
o
a.
o
s-
a.
o
S003 HUM S3TW3J NOIlMOdOMd
o
o
219
-------
14.4.6 Test for Normality
I 14.4.6.1 The first step of the test for normality is to center the
observations by subtracting the mean of all observations within a
concentration from each observation in that concentration. The centered
observations are listed in Table 21.
1| lAbLh 21. UtNlLKLU UBbtKVA 1 lUNb PUK 5HAPIRO-WILKS EXAMPLE
H Test Concentration (ppb)
• Replicate
H
m i
• 2
m 3
B 4
• 5
• 6
• 1
m 8
Control
0.13
0.13
-0.48
0.13
0.13
-0.32
0.13
0.13
50.0
0,07
-0.10
0.25
-
-0.03
0.07
-0.19
-0.10
100.0
0.09
0,26
-0.52
0.26
0.44
-0.52
0.00
~
14.4.6,2 Calculate the denominator, D, of the statistic:
n
D = z (Xi - X)2
Where X-j = the ith centered observation
of the centered observations
n = the total number of centered observations
14,4.6.3 For this set of data: n = 22
X = 1 (0.000) = 0,
22
D - 1.4412
14.4.6,4 Order the centered observations from smallest to largest
where X(i) denotes the ith ordered observation. The ordered
observations for this example are listed in Table 22,
220
-------
TABLE 22. ORDERED CENTERED .OBSERVATIONS FOR SHAPIRO-WILKS EXAMPLE
i
T v" ^ '
2
3
4
5
6
7
8
9
10
11
X(i)
-0.52
-0.52
-0.48
-0.32
-0.19
-0.10
-0.10
0,03
0.00
0.07
0.07
i
12
13
14
15
16
17
18
19
20
21
22
x(D
0.09 ,-,-.;./.
0.13 '*£•"
0.13
0.13
0.13
0.13
0.13 v:;;:X -
0.25
0.26
0.26
0.44
14.4.6.5 From Table 4, Appendix B, for the number of observations, n,
obtain the coefficients a], 32, ... aj< where k is approximately
n/2. For the data in this example, n = 22 and k = 11. The ai values
are listed in Table 23.
14.4.6.6 Compute the test statistic, W, as follows:
W = 1 [ E a-f (x(n-i-M) -
The differences
in this example:
- X<*) are listed in Table 23. For the data
^(1.1389)2=0.900
22]
-------
TABLE 23. COEFFICIENTS AND DIFFERENCES FOR SHAPIRO-WILKS EXAMPLE
X
- x(D
- X(2)
- X(3)
- X(4)
- X(5)
- X(6)
- X(7)
- X(8)
- xO)
- xOo)
- xdi)
14.4.6.7 The decision rule for this test is to compare W as calculated in
14.4.6.6 to a critical value found in Table 6, Appendix B. If the
computed W is less than the critical value, conclude that the data are
not normally distributed. For this set of data, the critical value at a
signficance level of 0.01 and n = 22 observations is 0.900. Since W =
0.897 is greater than the critical value, it is reasonable to assume that
the data are normally distributed.
14.4.7 Test for Homogeneity of Variance
14.4.7.1 The test used to examine whether the variation in proportion of
female mysids with eggs is the same across all concentration levels
including the control, is Bartlett's Test (Snedecor and Cochran, 1980).
The test statistic is as follows:
B =
[ ( I Vj) In
1=1
In
1=1
Where: V-j = degrees of freedom for each copper concen-
tration and control, V-j = (nj - 1)
p = number of concentration levels including the control
222
-------
S2 =
P
Z V1
1=1
C = 1 + ( 3(p-l))-l [ L 1/Vj - ( I ViH ]
1=1 1=1
In = loge
i = 1, 2, ..., p where p is the number of concentrations
including the control i;;,c
n-} = the number of replicates for concentration i.
4.4.7.2 For the data in this example, (See Table 20} n] = 8, r\z = 7
ind ns = 7, Thus, the respective degrees of freedom are 7, 6 and 6.
14.4.7.3 Bartlett's statistic is therefore:
B = [(19)ln(0.077) - (7 ln(0.064) + 6 ln(0.021) 4 6 ln(0.147))]/l.07
* [19(-2.564) - (-53.925JJ/1.07
* [-48.716 - (-53.925)]/1.07 -/-:;,
= 4.868
fl4.4.7.4 B is approximately distributed as chi-square with p - 1 degrees of
Ifreedom, when the variances are in fact the same. Therefore, the
ippropriate critical value for this test, at a significance level of 0.01
fith two degrees of freedom, is 9.210. Since B = 4.868 is less than the
critical value of 9.210, conclude that the variances are not different.
H4.4.8 Bonferroni's T-test
114.4.8.1 Bonferroni's T-test is used as an alternative to Dunnett's
'rocedure when, as in this set of data, the number of replicates is not the
fsame for all concentrations. Like Dunnett's Procedure, it uses a pooled
[estimate of the variance, which is equal to the error value calculated in an
^analysis of variance. To obtain an estimate of the pooled variance,
fconstruct an ANOVA table as described in Table 24.
223
-------
Table 24. ANOVA TABLE
Source
df
Total
N - 1
Sum of Squares
(SS)
SST
Mean Square(MS)
(SS/df)
Between
Within
P
N
- 1
- P
SSB
SSW
2
SB =
2
sw =
SSB/(p-1)
SSW/(N-p)
Where:
p
N
n-j
= number concentration levels including the control
= total number of observations n] + r\2 ••• +np
= number of observations in concentration i
P
SSB = Z
Between Sum of Squares
SST = I iVfV
1=1 j=l
SSW = SST - SSB
- G2/N
Total Sum of Squares
Within Sum of Squares
i
G = the grand total of all sample observations, G = I T-j
i = 1
T-j = the total of the replicate measurements for
concentration "i"
Yij = the jth observation for concentration "i" (represents
the proportion of females with eggs for concentration
i in test chamber j)
14.4.8,2 For the data in this example:
n] - 8 n2 = 7 n3 = 7
N « 22
T] = YH + YIZ + ... + YIB = 11.5 ..- :
T2 = Y2] + Y22 + ... + Y27 = 4.94 ;v
T3 = Y31 + Y32 + .- + Y37 = 3.65
G = TI 4 T2 + TS + T4 = 20.09
224
-------
SSB = z T^/ni - G2/N
132.25 + 24.40 + 13.32 - 403,6
SST =
P ri
I Z
7
- Q2/N
= 23.396 - 403.61 = 5.05
22
SSW = SST - SSB = 5.05 - 3.57 = 1,48
SB2 = SSB/p-1 .= 3.57/3-1 = 1.785
SW2 = sSW/N-p = 1.48/22-3 = 0.078
14.4.8.3 Summarize these calculations in the ANOVA table (Table 25)
Table 25. ANOVA TABLE FOR DUNNETT'S PROCEDURE EXAMPLE
Source
Between
Within
Total
df
2
19
21
Sum of Squares
(SS)
3.57
1.48
5.05
Mean Square(MS)
(SS/df)
1.785
0.078
14.4.8.4 To perform the individual comparisons, calculate the t
statistic for each concentration, and control combination as follows
Where
Sw
nl
»- d/nj)
mean proportion of females with eggs for concentration i
mean proportion of females with eggs for the control
square root of within mean square
number of replicates for control
number of replicates for concentration i.
22S
-------
14.4.8.5 Table 26 includes the calculated t values for each
concentration and control combination. In this example, comparing the
50.0 ppb concentration with the control the calculation is as follows:
{ 1.44 - 0.52 )
[ 0.279V U/8J + (1/7) ]
TABLE 26. CALCULATED T-VALUES
Test Concentration (ppb)
50.0
100.0
2
3
5.05
6.37
14.4.8.6 Since the purpose of this test is to detect a significant
reduction in mean proportion of females with eggs, a (one-sided) test is
appropriate. The critical value for this one-sided test is found in
Table 5, Appendix E, Critical Values for Bonferroni's "T". For an
overall alpha level of 0.05, 19 degrees of freedom for error and two
concentrations (excluding the control) the approximate critical value is
2.094. The mean proportion for concentration "1" is considered
significantly less than the raean proportion for the control if t-; is
greater than the critical value. Therefore, the 50.0 ppb and the
100.0 ppb concentrations have significantly lower mean proportion of
females with eggs than the control. Hence the LOEC for fecundity is 50.0
ppb.
14.4.8.7 To quantify the sensitivity of the test, the minimum
significant difference (MSD) that can be detected statistically may be
calculated.
jWhere: t
Sw
n -
= t Sw v7 (l/ni) + (1/n)
the critical value for Bonferroni's t-test
the square root of the within mean square
the common number of replicates at each concentration
(this assumes equal replication at each concentration
the number of replicates in the control.
14.4.8.8 In this example:
MSD = 2.094 (0.279) / (1/8) + (1/7)
= 2.094 (0.279)(0.518)
= 0.303
226
-------
14.4.8.9 Therefore, for this set of data, the minimum difference that
Kan be detected as statistically significant is 0.30.
E
fl4.4.8.10 The MSD (0.30) is in transformed units. To determine the MSD
|in terms of percent of females with eggs, carry out the following
inversion.
§4.4.8.10.1 Subtract the MSD from the transformed control mean.
1.44 - 0.30 = 1.14
14.4.8.10.2 Obtain the untransformed values for the control mean and
;he difference calculated in 4.10.1.
[Sine (1.44) ]Z = 0.983
[Sine (1.14) ]Z = 0.823
[14.4.8.10.3 The untransformed MSD (MSDU) is determined by subtracting
[the untransformed values from 14.4.8.10.2.
MSDU = 0.983 - 0.823 = 0.16
[14.4.8.11 Therefore, for this set of data, the minimum difference in
pean proportion of females with eggs between the control and any copper
fconcentration that can be detected as statistically significant is 0.16.
14.4.8.12 This represents a 17% decrease in proportion of females with
eggs from the control.
14.4.9 Probit Analysis
;14.4.9.1 The data used for the probit analysis is summarized in
[Table 27. For the probit analysis, the test concentration with 0%
ifemales with eggs in all eight replicates was considered. To perform the
probit analysis, run the EPA Probit Analysis Program, using the option to
[adjust for response in the controls. An example of the program out is
'provided in Table 28 and Figure 13.
14.4.9.2 For this example, the chi-square test for heterogeneity was not
significant. Thus probit analysis appears to be appropriate for this set
of data.
227
-------
TABLE 27. DATA FOR PROBIT ANALYSIS
Test Concentration (ppb)
Control 50.0 100.0 210.0
No. Females W/0 Eggs 2
No. Females 19
13
22
10
16
14
14
228
-------
TABLE 28. OUTPUT FROM EPA PROBIT ANALYSIS PROGRAM, VERSION 1.4.
MYSID FECUNDITY DATA.
Mysidopsis Bahia Fecundity Data Analysis
Cone.
Control
50.0000
100.0000
210.0000
Number
Exposed
19
22
16
14
Number
Resp.
2
13
10
14
Observed
Proportion
Responding
0.1053
0.5909
0.6250
1.0000
Adjusted
Proportion
Responding
0.0000
0.5411
0.5793
1.0000
Predicted
Proportion
Responding
0.1086
0.4695
0.7454
0.9263
Chi - Square Heterogeneity = 3.343
Mu
Sigma
Parameter
1.730247
0.408592
Estimate
std. Err.
95% Confidence Limits
Intercept
slope
Spontaneous
Response Rate
0.765340
2.447431
0.108593
1.796586
0.937746
0.071352
-2.755967,
0.609448,
-0.031257,
4.286648)
4.285414)
0.248444)
Estimated EC Values and Confidence Limits
Point
EC 1.00
EC 5.00
EC10.00
EC15.00
EC50.00
EC85.00
EC90.00
EC95.00
EC99.00
Cone.
Lower Upper
95% Confidence Limits
6.
11,
16,
20.
53.
142.
179.
252.
479.
0220
4328
0915
2667
7337
4661
4314
5455
4620
0.0022
0.0289
0.1127
0.2814
12.0495
92,5911
111.0103
140.4689
209.9131
19.2441
28.1558
34,6456
39.9812
81.7779
932.0419
2239.7014
8489.1182
107515.0700
229
-------
Probit
10+
s+
8+
7+
6+
4 +
3 +
2-
1+
0+
EC01
EC10 EC25 EC50 EC75 EC90
EC99
Figure 13. Plot of adjusted probits and predicted regression line
230
-------
:5. PRECISION AND ACCURACY
i PRECISION
-5.1.1 Data on the single laboratory precision of the mysid survival,
Browth, and fecundity using copper sulfate (CU) and sodium dodecyl
ulfate (SDS) in natural seawater are shown in Tables 29 and 30.
urvival NOEC/LOEC pairs showed good precision, and were the same in four
the six tests with CU and SDS. Growth and fecundity were generally
ot acceptable end points in either sets of tests.
[5.1.1 The multi-laboratory precision of the test has not yet been
Fetermined.
5.2 ACCURACY
.5.2.1 The accuracy of toxicity tests cannot be determined.
231
-------
TABLE 29. SINGLE LABORATORY PRECISION OF THE MYSID (MYSIDQPSIS BAHIA)
SURVIVAL, GROWTH, AND FECUNDITY TEST PERFORMED IN NATURAL
SEA WATER, USING JUVENILES FROM HYSIDS CULTURED AND SPAWNED IN
NATURAL SEAWATER, AND COPPER (CU) AS A REFERENCE
TOXICANTl.2 34567
"
Survival
i Test
L
1 ,
r 2
1 3
«
1 5
1 6
NOEC
(ug/L)
63
(5)
125
125
125
125
LOEC
(ug/L)
125
(5)
250
250
250
250
Growth
NOEC
(ug/L)
(6)
(6)
(6)
(6)
(6)
(6)
LOEC
(ug/L)
(6)
(6)
(6)
(6)
(6)
(6)
Reproduction
NOEC
(ug/L)
(6)
(6)
(6)
(5)
(6)
125
LOEC
(ug/L)
(6)
(6)
(6)
(5)
(6)
(7)
Most
Sensitive
End Point
S
s
S
s
s
''Tests performed by Randy Cameleo, Environmental Research Laboratory,
U. S. Environmental Protection Agency, Narragansett, Rhode Island.
2Eight replicate exposure chambers, each with five juveniles, were
used for the control and each toxicant concentration. The temperature
of the test solutions was maintained at 26 + 1°C.
3Copper concentrations in Tests 1-2 were: 8, 16, 31, 63, and 125 ug/L.
Copper concentrations in Tests 3-6 were, 16, 31, 63, 125, and 250 ug/L.
4For a discussion of the precision of data from chronic toxicity
tests see Section 4, Quality Assurance.
5Test results inconclusive.
6No effect.
7SE = Survival effects. Fecundity data at these toxicant concentrations
were disregarded because there was a significant reduction in survival.
232
-------
STABLE 30. SINGLE LABORATORY PRECISION OF THE MYSID (MYSIDOPSIS BAH-IA)
SURVIVAL, GROWTH, AND FECUNDITY TEST PERFORMED IN NATURAL
SEA WATER, USING JUVENILES FROM MYSIDS CULTURED AND SPAWNED IN
NATURAL SEAWATER, AND SODIUM DODECYL SULFATE (SDS) AS A
REFERENCE TOXICANTl,2 3 4 5 6 7
i Survival
;Test
i
1
1
! 2
f 3
4
5
6
NOEC
(mg/L)
2.5
(6)
(6)
5,0
2.5
5.0
LOEC
(mg/L)
5.0
(6)
(6)
10.0
5.0
10,0
Growth
NOEC
(mg/L)
(6)
(6}
(6)
(6)
(6)
(6)
LOEC
(mg/L)
(6)
(6)
(6)
(6)
(6)
(6)
Reproduction
NOEC
(mg/L)
(6)
(6)
(6)
(6)
(6)
5.0
LOEC
(mg/L)
(6)
(6)
(6)
(6)
(6)
(7)
Most
Sensitive
End Point
S
-
_
S
S
-
^Tests performed by Randy Cameleo, Environmental Research Laboratory,
U. S. Environmental Protection Agency, Narragansett, Rhode Island.
replicate exposure chambers, each with five juveniles, were
used for the control and each toxicant concentration. The temperature
of the test solutions was maintained at 26 +
concentrations in Tests 1-2 were: 0.3, 0.6, 1.3, 2.5, and
5.0 mg/L. SDS concentrations in Tests 3-4 were: 0.6, 1.3, 2.5, 5.0 and
10.0 mg/L, SDS concentrations in Tests 5-6 were: 1.3, 2.5, 5.0, 10.0,
and 20.0 mg/L.
a discussion of the precision of data from chronic toxicity
tests see Section 4, Quality Assurance.
}Test results inconclusive.
'No effect.
SE = Survival effects. Growth data at these toxicant concentrations
were disregarded because there was a significant reduction in survival.
233
-------
f-'igure 14. Data sheet for water quality measurements
From Lussler, Kuhn, and Sewall, 1987.
TEST:
START DATE;
SALINITY:
DAY 1
DAv 2
DAY 3
DAY 4
DAY 5
DAY 6
^AY 7
DAY 1
DAY ?
DAY 3
DAY 4
DAY 5
DAY 6
DAY 7
TRTMT
RFP
RFP
qc-p
HEP
REP
REP
REP
PEP
REP
REP
REP
REP
3eE
REP
TRTMT
REP
REP
PEP
RFP
REP
REP
REP
REP
REP
REP
-HEP
REP
REP
REP
TEMP
rt'Mf
SALINITY
SALINITY
DO
DO
pH
pH
TRTMT
T R 1 M r
TEMP
TEMP
SALINITY
SAL IN'"-V
• DO
I) O
pH
pH
234.
-------
Figure 15. Data sheet for survival and fecundity data
From Ussier, Kuhn, and Sewall, 1987.
TEST:
START DATE:
SALINITY:
TREATMENT/
REPLICATE
1
2
3
4
5
6
7
8
1
2
3
4
1
5
6
7
8
1
2
3
4
2
f
6
7
8
DAY 1
f ALIVE
DAY 2
t ALIVE
DAYS
# ALIVE
-
DAY 4
1 ALIVE
DAYS
if ALIVE
DAY 6
* ALIVE
DAY?
/ALIVE
FEMALES
W/EGGS
FEMALES
NO EGGS
MALES
MMATURES
•^^^•MHi
235
-------
Figure 15. Continued.
TEST:
START DATE:
I
iSALINITY:
TREATMENT/
REPLICATE
1
2
3
4
3
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
5
6
7
8
DAY 1
* ALIVE
DAY 2
* ALIVE
DAY 3
# ALIVE
•
DAY 4
* ALIVE
DAYS
* ALIVE
DAY 6
t ALIVE
DAY?
* ALIVE
FEMALES
W/EGGS
FEMALES
NO EGGS
MALES
iMMATURES
236
-------
Figure 16. Data sheet for dry weight measurements
From Lussier, Kuhn, and Sewall, 1987.
*EST:
START DATE:_
SALINITY:
TREATMENT
; REPLICATE
2
3
4
C
5
6
7
8
1
2
3
4
1
6
7
8
1
2
3
4
2
5
6
7
8
PAN*
TARE
WT.
TOTAL
WT.
ANIMAL
WT.
#OF
ANIMALS
XWT./
ANIMAL
237
-------
Figure 16. Continued.
iTEST:
JTART DATE:_
[SALINITY:
TREATMENT
REPLICATE
1
2
3
4
3
5
6
7
8
1
2
3
4
4
5
6
7
8
1
2
3
4
5
6
7
8
PAN*
TARE
WT.
TOTAL
WT.
ANIMAL
WT.
#OF-
ANIMALS
XWT./
ANIMAL
238
-------
SECTION 15
TEST METHODl.2
SEA URCHIN (ARBACIA PUNCTULATA) FERTILIZATION TEST
METHOD 1008
SCOPE AND APPLICATION
_.l This method measures the toxicity of effluents and receiving water to the
jametes of the sea urchin, Arbac i a punctulata, during a 1 h and 20 min
jxposure. The purpose of the sperm cell toxicity test is to determine the
Concentration of a test substance that reduces fertilization of exposed
gametes relative to that of the control.
>1.2 Detection limits of the toxicity of an effluent or pure substance are
[organism dependent.
|1.3 Single or multiple excursions in toxicity may not be detected using 24-h
^composite samples. Also, because of the long sample collection period
'involved in composite sampling and because the test chambers are not sealed,
^highly volatile and highly degradable toxicants in the source may not be
'detected in the test.
1.4 This method should be restricted to use by, or under the supervision of,
professionals experienced in aquatic toxicity testing.
2. SUMMARY OF METHOD
t2.1 The method consists of exposing dilute sperm suspensions to effluents or
'receiving waters for one hour. Eggs are then added to the sperm suspensions.
Jwenty minutes after the eggs are added, the test is terminated by the
addition of preservative. The percent fertilization is determined by
•microscopic examination of an aliquot from each treatment. The test results
'are reported as the concentration of the test substance which causes a
^statistically significant reduction in fertilization, compared to the
'controls.
[3. DEFINITIONS
(Reserved for addition of terms at a later date).
INTERFERENCES
4.1 Toxic substances may be introduced by contaminants in dilution water,
glassware, sample hardware, and testing equipment (see Section 5, Facilities
and Equipment).
format used for this method was taken from Kopp, 1983.
2This method was adapted from Nacci, Walsh, and Jackim, 1987, Environmental
Research Laboratory, U. S. Environmental Protection Agency, Narragansett,
Rhode Island.
239
-------
[4.2 Improper effluent sampling and handling may adversely affect test
'results (see Section 8, Effluent and Receiving Water Sampling and Sample
Handling).
SAFETY
15.1 See Section 3, Health and Safety.
APPARATUS AND EQUIPMEiNT
.l Facilities for holding and acclimating test organisms.
Laboratory Arbacia punctulata culture unit — See cuHuring methods
ielow. To test effluent or receiving water toxicity, sufficient eggs and
Sperm must be available.
[-6.3 Samplers -- automatic sampler, preferrably with sample cooling
Icapability, that can collect a 24-h composite sample of 1 L.
;6.4 Environmental chamber or equivalent facility with temperature control
(20 +_ 1°C) for controlling temperature during exposure.
•6.5 Water purification system -- Millipore Super-Q, Deionized water (DI) or
^equivalent.
i
6.6 Balance -- Analytical, capable of accurately weighing to 0.0001 g.
,6.7 Reference weights, Class S -- for checking performance of balance.
6.8 Air pump -- for supplying air.
i
'6.9 Air lines, and air stones -- for aerating water containing adults.
,6.10 Vacuum suction device -- for washing eggs.
i
i
;6.11 pH and DO meters -- for routine physical and chemical measurements.
jUnless the test is being conducted to specifically measure the effect of one
[of these two parameters, portable, field-grade instruments are acceptable.
6.12 Standard or micro-Winkler apparatus — for determining DO (optional).
L
6.13 Transformer, 12 Volt, with steel electrodes -- for stimulating
release of eggs and sperm.
^6.14 Centrifuge, bench-top, slant-head, variable speed -- for washing eggs.
f
;6.15 Fume hood -- to protect the analyst from formaldehyde fumes.
;6.16 Dissecting microscope -- for counting diluted egg stock.
:6.17 Compound microscope — for examining and counting sperm cells and
|fertilized eggs.
240
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.18 Sedgwick-Rafter counting chamber -- for counting egg stock.
..19 Hemacytometer, Neubauer -- for counting sperm.
06.20 Count register, 2-place -- for recording sperm and egg counts.
|6.21 Refractometer -- for determining salinity.
1
|p.22 Thermometers, glass or electronic, laboratory grade -- for measuring
f|/ater temperatures.
i.23 Thermometers, bulb-thermograph or electronic-chart type -- for
Continuously recording temperature.
i.24 Thermometer, National Bureau of Standards Certified (see USEPA METHOD
|170.1, USEPA, 1979) — to calibrate laboratory thermometers.
16.25 Ice bucket, covered -- for maintaining live sperm.
j
|6.26 Centrifuge tubes, conical -- for washing eggs.
..27 Cylindrical glass vessel, 8-cm diameter -- for maintaining dispersed
;gg suspension.
15.28 Beakers -- six Class A, borosilicate glass or non-toxic plasticware,
iflOOO ml for making test solutions.
J
15.29 Glass dishes, flat bottomed, 20-cm diameter -- for suspending eggs.
i
p.30 Wash bottles -- for deionized water, for rinsing small glassware and
finstrument electrodes and probes.
'.31 Volumetric flasks and graduated cylinders -- Class A, borosilicate
fglass or non-toxic plastic labware, 10-1000 ml for making test solutions.
i.32 Syringes, 1-mL, and 10-mL, with 18 gauge, blunt-tipped needles (tips
:ut off) -- for collecting sperm and eggs.
|fe.33 Pipets, volumetric -- Class A, 1-100 ml.
i.34 Pipets, automatic -- adjustable, 1-100 ml.
..35 Pipets, serological -- 1-10 mL, graduated.
§5.36 Pipet bulbs and fillers — PRQPIPETR, or equivalent.
I
[6.37 Tape, colored -- for labelling tubes.
I
[6.38 Markers, water-proof -- for marking containers, etc.
241
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7. REAGENTS AND CONSUMABLE MATERIALS
7.1 Sea Urchins, Arbacia punctulata (approximately 12 of each sex).
7.2 Food — kelp, Laminaria sp., or romaine lettuce for A, punctulata.
7.3 Standard salt water aquarium or Instant Ocean Aquarium {capable of
maintaining sea water at IB^C), with appropriate filtration and aeration
system.
.4 Sample containers — for sample shipment and storage (see Section 8,
Affluent and Receiving Water Sampling and Sample Handling).
'.5 Scintillation vials, 20 ml, disposable — to prepare test
^concentrations,
|7.6 Parafilm — to cover tubes and vessels containing test materials.
|7.7 Gloves, disposable — for personal protection from contamination.
I
7.8 Data sheets (one set per test) — for data recording (see Figures 4, 5,
[and 6).
1
.7.9 Acetic acid, 10%, reagent grade, in sea water -- for preparing killed
|sperm dilutions.
I
7.10 Formalin, }Q%S buffered (1,620 ml distilled water, 620 ml
[formaldehyde, reagent grade)9(6.48 g NaH2P04 or KH2PG4, 10,5 g
P04 or K2HP04) -- for preserving eggs.
.7.11 pH buffers 4, 79 and 10 (or as per instructions of instrument
^manufacturer) for standards and calibration check (see USEPA Method 150.1,
USEPA, 1979).
J7.12 Membranes and filling solutions for dissolved oxygen probe (see USEPA
jMethod 360.1, USEPA, 1979), or reagents for modified Winkler analysis.
|7.13 Laboratory quality assurance samples and standards for the above
• methods.
<7.14 Reference toxicant solutions (see Section 4, Quality Assurance).
I
j7.15 Reagent water -- defined as distilled or deionized water that does not
^contain substances which are toxic to the test organisms.
7.16 Effluent, surface water, and dilution water — see Section 7, Dilution
Water, and Section 8, Effluent and Surface Water Sampling and Sample
Handling.
7.16.1 Saline test and dilution water -- The salinity of the test water
must be 30 °/oo. The salinity should vary by no more than + 2 o/oo
among the replicates.
242
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7.16.2 The overwhelming majority of industrial and sewage treatment
effluents entering marine and estuarine systems contain little or no
measurable salts. Exposure of sea urchin eggs and sperm to these effluents
will require adjustments in the salinity of the test solutions. It is
important to maintain a constant salinity across all treatments. Two
methods are available to adjust salinities hypersaline brine derived from
natural seawater or artificial sea salts. Use of hypersaline brine will
limit the concentration of effluent tested to 703.
7.16.3 Hypersaline brine: Hypersaline brine (HSB) has several advantages
that make it desirable for use in toxicity testing. It can be made from any
high quality, filtered seawater fay evaporation, and can be added to the
Affluent or to deionized water to increase the salinity. HSB derived from
atura! seawater contains the necessary trace metals, biogenic colloids, and
|Some of the microbial components necessary for adequate growth, survival,
|ind/or reproduction of marine and estuarine organisms, and may be stored for
•"rolonged periods without any apparent degradation.
7.16.3.1 The ideal container for making HSB from natural seawater is one
|that (1 has a high surface to volume ratio, (2) is made of a non-corrosive
^material, and (3) is easily cleaned (fiberglass containers are ideal).
jSpecial care should be used to prevent any toxic materials from coming in
Pcontact with the seawater being used to generate the brine. If a heater is
hmmersed directly into the seawater, ensure that the heater materials do not
.corrode or leach any substances that would contaminate the brine. One
^successful method used is a thermostatically controlled heat exchanger made
pom fiberglass. If aeration is used, use only oil-free air compressors to
Jprevent contamination. .
p.16.3.2 Before adding seawater to the brine generator, thoroughly clean
|the generator, aeration supply tube, heater, and any other materials that
.will be in direct contact with the brine. A good quality biodegradable
|detergent should be used, followed by several thorough deionized water
rinses. High quality (and preferably high salinity) seawater should be
|Filtered to as least 10 urn before placing into the brine generator. Water
^should be collected on an incoming tide to minimize the possibility of
icontamination.
1
J.16.3.3 The temperature of the seawater is increased slowly to 40°C.
LThe water should be aerated to prevent temperature stratification and to
increase water evaporation. The brine should be checked daily (depending on
|the volume being generated) to ensure that the salinity does not exceed
1100 o/oo and that the temperature does not exceed 4QQC. Additional
^seawater may be added to the brine to obtain the volume of brine required.
|.16.3.4 After the required salinity is attained, the HSB should be
pltered a second time through a 1-um filter and poured directly into
.portable containers (20-L cubitainers or polycarbonate water cooler jugs are
^suitable). The containers should be capped and labelled with the date the
i>rine was generated and its salinity. Containers of HSB should be stored in
dark and maintained under room temperature until used.
243
-------
(7.16.3.5 If a source of HSB is available, test solutions can be made by
^following the directions below. Thoroughly mix together the deionized water
and brine before mixing in the effluent.
I
7.16.3.6 Divide the salinity of the HSB by the expected test salinity to
[determine the proportion of deionized water to brine. For example, if the
|salinity of the brine is 100 o/oo and the test is to be conducted at 30
|°/oo, 100 °/oo divided by 30 °/oo = 3.3. The proportion of brine is
|1 part in 3.3 (one part brine to 2.3 parts deionized water).
17.16.3.7 To make 1 L of seawater at 30 °/oo salinity from a hypersaline
irine of 100 °/oo, 300 ml of brine and 700 ml of deionized water are
Inquired.
I
^7.16.3.8 Table 1 illustrates the preparation of test solutions at 30 °/oo
.if they are made by combining effluent (0 °/oo), deionized water and HSB
(100 °/oo), or Forty Fathoms^ sea salts.
7.16.4 Artificial sea salts: Forty FathomsR brand sea salts have been
used successfully at the EMSL-Cincinnati Newtown Facility for long-term
(6 to 12 months) maintenance of stock cultures of sexually mature sea
urchins and to perform the sea urchin fertilization test.
7.17 SEA URCHINS
7.17.1 Adult sea urchins (Arbacia punctulata) can be obtained from
commercial suppliers. After acquisition, the animals are sexed by briefly
stimulating them with current from a 12 V transformer. Electrical
stimulation causes the immediate release of masses of gametes that are
readily identifiable by color -- the eggs are red, and the sperm are white.
7.17.2 The sexes are separated and maintained in 20-L, aerated fiberglass
tanks, each holding about 20 adults. The tanks are supplied continuously
(approximately 5 L/min) with filtered natural seawater, or salt water
prepared from commerical sea salts is recirculated. The animals are checked
daily and any obviously unhealthy animals are discarded.
7.17.3 The culture unit should be maintained at 15°C + 3°C, with a
water temperature control device.
7.17.4 The food consists of kelp (Laminaria sp.), gathered from known
uncontaminated zones or obtained from commerical supply houses whose kelp
comes from known uncontaminated areas, or romaine lettuce. Fresh food is
introduced into the tanks at approximately one week intervals. Decaying
food is removed as necessary. Ample supplies of food should always be
available to the sea urchins.
7.17.5 Natural or artificial seawater with a salinity of 30 °/oo is used
to maintain the adult animals, for all washing and dilution steps, and as
the control water in the tests (see Par. 7.16).
244
-------
TABLE 1.
Control
0.0
Solutions To Be Combined
•Effluent
JH;So1ution
I1
H 2
1 3
• 4
•
Effluent
Cone.
(%}
loo?
32
10
3.2
1.0
Volume of Volume of Diluent
Effluent Seawater (30 o/00)
Solution
600 ml
200 ml Solution 1 +
200 ml Solution 2 +
200 ml Solution 3 +
200 ml Solution 4 +
— __
400 ml
400 ml
400 ml
400 ml
400 ml
Total
2000 ml
his illustration assumes: (1) the use of 5 ml of test
solution in each of four replicates {total of 20 ml) for the control
82 nf]veConcentrations of effluent, (2) an effluent dilution factor
ot u.J, (3) the effluent lacks appreciable salinity, and (4) 400 ml of
each test concentration is used for chemical analysis.. A sufficient
initial volume (600 ml) of effluent is prepared by adjusting the
salinity to 30 o/oo. In this example, the salinity is adjusted by
adding artificial sea salts to the 100% effluent, and preparing a
serial dilution using 30 o/00 seawater {natural seawater,
hypersaline brine, or artificial seawater}. Stir solutions 1 h to
?nn*re«5at !h? SaItS d1ssolve- The salinity of the initial 600 ml of
100% effluent is adjusted to 30 o/oo by adding 18 g of dry
artificial sea salts (Forty Fathoms*}. Test concentrations are then
made by mixing appropriate volumes of salinity adjusted effluent and
JO o/oo salinity dilution water to provide 400 ml of solution for
each concentration. If hypersaline brine alone (100 o/00) is used
to adjust the salinity of the effluent,-the highest concentration of
effluent that could be tested would be 7Q% at 30 o/00 salinity
245
-------
17.17.6 Adult male and female animals used in field studies are transported
in separate or partitioned insulated boxes or coolers packed with wet kelp
'or paper toweling. Upon arrival at the field site, aquaria (or a single
partitioned aquarium) are filled with control water, loosely covered with a
'styrofoam sheet and allowed to equilibrate to 15°C before animals are
padded. Healthy animals will attach to the kelp or aquarium within hours.
,-7.17.7 To successfully maintain about 25 adult animals for seven days at a
"field site, a screen-partitioned, 40-L glass aquarium using aerated,
^circulating, clean saline water {30 °/oo) and a gravel bed filtration
System, is housed within a water bath, such as an INSTANT OCEAN* Aquarium
(15°C). The inner aquarium is used to avoid contact of animals and water
iath with cooling coils.
. SAMPLE COLLECTION, PRESERVATION AND HANDLING
8.1 See Section 8, Effluent and Receiving water Sampling and Sample
Handling.
J9. CALIBRATION AND STANDARDIZATION
9.1 See Secion 4, Quality Assurance.
10. QUALITY CONTROL
10.1 See Section 4, Quality Assurance.
11. TEST PROCEDURE
11.1 TEST SOLUTIONS
11.1.1 Surface Waters
11.1.1.1 Surface water toxicity is determined with samples used directly as
collected.
11.1.2 Effluents
11.1.2.1 The selection of the effluent test concentrations should be based
on the objectives of the study. One of two dilution factors, approximately
0.3 or 0.5, is commonly used. A dilution factor of approximately 0.3 allows
testing between 100% and 1% effluent using only five effluent concentrations
,100%, 30%, 10%, 3%, and 1%). This series of dilutions minimizes the level
of effort, but because of the wide interval between test concentrations
246
-------
rovides poor test precision. A dilution factor of 0.5 provides greater
precision, but requires several additional dilutions to span the same range
.pf effluent concentrations. Improvements in precision decline rapidly as
the dilution factor is increased beyond 0.5.
£1.1.2.2 If the effluent is known or suspected to be highly toxic, a lower
jange of effluent concentrations should be used (such as 10%, 3%, 1%, and
. 1%).
11.1.3 Control Water
1.1.3.1 Prepare 3 L of control water at 30 o/00 using hypersaline brine
|r artificial sea salts (see Table 1). This water is used in all washing
gnd diluting steps and as control water in the test. Natural sea water and
local waters may be used as additional controls.
'11.1.4 Effluent Dilutions
m.1.4.1
[30 o/oo.
Effluent/receiving water samples are adjusted to salinity of
P
ill.1.4.2 Four replicates (minimum of three) are prepared for each test
Concentration, using 5 ml of solution in disposable liquid scintillation
Ivials. A 50% (0.5) concentration series can be prepared by serially
liluting test concentrations with control water.
111.1.4,3 All test samples are equilibrated at 2Q°C + 1°C before
addition of sperm.
ill.2. REFERENCE TOXICANT TEST
11.2.1 A reference toxicant test using copper sulfate is performed
;ide-by-side with each fertilization test, or set of tests, performed with a
liven batch of gametes (see Section 4, Quality Assurance).
|l.3. COLLECTION OF GAMETES FOR THE TEST
1.3.1 Select four males and place in shallow, bowls, barely covering the
nimals with seawater. Stimulate the release of sperm by touching the shell
ith steel electrodes connected to a 12 V transformer (about 30 seconds each
ime). Collect the sperm (about 0.5-1.0 ml) from each male, using a 1-3 mL
isposable syringe fitted with an 18-gauge, blunt-tipped needle. Pool the
|perm. Maintain the pooled sperm sample on ice. The sperm must be used in
toxicity test within 1 h of collection.
|11.3.2 Select four females and place in shallow bowls, barely covering the
jshell with seawater. Stimulate the release of eggs and collected with a
[needle as described above. Remove the needle from the syringe before adding
|the eggs to a conical centrifuge tube. Pool the eggs. The egg stock may be
leld at room temperature for several hours before use. Note: The egg
Isuspension may be prepared during the 1-h sperm exposure.
247
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11.4. PREPARATION OF SPERM DILUTION FOR USE IN THE TEST
11.4.1 Using control water, dilute the pooled sperm sample to a
concentration of about 5 X 107 sperm/mL (SPM). Estimate the sperm
concentration as described below:.
1. Make a sperm dilutions of 1:50, 1:100, 1:200, and 1:400, using
30 o/oo seawater, as follows:
a. Add 200 uL of collected sperm to 10 ml of sea water in Vial A
Mix by gentle pipetting using a 5-mL pipetter.
b. Add 5 ml of sperm suspension from Vial A to 5 ml of seawater in
Vial B. Mix by gentle pipetting using a 5-mL pipetter.
c. Add 5 mL of sperm suspension from Vial B to 5 mL of seawater in
Vial C. Mix by gentle pipetting using a 5-mL pipetter.
d. Add 5 mL of sperm suspension from Vial C to 5 mL of seawater in
Vial D. Mix by gentle pipetting using a 5-mL pipetter.
e. Discard 5 mL from Vial D. (The volume of all suspensions is 5 mL)
2. Make a 1:2000 killed sperm suspension and determine the SPM.
Cap Vial C and
Add 5 mL 10% acetic acid in seawater to Vial C.
mix by inversion.
Add 1 mL of killed sperm from Vial C to 4 ml of seawater in
Vial E. Mix by gentle pipetting with a 4-mL pipetter.
Add sperm from Vial E to both sides of the Neubauer
hemacytometer. Let the sperm settle 15 min.
Count the number of sperm in the central 400 squares on both sides
of the hemacytometer using a compound microscope (400X).
the counts from the two sides.
SPM in Vial E = 10^ x average count.
Averaae
3. Calculate the SPM in all other suspensions using the SPM in Vial E
above:
SPM in Vial A = 40 x SPM in Vial E
Spm in Vial B = 20 x SPM in Vial E
SPM in Vial D = 5 x SPM in Vial E
SPM in original sperm sample = 2000 x SPM in Via) E
4. Dilute the sperm suspension with a SPM greater than 5 x 10? SPM to
5 x 10' SPM.
Actual SPM/(5 x 107} = dilution factor (DF)
[(DF) x 5] - 5 = mL of seawater to add to vial.
5. Confirm the sperm count by sampling from the test stock. Add 0.1 mL
°f-^e^ s?ock to 9'9 mL of 10% acet1c ac1d i'n seawater, and count
with the hemacytometer. The count should average 50+5
248
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11.5 PREPARATION OF EGG SUSPENSION FOR USED IN THE TEST
Jl 1.5.1 Wash the pooled eggs three times using control water with gentle
:entrifugation (500xg for 3 min using a tabletop centrifuge). If the wash
later becomes red, the eggs have lysed and must be discarded.
1.5.2 Dilute the egg stock, using control water, to about 2000 eggs/mL.
1. Add control water to bring the eggs to a volume of 200 ml ("egg stock")
2. Mix the egg stock using an air-bubbling device. Using a wide-mouth
pipet tip, transfer 1 mL of eggs from the egg stock to a v^ial
containing 9 mL of control water. (This vial contains an egg
suspension diluted 1:10 from egg stock),
3. Mix the contents of the vial using gentle pipetting. Using a wide-
mouth pipet tip, transfer 1 ml of eggs from the vial to a
Sedgwick-Rafter counting chamber. Count all eggs in the chamber using
a dissecting microscope at 10X ("egg count").
4. Calculate the concentration of eggs in the stock. Eggs/mL = 10X (egg
count). Dilute the egg stock to 2000 eggs/mL by the formula below.
a. If the egg count is equal to or less than 200:
(egg count) - 200 = volume (ml) of control water to add
to egg stock
b. If the egg count is less than 200, allow the eggs to settle and
remove enough control water to concentrate the eggs to greater
than 200, repeat the count, and dilute the egg stock as in #1
above.
NOTE: It requires 24 mL of a egg stock solution for each test
with a control and five exposure concentrations.
c. Transfer 1 mL of the diluted egg stock to a vial containing 9 mL
of control water. Mix well, then transfer 1 mL from the vial to a
Sedgwick-Rafter counting chamber. Count all eggs using a
dissecting microscope. Confirm that the final egg count = 200/mL.
.6 START OF THE TEST
.6.1 Within 1 h of collection add 100 uL of appropriately diluted sperm
ito each test vial. Record the time of sperm addition.
!ll.6.2 Incubate all test vials at 20 +
for 1 h.
11.6.3 Mix the diluted egg suspension (2000 eggs/mL), using gentle
bubbling. Add 1 mL of diluted egg suspension to each test vial using a wide
mouth pipet tip. Incubate 20 min at 20 +
249
-------
11.7 TERMINATION OF THE TEST
.11.7.1 Terminate the test and preserve the samples by adding 2 mL of
•buffered formalin to each vial.
til. 7. 2 Vials may be evaluated immediately or capped and stored for as lonq
one week before being evaluated.
£1.7.3 To determine fertilization, transfer about 1 ml eggs from the bottom
pt_a test vial to a Sedgwick-Rafter counting chamber. Observe the eqqs
jsing a compound microscope (100 X). Count between TOO and 200
Leggs/sample. Record the number counted and the number unfertilized
ertilization is indicated by the presence of a fertilization membrane
urrounding the egg. Note: adjustment of the microscope to obtain proper
ontrast may be required to observe the fertilization membrane. Because
Camples are fixed in formalin, a ventilation hood is set-up surrounding the
microscope to protect the analyst from prolonged exposure to formaldehyde
•f
. ACCEPTABILITY OF TEST RESULTS
nK!rmieg? ratl'° routine]y employed should result in fertilization
of 70% to 90,4 of the eggs in the control chambers.
|13. SUMMARY OF TEST CONDITIONS
i — • —
,13.1 A summary of test conditions is listed in Table 2.
J14. DATA ANALYSIS
•14.1 General ...
i
.14.1.1 Tabulate and summarize the data. Calculate the percent of
(unfertilized eggs for each replicate. A sample set of test data is listed
Table 3.
i
;]4.1.2 The endpoints of toxicity tests using the sea urchin are based on
^rrc rr^ntl0n in Percent of e99s fertilized. Point estimates, such as ECU
;LLb, EC10 and EC50, are calculated using Probit Analysis (Finney, 1971) A
.hypothesis test approach such as Dunnett's Procedure (Dunnett, 1955} or
lS^M,a^°neiRank Tcst (Steel> 1959; Miller> 1981)» *s "sed to estimate
and LOEC values. See the appendices for examples of the manual
computations, program listings, and examples of data input and program
;output. 3
,14.1.3 Formal statistical analysis of the fertilization data is outlined in
Mgure 1. The response used in the analysis is the proportion of
250
-------
1- Test type
2- Salinity:
3- Temperature
4- Light quality:
5- Light intensity:
6. Test vessel si
ze
7- Test solution volume:
8. Number of sea urchins
9.
10.
11.
Number of replicate
chambers per treatment:
Dilution water:
Dilution factor:
Test durat
ion
Effects
measured:
Number of treatments
per test:
Static
30 o/00 ±
20
Ambient laboratory light
during test preparation;
10-20 u£/m2/Sa or 50-100 ft r
(AmfaTent laboratory levels)
5 mL
are used per test
2S.1S ,'?,a,s-M°'™»
(minimum of 3}
Uncontaminated source of -
0-3 or 0.5
1 n and 20 min
Fertilization of sea urchfn
Minimum of five effluent
concentrations and a control
251
-------
TABLE 3. DATA FROM SEA URCHIN FERTILIZATION TESTl
—
Copper Replicate
Concentration
(ug/L)
No. of Eggs No. of Eggs
Counted Unfertilized
Percent
Unfertilized
K ~- —
1 ° A
I n
' B
°
2.5 : A
n
B
C
5.0 A
B
C
10.0 A
B
C
20.0 A
B
C
40.0 A
B
C
—
— , —
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
— — ' '
15
22
13
19
35
29
37
26
22
37
34
49
59
59
63
ftfl
oo
70
74
~ —
15
22
13
19
35
29
37
26
22
37
34
49
59
59
63
88
70
74
MnnJeC.nical APP^"cat1ons Inc.,
Momtonng and Support Laboratory
252
-------
-^ss;i;-!',rsrs,^«;, IK
informat10n on the Bonferroni adjustment see Appendix"!
;
!
eggs compared to the control. In this analysis. tK?centaqesSf
unfertile eggs for all replicates at a given rtncentmK" combined.
f^^^irn^ -s ss.t.srjrr of
recommended for analysts who are not proficient in statistics.
253
-------
14.2 EXAMPLE OF ANALYSIS OF SEA URCHIN FERTILIZATION DATA.
114.2.1 This example uses toxicity data from a sea urchin (Arbacla
mnctulata) fertilization test performed with copper. The response of
pnterest is the proportion of unfertilized eggs, thus each replicate must
cirst be transformed by the arcsin transformation procedure described in
Appendix B. The raw and transformed data, means and standard deviations of
;he transformed observations at each copper concentration and control are
'isted in Table 4. The data are plotted in Figure 2.
TABLE 4. SEA URCHIN FERTILIZATION DATA
Copper Concentration (ug/L)
Replicate Control
2,5
5,0
10.0
20.0
40.0
m
mm A
IH RAW B
I
•
• ARC SINE A
: M TRANS- B
H FORMED C
K> j
Ssfc
M
0.15
0.22
0.13
0.398
0.488
0.369
0,418
0,004
1
0.19
0.35
0.29
0.451
0.633
0.569
0.551
0.008
2
0.37
0.26
0.22
0.654
0.535
0.488
0.559
0.007
3
0.37
0.34
0.49
0.654
0.622
0.775
0.684
0.001
4
0.59
0.59
0.63
0.876
0.876
0.917
0.890
0.0010
5
0.88
0.70
0.74
1.217
0.991
1.036
1.081
0.014
6
14.2.2 Test for Normality
14,2.2.1 The first step of the test for normality is to center the
observations by subtracting the mean of all observations within a
^concentration from each observation in that concentration. The centered
Observations are summarized in Table 5.
254
-------
STATISTICAL ANALYSIS OF SEA URCHIN FERTILIZATION TEST
FERTILIZATION DATA
PERCENT UNFERTILIZED
1
* 1
PROBIT ARCSIN
ANALYSIS TRANSFORMATION
j j
ENDPOINT FSTTMiTF ^HArinn WT! K" TI^T ^ N°
EC1 EC5 EC10 EC50
NORMAL DISTRIBUTION!
| BARTLETT'S TEST M
HOMOGENEOUS VARIANCE
i t
^ . EQUAL NUMBER OF EQUAL NUMBER C
REPLICATES? REPLICATES?
YES YES
v 1 i
InII|npnuTH DUNNETT'S STEEL'S MANY-ONE WIL
BuNi-tHHUNj, TF=;T RANK TFQT
ADJUSTMFNT ' tb f MANK ^tbl BOMFE
f
ENDPOINT ESTIMATES
NOEC, LOEC
RMAL DISTRIBUTION
HETEROGENEOUS
VARIANCE
F ^S
lr
:OXON RANK SUM
TEST WITH
RRONI ADJUSTMENT
Figure 1. Flow chart for statistical analysis of Arbacia data
255
-------
Dl
o»
QJ
O)
N
01
u
§
u
o
o
K
id
QJ
OJ
S333
256
-------
TABLE -5. CENTERED OBSERVATIONS FOR SHAPRIO-WILKS EXAMPLE
i Copper Concentration
I Replicate Control
1
i
1 A -0.
I B 0.
1 ° ~°*
020
070
049
2.
-0.
0.
0.
5
100
082
018
5.
0.
-0.
-0.
0
095
024
071
10.
-0.
-0.
0.
0
030
062
091
20
-0
-0
0
Cug/L)
.0
.014
.014
.027
40
0
-0
-0
.0
.136
.090
.045
[14.2.2,2 Calculate the denominator, D, of the statistic:
(Xi - X)2
Where X-\ = the ith centered observation
X = the overall mean of the centered observations
n = the total number of centered observations
14.2.2.3 For this set of data, n = 18
X = J_ (0) = 0
18
D = 0.0822
14.2.2.4 Order the centered observations from smallest to largest
X(l) - x<2> - ... - x(n)
Iwhere x(i) denotes the ith ordered observation. The ordered
^observations for this example are listed in Table 6.
TABLE 6. ORDERED CENTERED OBSERVATIONS FOR SHAPIRO-WILKS EXAMPLE
!
|
1
2
3
4
I 5
&
1 7
8
9
xH)
-0.100
-0.090
-0.071
-0.062
-0.049
-0.045
-0.030
-0.024
-0.020
i
10
n
12
13
14
15
16
17
18
xM>
-0.014
-0,014
0.018
0.027
0.070
0.082
0.091
0.095
0.136
257
-------
14.2.2.5 From Table 4, Appendix B, for the number of observations, n,
obtain the coefficients a]," 32, ... a^ where k is approximately
n/2. For the data in this example, n = 18 and k = 9. The ai values are
listed in Table 7.
15.2.2.6 Compute the test statistic, W, as follows:
i k
W = 1 [ 2 ai (x(n-i+D - X
- X(3)
- X<4)
- X(6)
- X(8)
14.2.2.7 The decision rule for this test is to compare W as calculated
in 2.6 to a critical value found in Table 6, Appendix B. If the computed
W is less than the critical value, conclude that the data are not
normally distributed. For the data in this example, the critical value
at a significance level of 0.01 and n = 18 observations is 0.858. Since
W = 0.942 is greater than the critical value, conclude that the data are
normally distributed.
14.2.3 Test for Homogeneity of Variance
14.2.3.1 The test used to examine whether the variation in the percent
of unfertilized eggs is the same across all copper concentrations
including the control, is Bartlett's Test (Snedecor and Cochran, 1980). •
The test statistic is as follows: ;
B =
p
[ ( I
1=1
-„
In S2 - i Vi in
1=7
258
-------
Where V-j = degrees of freedom for each copper concen
tration and control, V-j = (n-j - 1)
p = number of levels of copper concentration
including th-e control
S2 =
1 = 1
C = 1 + ( 3(p-l))-l [ I 1/Vi - ( I ViH ]
1=1 1=1
In = loge
i =1,2, ..., p where p is the number of concentrations
including the control
ni = the number of replicates for concentration i.
14.2.3.2 For the data in this example, (See Table 4} all copper
concentrations including the control have the same number of replicates
(ni = 3 for all i). Thus, Vj = 2 for all i,
14.2.3.3 Bartlett's statistic is, therefore:
' ' :"':/ P -"" . ; ;
B = [(I2)ln(0.007) - 2 I ln(Sj)2]/1.194 : T
1=1 ,.
= [12(-4.962) - 2(-31.604}]/1.194
- 3.664M.194
=3.069
14.2.3.4 B is approximately distributed as chi-square with p-1 degrees
of freedom, when the variances are in fact the same. Therefore, the
appropriate critical value for this test, at a significance level of 0.01
;with 5 degrees of freedom, is 15.09. Since B = 3,069 is less than the
critical value of 15.09, conclude that the variances are not different.
259
-------
14,2.4. Dunnett's Procedure .• .
14.2.4.1 Calculations :;
To obtain an estimate of the pooled variance for the Dunnett's Procedure
construct an ANOVA table as described in Table 8.
TABLE 8. ANOVA TABLE
Source df . Sum of Squares
(SS)
Between p - 1 . ,,. SSB
Within N - p SSW
Mean Square (MS)
(SS/df)
2
SB = SSB/(P-D
2
SW = SSW/(N-p)
Total N - 1 SST
Where:
p = number of copper concentrations including the control
N = total number of observations n-j 4- n;? ••« +np
n-j = number of observations in concentration 1
SSB = I T-j2/ni .
SST = i I YlM2 . G2/N
1-1 j=l J
SSW = SST - SSB
Between Sum of Squares
Total Sum of Squares
Within Sum of Squares
p
= the grand total of all sample observations, G = I
G
T-J = the total of the replicate Measurements for
concentration
-JJ = the jth observation for concentration "i" (represents
the percent of unfertilized eggs for copper
concentration i in test chamber j)
260
-------
14.2.4.2 For the data in this example:
N =18
T] = Yn + Yi2 + Yi3 = 1.255
T2 = Ygl + Y22 + Y23 = 1.653
TS = YSI + Y32 + Y33 = 1.677
T4 = Y4i + Y42 + Y43 = 2.051 .
T5 = Y5i + Y52 + Y53 = 2.669
T6 = Y61 + Y62 + Y63 = 3.244
G = 1] + T2 + T3 + T4 = 12.549
P o
SSB = I Tj2/ni - G2/N
= 1 (28.973) - (12.549)2 = 0.909
1
D n-i
SST =
= 9.740 - (12.549)2 = 0.991
18
SSW = SST - SSB = 0.991 - 0.909 = 0
SB2 = SSB/p-1 = 0.909/6-1 = 0.182
SW2 = SSW/N-p = 0.082/18-6 = 0.007
14.2.4.3 Summarize these calculations in the ANOVA table (Table 9}
Table 9. ANOVA TABLE FOR DUNNETT'S PROCEDURE EXAMPLE
Source
Between
Within
df
5
12
Sum of Squares
(SS)
0.909
0.082
Mean Square(MS)
CSS/df)
0.182
0.007
Total
17
0.991
261
-------
14.2.4.4 To perform the individual comparisons, calculate the t statistic
for .each concentration, and control combination as follows:
w
(1/ni) + (1/m)
Where Yi
n
- mean percent unfertilized eggs for copper concentration i
= mean percent unfertilized eggs for the control
= square root of within mean sqaure
= number of replicates for control
= number of replicates for concentration i.
Since we are looking for an increased response over control in percent
unfertilized eggs, the control mean is subtracted from the mean at a
concentration.
t!4.2.4.5 Table 10 includes the calculated t values for each
.concentration and control combination. In this example, comparing the
ug/L concentration with the control the calculation is as follows*
( 0.551 - 0.418 )
[ 0.084^ (1/3) + (1/3) ]
= 1.956
TABLE 10. CALCULATED T-VALUES
Copper Concentration (ug/L)
I 2.5
1 5.0
| 10.0 ;:
1 20.0
, 40.0
2
3
4
5
6
1.956
2.074
3.912
6.941
9.750
(14.2.4.6 Since the purpose of this test is to detect a significant
nncrease in percent unfertilized eggs, a (one-sided) test is
-appropriate. The critical value for this one-sided test is found in
liable 5, Appendix C. For an overall alpha level of 0.05, 12 degrees of
|freedom for error and five concentrations (excluding the control) the
^critical value is 2.50. The mean percent unfertilized eggs for
262
-------
I concentration "1" is considered significantly greater than the mean
.percent unfertilized eggs for the control if tj is greater than the
'critical value. Therefore, the 10.0, 20.0 and 40.0 ug/L concentrations
have a significantly higher mean percent of unfertilized eggs than the
{control. Hence the NOEC is 5.0 ug/L and the LOEC is 10.0 ug/L.
14.2.4.7 To quantify the sensitivity of the test, the minimum
significant difference (MSD) that can be statistically detected may be
calculated.
MSD = d SWV"
+ U/n)
[Where d = the critical value for the Dunnett's procedure
Sy = the square root of the within mean square
n = the common number of replicates at each concentration
(this assumes equal replication at each concentration
n-j = the number of replicates in the control.
14.2.4.8 In this example,
MSD = 2.50 (0.084) V (1/3) + (1/3)
= 2.50 (0.084H0.817)
= 0.172
14.2.4.9 The MSD (0.172) is in transformed units. To determine the MSD
in terms of percent survival, carry out the following conversion.
1. Subtract the
from the transformed control mean.
0.418 - 0.172 = 0.590
2. Obtain the untransformed values for the control mean and the
difference calculated in 4.10.1.
[Sine (0.418) ]2 = 0.165
,:. [Sine (0.590) ]2 = 0.310
3. The untransformed MSD (MSDU) is determined by subtracting
the untransformed values from 4.10.2.
MSDu = 0.310 - 0.165 = 0.145
J4.2.4.10 Therefore, for this set of data, the minimum difference in
jmean percent of unfertilized eggs between the control and any copper
^concentration that can be detected as statistically significant is 0.145.
14.2.4.11 This represents a
'control.
increase in unfertilized eggs from the
263
-------
(4.2.5 Probit Analysis
j
J4.2.5.1 The data used for the probit analysis is summarized in
gable 11. To perform the Probit Analysis, run the EPA Probit Analysis
Program. An example of the program output is provided in Table 12 and
3. 3.
[4.2.5.2 For this example, the chi-square test for heterogeneity was not
;ignificant. Thus Probit Analysis appears to be appropriate for-this set
Jf data.
TABLE 11. DATA FOR PROBIT ANALYSIS
Control
Copper Concentration (ug/L)
2.5 5.0 10,0 20.0 40.0
lumber Unfertilized
lumber Counted
50
300
83
300
85
300
120
300
181
300
232
300
264
-------
FABLE 12. OUTPUT FROM EPA PROBIT ANALYSIS PROGRAM, VERSION 1.3,
USED FOR CALCULATING EC VALUES
Probit Analysis of Sea Urchin Fertilization Data
Observed Adjusted Predicted
Number Number Proportion Proportion Proportion
Cone. Exposed Resp. Responding Responding Responding
Control
2 5000
:. 5 00 CO
1C . 0000
20 0000
40 0000
300
300
IOC
3C£
300
300
50
83
85
1 20
181
232
0 . 1667
0.2767
0.2833
0. 4000
0 . 6033
0 . 7733
0 0000
0 1085
0 1167
0 2605
5111
7206
0 . 1886
0.0495
0. 1362
0.2926
0- 5025
0.7117
Chi - Square Heterogeneity
5-238
Hu
Sigma =
Para me t er
Ir-tercepi
Elope ., ,
1 . 297567
0 . 545280
Estimate
2 . 62C368
1.813919
Std Err .
0 . 2346! 4 (
0 1 fi 2 1 2 7 (
9 5% Con f i dence
7 16C525 , 3 .
1 . 47 695C , 2 ,
Limits
080210)
190888)
Spontaneous
Response Rate
0.188637
0.020413
0 . 148627
0.228646)
Estimated EC Values and Confidence Limits
Point
Cone .
Lower Upper
95% Confidence Limits
EC 1
EC 5
! EC10
t EC15
EC50
i EC85
| EC90
EC95
EC99
00
00 • .''
00
00
00
00
00
00
00
1
2
3
5
19
72
99
156
368
0693
5156
9695
4006
8412
8947
1742
4945
1740
0
1
.:. 2
3
16
57
75
1 1 1
230
4955
4235
4927
6315
7757
8561
5491
6525
6104
1
3
5
7
23
IOC
145
254
729
8C71
7241
4894
1457
1 322
3032
6703
4105
2836
265
-------
Probi t
10-t
EC01
EC10 EC25 EC50
Figure 3. Plot of adjusted probits and predicted regression line
266
-------
15. PRECISION AND ACCURACY
15.1 PRECISION
15.1.1 Single laboratory precision data for the reference toxicants, copper
(CU) and sodium dodecyl sulfate (SDS) tested in FORTY FATHOMS* artificial
seawater and natural seawater are provided in Tables 13 and 14. The results
were similar in both types of seawater. The precision of the SDS data
(30.6% and 35.7%), expressed as a percent coefficient of variation, was
somewhat better than the CU data (44.5% and 48.0%).
15.1.2 No data are available on the multi-laboratory precision of the test.
15.2 ACCURACY
15.2.1 The accuracy of toxicity tests cannot be determined.
267
-------
[TABLE 13. SINGLE LABORATORY PRECISION OF THE SEA URCHIN (ARBACIA PUNCTULATA)
FERTILIZATION TEST PERFORMED IN FORTY FATHOMS* ARTIFICIAL
SEAWATER, USING GAMETES FROM ADULTS MAINTAINED IN FORTY
FATHOMS^ ARTIFICIAL SEAWATER, OR OBTAINED DIRECTLY FROM
NATURAL SOURCES, AND COPPER (CU) AND SODIUM DODECYL SULFATE
(SDS) AS REFERENCE TOXICANTS^,2,3,4,5
m
m
m
!
m
m
1
i
i
SI
I
P.,
|
2
3
4
5
EC50
(ug/L)
19.1
42.2
27,3
57.8
61.5
14
27
20
47
49
CI
(ug/L)
.9-24.6
.4-56.6
.4-35.3
.2-69.3
.5-77.1
CU
WOEC
(ug/L)
5.0
12.5
< 6.2
6.2
12.5
LOEC
(ug/L)
10.0
25.0
6.2
12.0
25.0
EC50
{mg/L}
1.2
1.9
3.3
2.9
3.0
1
1
2
1
1
CI
(mg/L)
.6-2.4
.4-2.5
.2-4.5
.8-4.0
.9-4.1
SDS
NOEC
(mg/L)
< 0.9
0.9
1.8
0.9
1.8
LOEC
(mg/L)
0,9
1.8
3.6
1.8
3.6
MEAN 41.6 + 44.5%
2.46 + 35.7%
performed by Dennis McMullen, Technical Applications Inc.,
Newtown Facility, Environmental Monitoring and Support Laboratory -
Cincinnati.
2A11 tests were performed using Forty Fathoms^ synthetic seawater.
Copper test solutions were prepared with copper sulfate. Copper
concentrations in Test 1 were: 2.5, 5.0, 10.0, 20.0, and 40.0 ug/L.
Copper concentrations in Tests 2-5 were: 6.25, 12.5, 25.0,
50.Os and 100.0 ug/L.
3SDS concentrations were: 0.9, 1.8, 3.6, 7.2, and 14.4 mg/L.
^Adults collected in the field.
5For a discussion of the precision of data from chronic toxicity
tests see Section 4, Quality Assurance.
268
-------
TABLE 14
SINGLE LABORATORY PRECISION OF THE SEA URCHIN (ARBACIA PUNCTULATA)
FERTILIZATION TEST PERFORMED IN NATURAL SEAWATER, USING GAMETES
FROM ADULTS MAINTAINED IN NATURAL SEAWATER AND COPPER (CU) AND
SODIUM DODECYL SULFATE (SDS) AS REFERENCE
TOXICANTSl,2,3,4,5
i —
I x cu
1
jTest
i
1 ^
i *
i
s
EC50 CI
(ug/L) (ug/L)
17.8 17.
45.7 42.
44,6 41.
25,4 23.
16.0 15.
0-18.8
9-48.6
9-47.3
1-28.0
1-17.1
NOEC
(ug/L)
12.2
12.2
24,4
< 6.1
6.1
LOEC
(ug/L)
24.4
24.4
48.7
6.1
12.2
SDS
EC50 CI
(mg/L) (mg/L)
2.6
4.6
2.7
2.4
2.6
2.5-2.6
4.4-4.8
2.7-2.8
2.3-2.5
2.5-2.6
NOEC
(mg/L)
1.8
1.8
1.8
0.9
1.8
LOEC
(mg/L)
3.6
3.6
3.6
1.8
3.6
Mean 29.9 + 48.
2.98 + 30.
]Tests performed by Ray Walsh and Wendy Greene, Environmental Research
^ Laboratory, U. S. Environmental Protection Agency, Narragansett, Rhode Island.
j2Copper concentrations were: 6.1, 12.2, 24.4, 48.7, and 97.4 ug/L.
|3SDS concentrations were: 0.9, 1.8, 3.6, 7.3, and 14.5 mg/L.
j4Adults collected in the field.
|5For a discussion of the precision of data from chronic toxicity
tests see,Section 4, Quality Assurance.
269
-------
Figure 4. Data sheet for (1) fertilization test using Arbacia punctulata.
•£ST DATE:
SAMPLE:
lOMPLEX EFFLUENT SAMPLE:
COLLECTION DATE:
SALINITY/ADJUSTMENT:
PH/ADJUSTMENT REQUIRED:
PHYSICAL CHARACTERISTICS:
STORAGE:
COMMENTS:
.SINGLE COMPOUND:
SOLVENT (CONC):
TEST CONCENTRATIONS:
DILUTION WATER:
CONTROL WATER:
TEST TEMPERATURE:
TEST SALINITY: _
COMMENTS:
270
-------
Figure 5. Data sheet (2) for fertilization test using Arbacia punctulata
[TEST DATE: '
ISAMPLE:
fSPERM DILUTIONS:
HEMACYTOMETER COUNT, E:
x TO* = SPM SOLUTION E =
SPERM CONCENTRATIONS: SOLUTION E x 40 = SOLUTION A =
SOLUTION E x 20 = SOLUTION B =
SOLUTION E x 5 = SOLUTION C =
SOLUTION SELECTED FOR TEST (
DILUTION: SPM/(5 x 10?) = _
[(DF) x 5) - 5 =
FINAL SPERM COUNTS =
= 5 x 10? SPM}:
DF
+ SW, mL
SPM
SPM
SPM
:EGG DILUTIONS:
INITIAL EGG COUNT =
ORIGINAL EGG STOCK CONCENTRATION = 10X (INITIAL
EGG COUNT)
VOLUME OF SW TO ADD TO DILUTE EGG STOCK TO 20GO/nt:
(EGG COUNT) - 200 =
CONTROL WATER TO ADD EGG STODK, mL =
FINAL EGG COUNT =
ITEST TIMES:
SPERM COLLECTED:
EGGS COLLECTED:
SPERM ADDED:
EGGS ADDED:
FIXATIVE ADDED:
SAMPLES READ:
271
-------
Figure 6. Data sheet (3) for fertilization test using Arbacia punctulata.
DATE TESTED:
I " ™" *" -" «'• • I I I ••••! i.n«il H II I I || • II I .•.., •i,|| , - •
I
'SAMPLE: ; . ;
TOTAL AND UNFERTILIZED EGG COUNT AT END OF TEST:
FEFFLUENT
(%)
REPLICATE VIAL
I
TOTAL-UNFERT
TOTAL-UNFERT
TOTAL-UNFERT
TOTAL-UNFERT
STATISTICAL ANALYSIS:
ANALYSIS OF VARIANCE:
CONTROL:
DIFFERENT FROM CONTROL (P
COMMENTS:
272
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SECTION 16
TEST METHOD^.2
ALGAL (CHAMPIA PARVULA) SEXUAL REPRODUCTION TEST
METHOD 1009
|. SCOPE AND APPLICATION
..1 This method measures the effects of toxic substances in effluents and
-eceiving water on the sexual reproduction of the marine macroalga, Champia
J.arvula. The method consists of exposing male and female plants to test
^Substances for two days, followed by a 5-to 7-day recovery period in control
jmediunj, during which the cystocarps mature.
substance
;1.3 Single or multiple excursions in toxicity may not be detected using 24-h
=compositetsamples. Also, because of the long sample collection period
(involved in composite sampling, highly volatile and highly deqradable
toxicants in the source may not be detected in the test.
1.4 This method should be restricted to use by, or under the supervision of,
professionals experienced in aquatic toxicity testing and algal culturing.
2. SUMMARY OF METHOD
| _ . ..,
|2.1 Sexually mature male and female branches of Champia paryula are exposed
nn astatic system for two days to different concentrations of effluent, or to
receiving water,followed by a 5- to 7-day recovery period in control medium.
line recovery period allows time for the development of cystocarps resulting
pom fertilization during the exposure period. The test results are reported
^s the concentration of the test substance which causes a statistically
;ignificant reduction in the number of cystocarps formed compared to control
)rganisrns •
DEFINITIONS
(Reserved for addition of terms at a later date).
INTERFERENCES
-.1 Toxic substances may be introduced by contaminants in dilution water,
jlassware, sample hardware, and testing equipment (see Section 5, Facilities
md Equipment].
|The format used for this method was taken from Kopp, 1983.
-This method was adapted from Thursby and Steele, 1987, Environmental
esearch Laboratory, U. S. Environmental Protection Agency, Narragansett,
(node Island.
• > ... 273
-------
|5. SAFETY
5.1 See Section 3, Safety and Health.
APPARATUS AND EQUIPMENT
j6.1 Facilities for holding and acclimating test organisms
~t.r (DII or
j6.6 Air pump -- for supplying air.
|6.7 Air lines, and air stones - for aerating cultures. v
6.8 Balance - Analytical, capable of accurately weighing to 0.0001 g
6.9 Reference weights, Class S - for checking performance of balance
,
parameter, a portable, field-grade instrument is acceptable
j6.11 Dissecting (stereoscope) microscope - for counting cystocarps.
j6.12 Compound microscope - for examining the condition of plants.
,6.13 Count register, 2-place - for recording cystocarp counts. ., ,,
incubatin9 exposure
the
274
-------
.15 Drying oven -- to dry glassware.
|5.16 Filtering apparatus -- for use with membrane filters (47mm).
.17 Refractometer -- for determining salinity.
i.T8 Thermometers, glass or electronic, laboratory grade -- for measuring
later temperatures.
..19 Thermometers, bulb-thermograph or electronic-chart type — for
Continuously recording temperature.
lf.20 Thermometer, National Bureau of Standards Certified (see USEPA METHOD
[70.1, USEPA, 1979) -- to calibrate laboratory thermometers.
|.21 Beakers -- Class A, borosilicate glass or non-toxic plasticware, 1000
iL for making test solutions.
.22 Erlenmeyer flasks, 250 ml, or 200 ml disposable polystyrene cups, with
:overs -- for use as exposure chambers.
..23 Bottles -- borosilicate glass or disposable polystyrene cups (200-400
|nL) for use as recovery vessels.
i.24 Wash bottles -- for deionized water, for rinsing small glassware and
finstrurnent electrodes and probes.
.25 Volumetric flasks and graduated cylinders -- Class A, borosilicate
Iglass or non-toxic plastic labware, 10-1000 ml for making test solutions.
..26 Micropipetters, digital, 200 and 1000 uL -- to make dilutions.
JU.27 Pipets, volumetric — Class A, 1-100 ml.
I
|.28 Pipetter, automatic -- adjustable, 1-100 ml.
.29 Pipets, serological -- 1-10 mi_s graduated.
.30 Pipet bulbs and fillers -- PROPIPETR, or equivalent.
;.31 Forceps, fine-point, stainless steel -- for cutting and handling
jranch tips.
REAGENTS AND CONSUMABLE MATERIALS
f.l Mature Champla parvula plants -- see Paragraph 7.14.
.2 Sample containers -- for sample shipment and storage (see Section 8,
Iffluent and Receiving Water Sampling and Sample Handling).
275
-------
J7.3 Petri dishes, polystyrene -- to hold plants for cystocarp counts and to
;cut branch tips. Other suitable containers may be used.
I
|7.4 Disposable tips for micropipetters.
.5 Aluminum foil, foam stoppers, or other closures -- to cover culture and
Itest flasks.
.6 Tape, colored — for labelling test chambers.
.7 Markers, water-proof -- for marking containers, etc.
.8 Data sheets (one set per test) -- for data recording.
.9 Buffers, pH 4, 7, and 10 (or as per instructions of instrument
lanufacturer) for standards and calibration check (see USEPA Method 150.1,
|JSEPA, 1979).
i
[7.10 Laboratory quality assurance samples and standards, for the above
[methods.
p.11 Reference toxicant solutions (see Section 4, Quality Assurance).
17.12 Reagent water — defined as distilled or deionized water that does not
fcontain substances which are toxic to the test organisms (see paragraph 6.5
above).
•7.13 Effluent, surface water, and dilution water -- see Section 7, Dilution
jjWater, and Section 8, Effluent and Surface Water Sampling and Sample
Dandling.
|7.13.1 Saline test and dilution water -- The use of natural seawater is
"recommended for this test. A recipe for the nutrients that roust be added to
;he natural sea water is given in Table 1. The salinity of the test water
lust be 30 °/oo, and vary no more than ± 2 °/oo among the replicates.
|7.13.2 The overwhelming majority of industrial and sewage treatment
feffluents entering marine and estuarine systems contain little or no
^measurable salts. Therefore, exposure of Champia parvula to effluents will
'usually require adjustments in the salinity of the test solutions. Tests
lust be performed with a minimum of 50% natural seawater at each toxicant
:oncentration. It is important to maintain a constant salinity across all
^treatments. The salinity of the effluent can be adjusted by adding brine
>repared from natural seawater (100 °/oo), concentrated (triple strength)
|salt solution (GP-2 described in Table 2), or dry GP-2 salts (Table 2), to
the effluent to provide a salinity of 30 °/oo. Control solutions should
prepared with the same percentage of natural seawater and at the same
salinity (using deionized water adjusted with dry salts, or brine) as used
|for the effluent dilutions.
I/.13.3 Artificial seawater -- The preparation of artificial seawater (GP-2)
s described in Table 2.
276
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7.14 CHAMPIA PARVULA CULTURES
7.14.1 Mature plants (Figure 1) are available from the Environmental
Research Laboratory, U. S. Environmental Protection Agency, South Ferry
Road, Narragansett, Rhode Island, 02882 (401-782-3000).
tetraaporongio
spermatia
fertilization
TETRASPOROPHYTE
—cystocarp
'igure 1. Life history of Champia parvula. Upper left: Size and degree of
Branching in female branch tips used for toxicity tests. From Thursby and
|5teeie, 1987.
277
-------
The adult plant body (thallus} is hollow, septate, and highly branched. New
cultures can be propagated asexually from excised branches, making it possible
to maintain clonal material indefinitely.
7.14.1.1 Stock cultures of both male and female plants are maintained in
separate, aerated, 1-L Erlenmeyer flasks, or equivalent, containing 800 ml of
culture medium. Several cultures of both males and females are maintained
simultaneously to keep a constant supply of plant material available. New
cultures should be started weekly, so that plants are available in different
stages of development (i.e., with different amounts of tissue per flasks). The
^total number of cultures maintained will depend on the expected frequency of
^testing.
p.14.1.2 Prior to use in toxicity tests, stock cultures should be examined to
^determine their condition. Females can be checked by examining a few branch
[rips under a compound microscope {100 X or greater). Several trichogynes
(reproductive hairs to which the spermatia attach) should be easily seen near
fthe apex {Figure 2).
sterile heirs
— trichogynes
1 mm
Figure 2. Apex of branch of female plants showing sterile hairs and
reproductive hairs (trichogynes). Sterile hairs are wider and generally much
longer than trichogynes, and appear hollow except at the tip. Both types of
hairs occur on the entire circumference of the thallus, but are seen easiest at
the "edges." Receptive trichogynes occur only near the branch tips. From
Thursby and Steele, 1987.
278
-------
7.14.1.3 Male plants should be visibly producing spermatic. This can be
checked by placing some male tissue in a petri dish, holding it against a
dark background and looking for the presence of spermatial sori. Mature
sori can also be easily identified by looking along the edge of the thallus
under a compound microscope (Figures 3 and 4).
1 cm
^•spermotial
sorus
Figure 3. A portion of the male thallus showing spermatial sori. The
•sorus areas are generally slightly thicker and somewhat lighter in color.
From Thursby and Steele, 1987.
•cuticle
thailus surface
Figure 4.
A magnified portion of a spermatial sorus. Note the rows of
cells that protrude from the thallus surface. From Thursby and
Steele, 1987.
279
-------
|f 'SlfflH
17.14.1.4 A final, quick way to determine the relative "health" of the maff|
'.stock culture is to place a portion of a female plant into some of the water
from the male culture for a few seconds. Under a compound microscope
numerous spermatia should be seen attached to both the sterile hairs and the
trichogynes (Figure 5).
'igure 5. Apex of a branch on a mature female plant that was exposed to
[spermatia from a male plant. The sterile hairs and trichogynes are covered
[with spermatia. Note that few or no spermatia attached to the older hairs
[(those more than 1 mm from the apex). From Thursby and Steele, 1987.
.14.2 Culture medium prepared from natural seawater is preferred
l(Table 1). However, as much as 50% of the natural seawater may be replaced
the artificial seawater (GP-2) described in Table 2.
.14.2.1 The seawater is autoclaved for 20 min at 15 psi. The culture
Tasks are capped with aluminum foil and autoclaved dry, for 10 min.
;ulture medium is made up by dispensing seawater into sterile flasks and
idding the appropriate nutrients from a sterile stock solution.
'.14.2.2 Alternately, 1-L flasks containing seawater can be autoclaved.
iterilization is used to prevent microalgal contamination, and not to keep
:ultures bacteria free.
SAMPLE COLLECTION, PRESERVATION AND HANDLING
U See Section 8, Effluent and Receiving water Sampling and Sample Handling
CALIBRATION AND STANDARDIZATION
[9.1 See Section 4, Quality Assurance. :
I ''••',.
110. QUALITY CONTROL
|10.1 See Section 4, Quality Assurance.
280
-------
TABLE 1. NUTRIENTS TO BE ADDED TO NATURAL SEAWATER AND TO ARTIFICIAL
' SEAWATER (GP-2) DESCRIBED-IN TABLE 2. THE CONCENTRATED NUTRIENT
STOCK SOLUTION IS AUTOCLAVED FOR 15 MIN (VITAMINS ARE
AUTOCLAVED SEPARATELY FOR 2 MIN AND ADDED AFTER THE NUTRIENT
STOCK SOLUTION IS AUTOCLAVED). THE PH OF THE SOLUTION IS
ADJUSTED TO APPROXIMATELY PH 2 BEFORE AUTOCLAVING TO MINIMIZE
THE POSSIBILITY OF PRECIPITATION.
Amount of Reagent Per Liter of Concentrated
Nutrient Stock Solution
Stock Solution For
Culture Medium
Stock Solution For
Test Medium
Nutrient Stock Solution^
Sodium Nitrate
(NaN03)
Sodium Phosphate
(NaH2P04- H20
Na2EDTA - 2 H20
Sodium Citrate
6.35 g
0.64 g
133 mg
51 mg
1.58 g
0.16 g
12,8 mg
Iron2
Vitamins3
Udd 10 ml of appropriate nutrient stock solution per liter of culture or
test medium.
,2A stock solution of iron is made that contains 1 mg iron/mL. Ferrous or
ferric chloride can be used. Add 9.75 mL of the iron stock solution to each
liter of culture medium and 2.4 mL to each liter of test medium.
|,3A vitamin stock solution is made by dissolving 4.88. g thiamine HC1,
2,5 mg biotin, and 2.5 mg B12 in 500 mL deionized water. Adjust to
approximately pH 4 before autoclaving 2 min. It is convenient to
subdivide the vitamin stock into 10 mL volumes in test tubes prior to
autoclaving. Add 10 ml of the vitamin stock solution to each liter of culture
medium and 2.5 mL to each liter of test medium.
281
-------
TABLE 2.
SALTS USED IN THE PREPARATION OF GP-2 ARTIFICIAL SEAWATER
S ALSEAWATER
Compound
Concentration (g/L)
21.03
3.52
0.6]
0.088
0.034
9.50
1.32
0.02
0.17
iThe original formulation calls for autoclaving anhydrous and hydrated
salts separately to avoid precipitation. However, if the sodium
SKV8 ?"toc1a^d separately (dry), all of the other salts can be
is nSJ cHt5S? Kr'a«]nC%n; n*Utn'ent? are ddded unt11 needed> autoclaving
IL \•* ? °r effluent testing. To minimize microalgal contamination
the artificial seawater should be autoclaved when used for stock culture
f°r * ^ ]° " and ™
I NaCI
I-
1 Na2S04
1 KC1
1 KBr
I Na2B407
HgCl2 •
f CaCl2 -
SrCl2 •
NaHC03
— • • — — • — -
• 10 H20
6 H20
2 H20
6 H20
,2Prepare in 10-L to 20-L batches.
J3A stock solution of 68 mg/ml sodium bicarbonate is prepared by autoclaving
lar^Ht^nf0^' 3nd ohcn ,disS°1Jn'ng n 1n sterile ^Ionized water. For
each liter of GP-2, use 2.5 ml of this stock solution.
prom Spotte, et al., 1984.
Affluent salinity adjustment to 30 o/00 can be made by adding the
5 appropriate amount of dry salts from this formulation, by using a
™npirstre??th br1ne PrePared from this formulation, or by using a
100 o/oo salinity brine prepared from natural seawater.
'Nutrients listed in Table 1 should be added to the artificial seawater in
the same concentration described for natural seawater.
282
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11. TEST PROCEDURES
11.1 TEST SOLUTIONS
11.1.1 Surface Waters
collected.
11.1.2 Effluents
tOXlC1'ty 1S determined witb samples used directly as
t«t °f th! re(lul>eillent t° use a minimum of 50% natural seawater
test solutions, the concentration of effluent used in this test if
" ^ ' " eved
nf th + 3! thn eff]uent test concentrations should be based on
0.5, is conmonlv u ed Tdi1u?L f^ d11Jt1on faCt°rS' Wox1n,ately 0.3 or
betwPPn Rni ann i* fJii dilution factor of approximately 0.3 allows testing
II 9* ,nH ni«\ e;;|uent using only five effluent concentrations (50%, 17«,
6%, 2%, and 0.7%). This series of dilutions minimizes the level of effort
tP but it is not critical for the recovery
"? U1"? seawater ^all'ty can vary among laboratories, a more
nt medfUm (e'9' + EDTA) m* result in "«ter growth and
therefore faster cystocarp development) during the recovery period.
11.2 PREPARATION OF PLANTS FOR TEST
11.2.1 Once cultures are determined to be usable for toxicity testina (have
trie ogynes, and sori with spermatia), plant cuttings shoud be prepared for
jthe test, using a fine-point forceps, with the plants in a littleP seawater in
283
-------
a petri dish. For female plants, five cuttings, severed 7-to-10 mm from the
ends of the branch, should be prepared for each treatment chamber. Try to
be consistent in the number of branch tips on each cutting. For male
plants, one cutting, severed 1.5-to-2 cm from the end of the branch, is
prepared for each test chamber. Prepare the female cuttings first, to
minimize the chances of contaminating them with water containing spermatia
from the male stock cultures.
11.3. STAKT OF TEST
11.3.1 The test should begin as soon as possible, preferably within 24 h of
sample collection. If the persistence of the sample toxicity is not known,
the maximum holding time (time elapsed from the removal of the sample from
the sampling device) should not exceed 36 h. In no case should the test be,
started more than 72 h after sample collection. Just prior to testing, thMi
temperature of the sample should be adjusted to that of the test '";
(23 + 1°C) and maintained at that temperature until portions are added
to the dilution water.
11.3.2 Set up and label four test chambers (minimum of three) per treatment
and controls.
11.3.3 Fill the test chambers with 100 mL of control or treatment water
(28-to-32 o/oo). For reference toxicant tests, all test chambers can be
filled with control water and the toxicant added with a pipet. For toxicant
volumes exceeding 1 mL, adjust the amount of dilution water to give a final
volume of 100 mL.
11.3.4 Add five female branches and one male branch to each test chamber.
The toxicant must be present before the male plant is
11.3.5 Place the test chambers under cool-white light (approx.
100 uE/m2/s, or 500 ft-c), with a photoperiod of 16 h light and 8 h
darkness. Maintain the temperature between 22 and 24°C. Check the
temperature by placing a laboratory or recording thermometer in a flask of
water among the test chambers. Record the temperature daily.
11.3.6 Gently hand-swirl the chambers twice a day, or shake continuously at
100 rpm on a rotary shaker.
11.3.7 If desired, the media can be changed after 24 h.
11.4 TRANSFER OF PLANTS TO CONTROL WATER AFTER 48 H
11.4.1 Label the recovery vessels. These vessels can be almost any type of
container or flask containing 100 to 200 mL of seawater and nutrients (see
Tables 1 and 2). Smaller volumes can be used, but should be checked to make
sure that adequate growth will occur without having to change the medium.
284
-------
11.4.2 With forceps, gently remove the female branches from test chambers
and place into recovery bottles. Add aeration tubes and foam stoppers.
11.4.3 Place the vessels under cool-white light (at the same irradiance as
the stock cultures) and aerate for the 5- to 7-day recovery period. If a
shaker is used, do not aerate the solutions (this will enhance the water
motion).
11.5 TERMINATION OF THE TEST .
11.5.1 At the end of the recovery period, count the number of cystocarps
{Figs. 6, 7, and 8) per female and record the data (Figure 12). Cystocarps
may be counted by placing females between the inverted halves of a a
polystyrene petri dish or other suitable containers with a small amount <|f
seawater (to hold the entire plant in one focal plane). Cystocarps can be
easily counted under a stereomicroscope, and are distinguished from young;
branches, because they possess an apical opening for spore release (ostiole)
and darkly pigmented spores.
11.5.2 One advantage of this test procedure is that if there is uncertainty
about the identification of an immature cystocarp, it is only necessary to
aerate the plants a little longer in the recovery bottles. Within 24 to
48 h, the presumed cystocarp will either look more like a mature cystocarp
or a young branch, or will have changed very little, if at all (i.e., an
aborted cystocarp). No new cystocarps will form since the males have been
removed, and the plants will only get larger. Occasionally, cystocarps will
abort, and these should not be included in the counts. Aborted cystocarps
are easily identified by their dark pigmentation and, often, by the
formation of a new branch at the apex.
12. SUMMARY OF TEST CONDITIONS
12.1 A summary of test conditions is listed in Table 3.
13. ACCEPTABILITY OF TEST RESULTS
13.1 A test is not acceptable if the control mortality exceeds 20%.
(Generally there is no control mortality.) ..
13.2 If plants fragment in the controls or lower exposure concentrations,
it may be an indication that they are under stress.
13.3 Control plants should average 10 or more cystocarps.
285
-------
ostiole
-spores
1mm
Figure 6. A mature cystocarp. In the controls and lower effluent
concentrations, cystocarps often occur in clusters of 10 or 12. From Thursby
and Steele, 1987.
young branch
cells
immature
cystocarp
Figure 7. Comparison of a very young branch and an immature cystocarp. Both
can have sterile tiairs* Trichogynes might or might not be present on a young
branch, but are never present on an immature cystocarp. Young branches are
more pointed at the apex and are made up of larger cells than immature
cystocarps, and never have ostioles. From Thursby and Steele, 1987.
1mm
Figure 8. An aborted cystocarp. A new branch will eventually develop at the
apex. From Thursby and Steele, 1987.
OQC
-------
TABLE 3. SUMMARY OF RECOMMENDED TEST CONDITIONS FOR
CHAMPIA PARVULA SEXUAL REPRODUCTION TEST
1. Test type:
2. Salinity:
3. Temperature:
4. Photoperiod:
5. Light intensity:
6. Light source:
7. Test chamber:
8. Test solution volume
9. Dilution water:
10. Dilution factor:
11. Number of Dilutions
12. Number of replicate Chambers
per treatment:
13. Number of organisms
per test chamber:
14. Test duration:
15. Effects measured:
Static, non-renewal
30 o/oo + 2 o/oo
22 - 24°C
16 h light, 8 h dark
100 uE/m2/s (500 ft-c)
Cool-white fluorescent lights
200 mL polystyrene cups, or
250 mL Erlenmeyer flasks
100 mL
30 °/oo salinity natural seawater,
or a combination of 50% 30 °/oo
salinity natural seawater and 50%
30 o/oo salinity artificial seawater
Approximately 0.3 or 0.5
At least 5 and a control
4 (minimum of 3)
5 female branch tips and
1 male plant
2-day exposure to efflent,
followed by 5- to 7-day recovery
period in control medium for
cystocarp development
Reduction in cystocarp production
compared to controls
-------
14. DATA ANALYSIS
14.1 GENERAL
14.1.1 Tabulate and summarize the data.
Is listed in Table 4.
A sample set of reproduction data
14.1.2 The end points of the Champia parvula toxicity test are based on the
adverse effects on sexual reproduction. Statistically significant
differences in the mean number of cystocarps, yielding NOEC and LOEC end
points, are determined in most cases by a hypothesis test such as Dunnett's
Procedure (Dunnett, 1955) or Steel's Many-one Rank Test (Steel, 1959;
Miller, 1981). : ,;
14.1.3 Formal statistical analysis of the data is outlined in Figure 9.
Concentrations that have exhibited no sexual reproduction (less than 5% of
controls) are excluded from the statistical treatment of the test data for
calculation of the NOEC and LOEC by Dunnett's Procedure or Steel's Many-one
Rank Test. The response used in the statistical tests is the mean number of
cystocarps.
14.1.4 When equal numbers of replicates occur across all concentrations and
the control, the statistical analysis consists of a parametric test,
Dunnett's Procedure, and a non-parametric test, Steel's Many-one Rank Test.
The underlying assumptions of the Dunnett's Procedure, normality and
homogeneity of variance, are formally tested. The test for normality is the
Shapiro-Wilks Test and Bartlett's Test is used to test for homogeneity of
variance. Tests for normality and homogeneity of variance are included in
Appendix B. If either of these tests fail, the non-parametric test, Steel's
Many-one Rank Test, is used to determine the NOEC and LOEC end points. If
the assumptions of Dunnett's Procedure are met, the end points are
determined by the parametric test.
14.1.5 Additionally, if unequal numbers of replicates occur among the
concentration levels tested there are parametric and non-parametric
alternative analyses. The parametric analysis is the Bonferroni t-test. The
Wilcoxon Rank Sum Test with the Bonferroni adjustment is the non-parametric
alternative. For detailed information on the Bonferroni adjustment, se.e
Appendix D.
14.1.6 The statistical tests described here must be used with a knowledge
of the assumptions upon which the tests are contingent. The assistance of a
statistician is recommended for analysts who are not proficient in
statistics.
288
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TABLE 4. DATA FROM CHAMPIA PARVULA EFFLUENT TOXICITY TEST,
CYSTOCARP COUNTS FOR INDIVIDUAL PLANTS AND MEAN
COUNT PER TEST CHAMBER FOR EACH EFFLUENT
CONCENTRATION 1
Effluent
Concentration
(%)
Control
0.8%
1.3%
2.2%
3.6%
6.0%
10.0%
i
Replicate
Test
Chamber
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
Plant
1
19
19
17
10
12
12
10
6
4
1
7
3
Z
3
0
1
1
0
0
1
2
2
20
12
25
16
10
9
0
4
4
2
9
2
1
4
4
0
2
4
0
0
1
3
24
21
18
11
6
9
3
4
2
5
9
2
1
6
3
0
1
3
0
0
0
4
7
11
20
12
9
13
5
8
6
4
4
0
5
4
1
0
0
1
0
0
0
5
18
23
16
11
10
8
4
4
4
0
6
0
0
2
3
0
0
3
_
0
0
Mean
Cystocarp
Count
17.60
17.20
19.20
12.00
9.40
10.20
4.40
5.20
4.00
2.40
7.00
1.40
1.80
3.80
2.20
0.20
0.80
2.20
0.00
0.20
0.60
bata provided by the Environmental Research Laboratory, U. S. Environmental
Protection Agency, Narragansett, Rhode Island.
289,.
-------
14.2 EXAMPLE OF ANALYSIS OF CHAMPIA REPRODUCTION DATA
14.2.1 In this example, the data, mean and standard deviation of the
observations at each concentration including the control are listed in Table
5. The data are plotted in Figure 10. As can be seen from the data in the
table, mean reproduction per chamber in the 10% effluent concentration is less
than 5% of the control. Therefore the 10% effluent concentration is not
included in the subsequent analysis.
TABLE 5. CHAMP IA PARVULA SEXUAL REPRODUCTION DATA
Effluent Concentration (%)
Replicate Control
0.8
1.3 2.2
3.6
6.0 ' 10
A
B
C
Mean(Yi)
Si2
i
17
17
19
18
1
1
.60
.20
.20
.12
12
9
10
10
1
2
.00
.40
.20
.53
.77
4.40
5.20
4.00
4.53
0.37
3
2.40
7.00
1.40
3.60
8.92
4
1.80
3.80
2.20
2.60
1.12
5
0.
0.
2.
1.
1.
6
20
80
20
07
05
0.00
0.20
0.60
0.27
0.09
7
14.2.2 Test for Normality
14.2.2.1 The first step of the test for normality is to center the
observations fay subtracting the mean of all the observations within a
concentration from each observation in that concentration. The centered
observations are summarized in Table 6.
TABLE 6. CENTERED OBSERVATIONS FOR SHAPIRO-WILKS EXAMPLE
Replicate Control
Effluent Concentration^)
0.8
1.3
2.2
3.6
6.0
A -0
B -0
C 1
.40
.80
,20
1.
-1.
-0.
47
13
33
-0
0
-0
.13
.67
.53
-1
3
-2
.20
.40
.20
-0
1
-0
.80
.20
.40
-0
-0
1
.87
.27
.13
-------
STATISTICAL ANALYSIS OF CHAMPIA PARVULA SEXUAL
REPRODUCTION TEST
REPRODUCTION DATA
MEAN CYSTOCARP COUNT
SHAPIRO-WILKS TEST
NON-NORMAL DISTRIBUTION
NORMAL DISTRIBUTION
HOMOGENEOUS VARIANCE
NO
BARTLETT'S TEST
HETEROGENEOUS
VARIANCE
EQUAL NUMBER OF
REPLICATES?
EQUAL NUMBER OF
REPLICATES?
YES
YES
T-TEST WITH
BONFERRONI
ADJUSTMENT
DUNNETT'S
TEST
•
STEEL'S MANY-ONE
RANK TEST
WILCOXON RANK SUM
TEST WITH
BONFERRONI ADJUSTMENT
ENDPOINT ESTIMATES
NOEC. LOEC
Figure 9. Flow chart for statistical analysis of Champla parvula data,
-------
l/JED
Ziu
o
o
o
(O
en
-------
14.2.2,2 Calculate the denominator, D9 of the test statistic
"•."•-,--• n
D -
_
i - x)2
Where Xj = the ith centered observation
X = the overall mean of the centered observations
n = the total number of centered observations.
n s 18
X = 1 (0.01) - 0.0006
For this set of data,
D - 28.7201
14.2.2.3 Order the centered observations from smallest to largest
Where xH) is the ith ordered observation. These ordered observations
are listed in Table 7.
TABLE 7. ORDERED CENTERED OBSERVATIONS FOR SHAPIRO-WILKS EXAMPLE
i
1
2
3
4
5
6
7
8
9
x(D
-2.20
-1.20
-1.13
-0.87
-0.80
-0.80
-0.53
-0.40
-0.40
i
10
11
12
13
14
15
16
17
18
;;- x(D
-0.33
-0.27
-0.13
0.67
1.13
1.20
1.20
1.47
3.40
14.2.2.4 From Table 4, Appendix B, for the number of observations, n,
obtain the coefficients a], a2, ..., ak where k is approximately
n/2. For the data in this example, n = 18, k = 9. The a, values are
listed in Table 8.
-------
14.2.2.5 Compute the test statistic, W, as follows:
i k
W = ~ [ I ai (xfn
the differences x(n-
of data,
w =
are listed in Table 8. For this set
(5-U25)2 = °-921
TABLE 8. COEFFICIENTS AND DIFFERENCES FOR SHAPIRO-WILKS EXAMPLE
1
2
3
4
5
6
7
8
9
0.4886
0.3253
0.2553
0.2027
0.1587
0.1197
0.0837
0.0496
0.0163
5.60
2.67
2.33
2.07
1.93
1.47
0.40
0.13
0.07
XH8)
X
-------
$2 =
i Sj2)
In = loge
1 = 1, 2, ..., p where p is the number of concentrations
including the control
rij = the number of replicates for concentration i.
14.2.3.2 For the data in this example (See Table 5) all effluent
same number of replicates
14.2,3.3 Bartlett's statistic is therefore:
B = [U2Mn(2.39l7J - 2 £ ln(S1)2]/K1944
= [12(0.8720) - 2(ln(1.12)+ln(1.77)+...+ln(1.05))]/1.1944
= (10.4640 - 4.0809)71.1944
= 5.34
14.2.3.4 B is approximately distributed as chi-square with p - 1 deqrees
of freedom, when the variances are in fact the same. Therefore, the
appropriate critical value for this test, at a significance level of 0.01
with five degrees of freedom, is 15.09. Since B = 5.34 is less than the
critical value of 15.09, conclude that the variances are not different
14.2.4 Dunnett's Procedure
14.2.4.1 Calculations
To obtain an estimate of the pooled variance for the Dunnett's Procedure
construct an ANOVA table as described In Table 9. rroceaure,
-------
TABLE 9. ANOVA TABLE
Source
Total
df
Sum of Squares
(SS)
N - 1
SST
Mean Square(MS)
(SS/df)
HH
HB
Hra Between
H Within
BK
P
N
- 1
- P
SSB
SSW
2
SB =
2
SW =
SSB/(p -
SSW/(N -
1)
P) ;
m
Hi Where:
B9H
H
m
p
N
n-i
= number effluent concentrations including the control.
= total number of observations n-| + n2 ... +np.
= number of observations in concentration i.
P
SSB = Z
Between Sum of Squares
n-f
SST = I I Yt12 - Q2/N
i • •> "
1=1 J=1
SSW = SST - SSB
Total Sum of Squares
Within Sum of Squares
G = the grand total of all sample observations, G = Z T-f
i = l
Tj = the total of the replicate measurements for
concentration "i"
Yjj = the jth observation for concentration "i" (represents
the mean (across plants) number of cystocarps for
effluent concentration i in test chamber j)
14.2.4.2 For the data in this example:
"1
N
T]
T2
TS
T4
T5
T6
G
= n2 = n3 = r
= 18
= Y]] + Yi2 -i
= Y2] + Y22 i
- Y31 + Y32 H
= Y4i + Y42 H
= YSI + Ys2 H
s Y61 + Ye2 H
= T-j + T2 + 1
14 = ns = ng =
^ Y13
•• Y23
^ Y33
•• Y43
»• Y53
^ Y63
[3 + 1
= 17
= 12
= 4
— 0
= 1
= 0
r^ +
*
.
*
*
•
•
6 +
0 +
4 +
4 +
8 +
2 -*•
"7
17
9
5
7
3
0
=
.2
.4
.2
.0
.8
.8
1"5 + ^6 =
3
+ 19.
+ 10.
+ 4.
+ 1.
+ 2.
+ 2.
121.0
2
2
0
4
2
2
= 54
= 31
= 13
= 10
— 7
= 3
.6
.6
.8
.8
.2
296
-------
SSB = £ Tj2/ni - G2/N
i = l
= J_ (4287.24) - (121.0)2 = 515.59
3 18
P ni
SST = I I
1=1 =l
- Q2/N
= 1457.8 - (121.0)2 = 644.41
18
SSW = SST - SSB = 644.41 - 615.69 = 28,72
= SSB/p-1 = 615.69/6-1 = 123.14
* = SSW/N-p = 28.72/18-6 = 2.39
14.2.4.3 Summarize these calculations in the ANOVA table (Table 10).
TABLE 10. ANOVA TABLE FOR DUNNETT'S PROCEDURE EXAMPLE
Source
Between
Within
Total
df
5
12
17
Sum of Squares
(SS)
615.69
28.72
644.41
Mean Square(MS)
(SS/df)
123.14
2.39
14,2.4.4 To perform the individual comparisons, calculate the t
statistic for each concentration, and control combination as follows:
SwvMl/ni) + HAM)
Where Yi = mean number of cystocarps for effluent concentration i
YI = mean number of cystocarps for the control
$W = square root of within mean sqaure
ni = number of replicates for control
n-j = number of replicates for concentration i.
297
-------
14.2,4.5 Table 11 Includes the calculated t values for each
concentration and control combination. In this example, comparing the
0.8% concentration with the control the calculation is as follows:
( 18 - 10.53 )
t2 =
-5.90
[ 1.55 V (1/3) f (1/3) ]
TABLE 11. CALCULATED T-VALUES
Effluent Concentration^)
0.8
1.3
2.2
3.6
6.0
2
3
4
5
6
5.90
0.64
1.38
2.17
3.38
14.2.4.6 Since the purpose of this test is to detect a significant
reduction in cystocarp production, a (one-sided) test is appropriate.
The critical value for this one-sided test is found in Table 5,
Appendix E. For an overall alpha level of 0.05, 12 degrees of freedom
for error and five concentrations (excluding the control) the critical
value is 2.50. Mean cystocarp production for concentration "i" is
considered significantly less than mean cystocarp production for the
control if t^ is greater than the critical value. Therefore, all
effluent concentrations in this example have significantly lower
cystocarp production than the control. Hence the NQEC is Q% and the LOEC
is 0.8%.
14.2.4.7 To quantify the sensitivity of the test, the minimum
significant difference (MSU) that can be statistically detected may be
calculated.
MSD 7 d. SWv/ (1/ni) +
Where d = the critical value for the Dunnett's procedure
Sy = the square root of the wjthin mean square
n = the common number of replicates at each concentration
(this assumes equal replication at each concentration
n-j = the number of replicates in the control.
14.2.4.8 In this example,
MSD - 2.50
= 2.50
= 3.16
(1.55)
(1.55
(1/3) +
.8165)
(1/3)
298
-------
14.2.4.9 Therefore, for this set of data, the minimum difference that
can be detected as statistically significant is 3.16 cystocarps.
14.2.4.10 This represents a 17.6% reduction in cystocarp production from
the control.
15. PRECISION AND ACCURACY
15.1 PRECISION
15.1.1 The single laboratory precision data from six tests with copper
sulfate (CU) and six tests with sodium dodecyl sulfate (SDS) are listed
;in Table 12. The NOECs with CU differed by only one concentration
interval (factor of two), showing good precision. The precision of the
first four tests with SDS was somewhat obscured by the choice of toxicant
concentrations, but appeared similar to that of CU in the last two tests.
15.1.1 The multilaboratory precision of the test has not yet been
determined.
15.2 ACCURACY
15.2.1 The accuracy of toxicity tests cannot be determined.
299
-------
TABLE 12. SINGLE LABORATORY PRECISION OF THE CHAMP IA PARVULA
REPRODUCTION TEST PERFORMED IN A 50/50 MIXTURE OF NATURAL
SEAWATER AND GP-2 ARTIFICIAL SEAWATER, USING GAMETES FROM
ADULTS CULTURED IN NATURAL SEAWATER. THE REFERENCE
TOXICANTS USED WERE COPPER (CU) AND SODIUM DODECYL
SULFATE (505)1,2,3,4
CU
Test
1
2
3
4
5
6
NOEC
(ug/L)
1.0
1.0
1.0
1.0
0.5
0.-5
LOEC
(ug/L)
2.5
2.5
2.5
2.5
1.0
1.0
SDS
NOEC
(mg/L)
< 0.8
0.48
< 0.48
< 0.48
0.26
0.09
LOEC
(mg/L)
0.8
0.8
0.48
0.48
0.43
0.16
^Tests performed by Glen Thursby and Mark Tagliabue, Environmental
Research Laboratory, U, S. Environmental Protection Agency,
Narragansett, Rhode Island. Tests were conducted at a temperature
of 22°C, in 50/50 GP2 and natural seawater at a salinity of
300/00.
2Copper concentrations were: 0.5, 1.0, 2.5, 5.0, 7.5, and
lO.O.ug/L.
3SDS concentrations for Test 1 were: 0.8, 1.3, 2.2, 3.6, 6.0, and
10.0 mg/L. SDS concentrations for Tests 2, 3, and 4 were: 0.48,
0.8, 1.3, 2.2, 3.6, and 6.0 mg/L. SDS concentrations for Tests 5
and 6 were: 0.09, 0.16, 2.26, 0.43, 0.72, and 1.2 mg/L.
| 4For a discussion of the precision of data from chronic toxicity
tests see Section 4, Quality Assurance.
300
-------
'I?-1
Figure 11. Data sheet for Champia parvula sexual reproduction test,
Receiving water summary sheet.
SITE
COLLECTION DATE '•
TEST DATE
LOCATION
INITIAL
SALINITY
FINAL
SALINITY
SOURCE OF SALTS FOR
SALINITY ADJUSTMENT*
Ve. natural seawater, GP2 brine, GP2 salts, etc.
(include some indication of amount)
COMMENTS:
LFrom Thursby and Steele, 1987.
301
-------
Figure 12. Data sheet for Champla parvula sexual reproduction test
Cystocarp data sheet.
COLLECTION DATE
EXPOSURE BEGAN (date)
RECOVERY BEGAN (date)_
COUNTED (date)
EFFLUENT OR TOXICANT
TREATMENTS (% EFFLUENT, ^G/L, or REC. WATER SITES)
888
•
BHBI
•
•
1
i
0
1
I
I
I
IS
B9E
H
| REPLICATES
A 1
2
3
4
MEAN
;
B 1
2
3
4
MEAN
CONTROL
I ' • "• ~
C 1
2
3
4
MEAN
OVERALL
MEAN
Temperature
Salinity
Light
^Source of Dilution Water
f 5e
|rom Thursby and Steele, 1987
302
-------
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«:
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318
-------
APPENDIX
filA Independence, Randomization and Outliers . 320
|||B. Validating Normality and Homogeneity of Variance
''*"" Assumptions , 323
1. Introduction 323
2. Test for Normal Distribution of Data 323
3, Test for Homogeneity of Variance 331
4. Transformations of Data 332
|C. Dunnett's Procedure 335
1, Manual Calculations 335
2. Computer Calculations 342
ip D. Bonferroni's T-test 381
ffTI
I IE. Steel's Many-one Rank Test 337-
U|F. Wilcoxon Rank Sum Test . qq?
ji^|||s ••«••«••«««.**••...,, •jjc.
Probit Analysis . 393
319
-------
APPENDIX A
INDEPENDENCE, RANDOMIZATION, AND OUTLIERS?
tl. STATISTICAL INDEPENDENCE
p.l Dunnett's Procedure and Bonferroni's T-test are parametric procedures
fbased on the assumptions that (1) the observations within treatments are
[independent and normally distributed, and (2) that the variance of the
observations is homogeneous across all toxicant concentrations and the
tontrol. Of the three possible departures from the assumptions,
fnon-normality, heterogeneity of variance, and lack of independence, those
paused by lack of independence are the most difficult to deal with (see
iScheffe, 1959). For toxicity data, statistical independence means that
fgiven knowledge of the true mean for a given concentration or control,
fknowledge of the error in any one actual observation whould provide no
^informtion about the error in any other observation. Lack of independence
n's difficult to assess and difficult to test for statistically. It may also
Ihave serious effects on the true alpha or beta level. Therefore, it is of
jutmost importance to be aware of the need for statistical independence
|between observations and to be constantly vigilant in avoiding any patterned
jexperimental procedure that might compromise independence. One of the best
[ways to help insure independence is to follow proper randomization
procedures throughout the test.
2. RANDOMIZATION
|2.1 Randomization of the distribution of test organisms among test vessels,
[and the arrangement of treatments and replicate vessels is an important part
of conducting a valid test. The purpose of randomization is to avoid
situations where test organisms are placed serially into test vessels, or
jWhere all replicates for a test concentration are located adjacent to one
.another, which could introduce bias into the test results.
;2.2 An example of randomization is described using the Sheepshead Minnow
larval Survival and Growth test. For a test design with five treatments, a
[control, and three replicates at each treatment, there would be 18
^experimental units, i.e., 18 positions to be randomized. There are several
sways to randomly assign the positions. Random numbers may be selected from
random numbers table or generated by computer software.
12.3 In this example, the first three random numbers selected would be used
por the three control replicates. The selction of random numbers would be
^continued, three at a time, and assigned to a particular treatment,
^progressing from the lowest to the highest test concentration. The rank
[ordering of these random numbers would determine the relative positioning
jfor the controls and concentration levels.
^Prepared by Ron Freyberg, Florence Kessler, John Menkedick and Larry
.Wymer, Computer Sciences Corporation, 26 W. Martin Luther King Drive,
Cincinnati, Ohio 45268; Phone 513-569-7968.
320
-------
2.4 The result of this randomization procedure is presented in Table A.I,
using an effluent concentration series of 1.0%, 3.2%, 10.0%, 32.0%, and
100%.
TABLE A.I. RANDOMIZATION OF THE POSITIONS OF EXPERIMENTAL UNITS USING A
DESIGN OF THREE ROWS AND SIX COLUMNS
|H 3.2%
BiQii
Hi 32.0%
Hf i>o%
mm
32.0%
10.0%
Control
3.2%
Control
10.0%
1.0%
3.2%
32.0%
100%
Control
100%
10.0%
1.0%
100%
3. OUTLIERS
3.1 An outlier is an inconsistent or questionable data point that
appears unrepresentative of the general trend exhibited by the majority
of the data. Outliers may be detected by tabulation of the data,
plotting, and by an analysis of the residuals. An explanation should be
sought for any questionable data points. Without an explanation, data
points should be discarded only with extreme caution. If there is no
explanation, the analysis should be performed both with and without the
outlier, and the results of both analyses should be reported.
3.2 Gentleman Wilks1 A statistic gives a test for the condition that the
extreme observation may be considered an outlier. For a discussion of
this, and other techniques for evaluating outliers, see Draper and John
(1981).
321
-------
TABLE A.2. TABLE OF RANDOM NUMBERS?
09 73 25 33
37 64 20 48 05
42 26 89 63
01 90 25 29
IS 80 79 99 70
|66 06 57 47 17
f3I 06 01 08 05
85 26 97 76 02
63 57 33 21 35
73 79 64 57 53
98 52 01 77 67
11 80 50 54 31
83 45 29 96 34
88 68 54 02 00
99 59 46 73 48
65 48 11 76 74
80 12 43 56 35
74 35 09 98 17
69 91 62 68 03
09 89 32 05 05
91 49 91 45 23
80 33 69 45 98
44 10 48 19 49
12 55 07 37 42
63 60 64 93 29
61 19 69 04 46
15 47 44 52 66
94 55 72 85 73
42 48 11 £2 13
23 52 37 83 17
04 49 35 24 94
00 54 99 76 54
35 96 31 53 07
59 80 80 83 91
46 05 88 52 36
32 17 90 05 97
69 23 46 14 06
19 56 54 14 30
45 15 51 49 38
W 86 43 19 94
98 08 62 48 26
33 18 51 62 32
80 95 10 04 06
79 75 24 91 40
18 63 33 25 37
76 52 01 35 86
64 89 47 42 96
19 64 50 93 03
09 37 67 07 15
80 16 73 61 47
34 07 27 68 50
45 57 18 24 06
02 05 16 56 92
05 32 54 70 48
O3 52 96 47 78
14 90 56 86 07
39 80 82 77 32
06 28 89 80 83
86 50 75 84 01
87 51 76 49 69
17 46 85 09 50
17 72 70 80 15
77 40 27 72 14
66 25 22 91 48
14 22 56 85 14
68 47 92 76 86
26 94 03 68 58
85 15 74 79 54
11 10 00 20 40
16 50 53 44 84
26 45 74 77 74
95 27 07 99 53
67 89 75 43 87
97 34 40 87 21
73 20 88 98 37
75 24 63 38 24
64 05 18 81 59
26 89 80 93 54
45 42 72 68 42
01 39 09 22 86
87 37 92 62 41
20 11 74 52 04
01 75 87 53 79
19 47 60 72 46
36 16 81 08 51
45 24 02 84 04
41 94 15 09 49
96 38 27 07 74
71 96 12 82 96
98 14 50 65 71
34 67 35 48 76
24 80 52 40 37
23 20 90 25 60
38 31 13 11 65
64 03 23 66 53
36 69 73 61 70
35 30 34 26 14
68 66 57 48 18
90 55 35 75 48
35 80 83 42 82
22 10 94 05 68
50 72 56 82 48
13 74 67 00 78
36 76 66 79 51
91 82 60 89 28
58 04 77 69 74
45 31 82 23 74
43 23 60 02 10
36 93 68 72 03
46 42 75 67 88
46 16 28 35 54
70 29 73 41 35
32 97 92 65 75
12 86 07 46 97
40 21 95 25 63
51 92 43 37 29
59 36 78 38 48
54 62 24 44 31
16 86 84 87 67
68 93 59 14 16
80 95 90 91 17
20 63 61 04 02
15 95 33 47 64
88 67 67 43 97
?S 95 11 88 77
65 81 33 98 85
86 79 90 74 39
73 05 38 52 47
28 46 82 87 09
60 93 52 03 44
60 97 09 34 33
29 40 52 42 01
18 47 54 06 10
90 36 47 64 93
93 78 56 13 68
73 03 95 71 86
21 II 57 82 53
45 52 16 42 37
76 62 11 39 90
96 29 77 88 22
94 75 08 99 23
53 14 03 33 40
57 60 04 08 $1
96 64 48 94 39
43 65 17 70 82
65 39 45 95 93
82 39 61 01 18
91 19 04 25 92
03 0? II 20 59
26 25 22 96 63
45 86 25 10 25 61 96 27 93 35
96 II 96 38 96 54 69 28 23 91
33 35 13 54 62 77 97 45 00 24
83 60 94 97 00 13 02 12 48 92
77 28 14 40 77 93 91 08 36 47
05 56 70 70 07
15 95 66 00 00
40 41 92 15 85
43 66 79 45 43
34 88 88 15 53
44 99 90 88 96
69 43 £4 85 81
20 15 12 33 87
69 86 10 25 91
31 01 02 46 74
86 74 31 71 57
18 74 39 24 23
66 67 43 68 06
59 04 79 00 33
01 54 03 54 56
39 29 27 49 45
00 82 29 16 65
35 08 03 36 06
04 43 62 76 59
12 17 17 68 33
11 19 92 91 70
23 40 30 97 32
18 62 38 85 79
83 49 12 56 24
35 27 38 84 35
50 50 0? 39 98
52 77 56 78 51
68 71 17 78 17
29 60 91 10 62
23 47 83 41 13
40 21 81 65 44
14 38 55 37 63
96 28 60 26 55
94 40 05 64 18
54 38 21 45 98
37 08 92 00 48
42 05 08 23 41
22 22 20 64 13
28 70 72 58 15
07 20 73 17 90
42 58 26 05 27
33 21 !5 94 66
92 92 74 59 73
25 70 14 66 70
05 52 28 25 62
65 33 71 24 72
23 28 72 95 29
90 10 33 93 33
78 56 52 01 06
70 61 74 29 41
85 39 41 18 38
97 11 89 63 38
84 96 2& 52 07
20 82 66 95 41
05 01 45 11 76
39 09 47 34 07 35 44 13 18 80
88 69 54 19 94 37 54 87 30 43
25 01 62 62 98 94 62 46 11 71
74 85 22 05 39 00 38 75 95 7fl
05 45 56 H 27 77 93 89 19 38
74 02 94 39 02
64 17 84 56 11
11 66 44 98 83
48 32 47 79 28
69 07 49 41 38
77 55 73 22 70
80 99 33 71 43
52 07 98 48 27
31 24 96 47 10
87 63 79 19 76
97 79 01 71 19
05 33 51 29 69
59 38 17 15 39
02 29 53 68 70
35 68 40 44 01
52 52 75 80 21
56 12 71 92 £5
09 97 33 34 4O
32 30 75 75 46
10 51 82 16 15
80 81 45 17 48
36 04 09 03 24
88 46 12 33 56
15 02 00 99 94
01 Si 87 69 38
^From Dixon and Massey, 1983.
322
-------
APPENDIX B
VALIDATING NORMALITY AND HOMOGENEITY OF VARIANCE ASSUMPTIONS!
INTRODUCTION
.1 Dunnett's Procedure and Bonferroni's T-test are parametric procedures
Jased on the assumptions that the observations within treatments are
independent and normally distributed, and that the variance of the
[bservations is homogeneous across all toxicant concentrations and the
Sontrol. These assumptions should be checked prior to using these tests, to
fetermine if they have been met. Tests for validating the assumptions are
rovided in the following discussion. If the tests fail (if the data do not
eet the assumptions), a non-parametric procedure such as Steel's Many-One
jlank Test may be more appropriate. However, the decision on whether to use
larametric or non-parametric tests may be a judgement call, and a statistician
[should be consulted in selecting the analysis.
TEST FOR NORMAL DISTRIBUTION OF DATA
[2.1 A formal test for normality is the Shapiro-Wilks Test (1). The test
^statistic is obtained by dividing the square of an appropriate linear
|combination of the sample order statistics by the usual symmetric estimate of
[variance. The calculated W must be greater than zero and less than or equal
[to one. This test is recommended for a sample size of 50 or less. If the
tsample size is greater than 50, the Kolomogorov "D" statistic (2) is
[recommended. An example of the Shapiro-Wilks test is provided below.
[2.2 The example uses growth data from the Sheepshead Minnow Larval Survival
jand Growth Test. The same data are used in the discussion of the homogeneity
[of variance determination in Paragraph 3 and Dunnett's Procedure in
^Appendix C. The data and the mean and standard deviation of the observations
|at each concentration, including the control, are listed in Table B.I.
'2.3 The first step of the test for normality is to center the observations by
'subtracting the mean from each observation at its respective concen- tration
[and control. The centered observations are listed in Table B.2.
[2.4 Calculate the denominator, D, of the test statistic:
„
D = L (X.- X
Where: X-j = the centered observations and X is the overall mean^ of
the centered observations. For this set of data, X = 0,
and D = 0.1589.
^Prepared by Ron Freyberg, Florence Kessler, John Menkedick and Larry
'Wymer, Computer Sciences Corporation, 26 W. Martin Luther King Drive,
'Cincinnati, Ohio 45268; Phone 513-569-7968.
323
-------
2.5 Order the centered observations from smallest to largest
(n)
and let X-j denote the 1th order statistic. The ordered observations
are listed in Table B.3.
2,6 From Table B.4, for the number of observations, n, obtain the
^coefficients a^ a2, , ak, where k is approximately n/2. For the
data in this example, n = 15, k = 7, and the a* values are listed in
Table B.5.
2.7 Compute the test statistic, W, as follows:
1 = 1
a.
7
The differences, x(n-i+l) - xH), are listed in Table B.5.
2.8 The decision rule for this test is to compare the critical value from
Table B.6 to the computed W. If the computed value is less than the
critical value, conclude that the data are not normally distributed. For
this example, the critical value is 0.835. The calculated value, 0.9516, is
not less than the critical value. Thus, the conclusion of the test is that
the data are normally distributed.
2.9 In general, if the data fail the test for normality, a transformation
such as to log values may normalize the data. After transforming the data,
repeat the Shapiro-Wilks Test for normality.
\
324
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TABLE B.I. SHEEPSHEAD LARVAL GROWTH DATA {WEIGHT IN MG)
FOR THE SHAPIRO-WILKS TEST
H Effluent Concentration (%)
H
• Replicate
ii i
H 2
11;
II 3
11
ii Mean
Hi
If *
Control
1.017
0.745
0.862
0.875
0.14
1
1.0
1.157
0.914
0.992
1.021
0.12
2
3.2
0.998
0.793
1.021
0.937
0.13
3
10.0
0.837
0.935
0.839
0.882
0.05
4
32.0
0.715
0.907
1.044
0.889
0.17
5
TABLE B.2. EXAMPLE OF SHAPIRO-WILKS TEST CENTERED OBSERVATIONS
m
&m
|p
KReplicate Control
I
| 1 0.142
9.
m 2 ~ 0<13
1 3 " °*013
1.0
0.136
- 0.107
- 0.029
Effluent Concentration
3.2 10.0
0.061 - 0.009
- 0.144 0.053
0.084 - 0.043
{*>
32.0
- 0.174
0,018
0.155
325
-------
TABLE B.3. EXAMPLE OF THE SHAPIRO-WILKS TEST: ORDERED OBSERVATIONS
xd>
1
2
3
4
5
6
7
8
9
10
n
12
13
14
15
0.174
0.144
0.130
0.107
0.043
0.029
0.013
0.009
0.018
0.053
0.061
0.084
0.136
0.142
0.155
326
-------
TABLE B.4. COEFFICIENTS FOR THE SHAPIRO-WILKS
0.7071
0.7071
0.0000
0.6872
0.1667
0.6646
0.2413
0.0000
0.6431
0.2806
0.0875
0-6233
0.3031
0.1401
0.0000
0 6052
03164
0.1743
00561
0 5888
03244
0 1976
0 0947
0 0000
0 5739
03291
02141
0 1224
11
12
14
15
16
17
19
20
1
2
3
4
5
6
7
8
9
10
0.5601
0.3315
0.2260
0.1429
0.0695
0.0000
0.5475
0.3325
0.2347
0.1586
0.0922
0.0303
0.5359
0.3325
0.2412
0.1707
0 1099
0.0539
0.0000
0.5251
0.3318
0.2460
0.1802
0.1240
0.0727
0.0240
0.5150
0.3306
0.2495
0.1878
0.1353
0.0880
0.0433
0.0000
0.5056
0,3290
0.2521
0,1939
0.1447
0.1005
0.0593
0.0196
04968
0.3273
0.2540
0.1988
0.1524
0.1109
0.0725
0.0359
0.0000
04886
0.3253
02553
0.2027
0 1587
0 1197
0 0837
0.04%
OOV63
0.4808
0.3232
0,2561
0 2059
0.1641
0 1271
0 0932
0.0612
ft 0303
0 0000
0.4734
0.3211
0.2565
0.2085
0.1686
0.1334
0.1013
0.0711
0.0422
0.0140
0.4643
0.3185
0.2578
0.2119
0.1736
0,1399
0.1092
8 0.0804
9 0,0530
10 0.0263
11 0.0000
12 —
13 —
14 —
IS —
0.4590
0.3156
0.2571
0.2131
0.1764
0.1443
0.1150
0.0878
0.0618
0-0368
0.0122
0.4542
0.3126
0.2563
0.2139
0.1787
0.1480
0.1201
0.0941
0.0696
0.0459
0.0228
0.0000
0.4493
0,3098
0.2554
0.2145
0.1807
0.1512
0.1245
0.0997
0.0764
0.0539
0.0321
0.0107
0.4450
0.3069
0.2543
0.2148
0.1822
0.1539
0.1283
0,1046
0.0823
0.0610
0.0403
0.0200
0.0000
0.4407
0.3043
0.2533
0.2151
0.1836
0.1563
0.1316
0.1089
0.0876
0.0672
0.0476
0,0284
0.0094
0.4366
0.3018
0.2522
0.2152
0.1848
0.1584
0.1346
0.1128
0.0923
0.0728
0.0540
0,0358
0.0178
0.0000
0.4328
0.2992
0.2510
02151
0.1857
0.1601
0.13^2
0.1162
0.0965
0.0778
0.0598
0.0424
0.0253
0.0084
0.4291
0.2968
0.2499
0.2150
0.1864
0.1616
0.1395
0,1192
0.1002
0.0822
0.0650
0.0483
0.0320
0.0159
0.0000
0.4254
0.2944
0.2487
0.2148
0.1870
0.1630
0.1415
0.1219
0.1036
0.0862
0.0697
0.0537
0.0381
0.0227
0.0076
iTaken from: Conover, 1980,
327
-------
TABLE B.4 COEFFICIENTS FOR THE SHAPIRO-WILKS TEST (Continued)
V
\
1 N
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
'\n
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
31
\
0.4220
0.2921
0.2475
0.2145
0 1874
0.1641
0.1433
0 1243
0.1066
0.0899
0.0739
0.0585
0 0435
0.0289
0.0144
0.0000
—
__
—
—
41
\
0.3940
0.2719
0.2357
0.2091
0.1876
0.1693
0.1531
0.1384
0.1249
0.1123
0.1004
0.0891
0.0782
0.0677
0.0575
0.0476
0.0379
0.0283
0.0188
0.0094
0.0000
—
—
—
32
0.4188
0.2898
0.2462
0.2141
0.1878
0.1651
0.1449
0.1265
0.1093
0.0931
0.0777
0.0629
0.0485
0.0344
0.0206
0.0068
—
—
_.
—
42
0.3917
0.2701
0.2345
0.2085
0.1874
0.1694
0.1535
0.1392
0.1259
0.1136
0.1020
0.0909
0.0804
0.0701
0.0602
0.0506
0.0411
0.0318
0.0227
0.0136
0.0045
—
—
—
—
33
0.4156.
0.2876
0.2451
0.2137
0.1880
0.1660
0.1463
0.1284
0.1118
0.0961
0.0812
0.0669
0,0530
0.0395
0.0262
0.0131
0.0000
—
—
—
43
0.3894
0.2684
0.2334
0.2078
0.1871
0.1695
0.1539
0.1398
0.1269
0.1149
0.1035
0.0927
0.0824
0.0724
0.0628
0.0534
0.0442
0.0352
0.0263
0.0175
0.0087
0.0000
—
—
—
34
0.4127
0.2854
0.2439
0.2132
0.1882
0.1667
0.1475
0.1301
0.1140
0.0988
0.0844
0.0706
0.0572
0.0441
0.0314
0.0187
0.0062
—
—
—
44
0.3872
0"2667
0.2323
0.2072
0.1868
0.1695
0.1542
0.1405
0.1278
0.1160
0.1049
0.0943
0.0842
0.0745
0.0651
0.0560
0.0471
0.0383
0.0296
0.0211
0.0126
0.0042
—
—
—
35
0.4096
0.2834
0.2427
0.2127
0.1883
0.1673
0,1487
0.1317
0.1160
0.1013
0.0873
0.0739
0.0610
0.0484
0.0361
0.0239
0.0119
0.0000
—
—
45
0-3850
0.2651
0.2313
0.2065
0.1865
0.1695
0.1545
0.1410
0.1286
0.1170
0.1062
0.0959
0.0860
0.0765
0.0673
0.0584
0.0497
0.0412
0.0328
0.0245
0.0163
0.0081
0.0000
—
—
36
0.4068
0.2813
0.2415
0.2121
0.1883
0.1678
0.1496
0.1331
0.1179
0.1036
0.0900
0.0770
0.0645
0.0523
0.0404
0.0287
0.0172
0.0057
„
—
46
0.3830
0.2635
0.2302
0.2058
0.1862
0.1695
0,1548
0.1415
0.1293
0.1180
0.1073
0.0972
0.0876
0.0783
0.0694
0.0607
0.0522
0.0439
0.0357
0.0277
0.0197
0.0118
0.0039
—
—
37
0.4040
0.2794
0.2403
0.2116
0.1883
0.1683
0.1505
0.1344
0.1196
0.1056
0.0924
0.0798
0.0677
0.0559
0.0444
0.0331
0.0220
0.0110
0.0000
—
47
0.3808
0.2620
0.2291
0.2052
0.1859
0.1695
0.1550
0.1420
0.1300
0.1189
0.1085
0.0986
0.0892
0.0801
0.0713
0.0628
0.0546
0.0465
0.0385
0.0307
0.0229
0.0153
0.0076
0.0000
—
38
0.4015
0.2774
0.2391
0.2110
0.1881
0 1686
0.1513
0.1356
0.1211
0.1075
0.0947
0.0824
0.0706
0.0592
0.0481
0.0372
0.0264
0.0158
0.0053
—
4$
0.3789
0.2604
0.2281
0.2045
0.1855
0.1693
0 t5M
0.1423
0.1306
0.1197
0.1095
0.0998
0.0906
00817
0.0731
0.0648
0 0568
.0.0489
0.0411
0.0335
0.0259
0.0185
0.0111
0.0037
—
39
0.3989
0.2755
0.2380
0.2104
0.1880
0.1689
0.1520
0.1366
0.1225
0.1092
0.0967
0.0848
0.0733
0.0622
0.0515
0.0409
0.0305
0.0203
0.0101
0.0000
49
0.3770
0.2589
0.2271
0.2038
0.1851
0.1692
0.1553
0.1427
0.1312
0.1205
0.1105
0.1010
0.0919
0.0832
0.0748
0.0667
0.0588
0.05 3 1
0.0436
0.0361
0.0288
0.0215
0.0143
0.0071
0.0000
40
0.3964
0.2737
0.2368
0.2098
0.1878 ;•'
0.1691 ;
01526
0.1376
0.1237
0.1108
0.0986
0.0870
0.0759
0.0651
0.0546
0.0444
0.0343
0.0244
0.0146
0.0049
50
0.3751
0.2574
0.2260
0.2032
0.1847
0.1691
0.1554
0.1430
0.1317
0.1212
0.1113
0.1020
0.0932
0.0846 .
0.0764 .-.'
0.0685
0.0608
0.0532
0.0459
0.0386
0.0314
0.0244
0.0174
0.0104
0.0035
328
-------
TABLE B.5. EXAMPLE OF THE SHAPIRO-WILKS TEST:
TABLE OF COEFFICIENTS AND DIFFERENCES
0.5150
0.3306
0.2495
0.1878
0.1353
0.0880
0.0433
0.329
0.286
0.266
0.191
0.104
0.082
0.031
329
-------
^
TABLE B.6 QUANTILES OF THE SHAPIRO-W1LKS TEST STAT&IC1
n
3
4
5
6
7
8
9
10
11
12
13
14
IS
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
0.0 1
0.753
0.687
0.686
0.713
0.730
0.749
0.764
0.781
0.792
0.805
0.814
0.825
0.835
0.844
0.851
0.858
0.863
0.868
0.873
0.878
0.881
0.884
0.888 •
0.891
0.894
0.896
0.898
0.900
0.902
0.904
0.906
0.908
0.910
0.912
0.914
0.916
0.917
0.919
0.920
0.922
0.923
0.924
0.926
0.927
0.928
0.02
0.756
0.707
0.715
0.743
0.760
0.778
0.791
0.806
0.817
0.828
0.837
0.846
0.855
0.863
0.869
0.874
0.879
0.884
0.888
0.892
0.895
0.898
0.901
0.904
0.906
0.908
0.910
0.912
0.914
0.915
0.917
0.919
0.920
0.922
0.924
0.925
0.927
0.928
0.929
0.930
0.932
0.933
0.934
0.935
0.936
0.05
0.767
0.748
0.762
0.788
0.803 .
0.818
0.829
0.842
0,850
0.859
0.866
0.874'
0.881
0.887
0.892
0.897
0.901
0.905
0.908
0.911
0.914
0.916
0.918
0.920
0.923
0.924
0.926
0.927
0.929
0.930
0.931
0,933
0.934
0.935
0.936
0.938
0.939
0.940
0.941
0.942
0.943
0.944
0.945
0.945
0.946
O.JO
0.789
0.792
0.806
0.826
0.838
0.851
0.859
0.869
0.876
0.883
0.889
0.895
0.90.1
0.906
0.910
0.914
0.917
0.920
0.923
0.926
0.928
0.930
0.931
0.933
0.935
0.936
0.937
0.939
0.940
0.941
0.942
0.943
0.944
0.945
0.946
0.947
0.948
0.949
0.950
0.951
0.951
0.952
0.953
0.953
0.954
0.50
0.959
0.935
0.927
0.927
0.928
0.932
0.935
0.938
0.940
0.943
0.945
0.947
0.950
0.952
0.954
0.956
0.957
0.059
0.960
0.961
0.962
0.963
0.964
0.965
0.965
0.966
0,966
0.967
0.967
0.968
0.968
0.969
0.969
0.970
0.970
0.971
0.971
0.972
0.972
0.972
0,973
0,973
0.973
0.974
0.974
0.90
0.998
0.987
0.979
0.974
0.972
0.972
0.972
0.972
0.973
0.973
0.974
0.975
0.975
0.976
0.977
- 0.978
0.978
0.979
0.980
0.980
0.981
0.981
0.981
0.982
0.982
0,982
0.982
0.983
0.983
0.983
0.983
0.983
0.984
0.984
0.984
0.984
0.984
0.985
0.985
0.985
0.985
0.985
0.985
0.985
0.985
0.95
0.999
0.992
0.986
0.981
0.979
0.978
0.978
0.97H
0.979
0.979
0.979
0.980
0,980
0.981
0.981
0.982
0.982
0.983
0.983
0.984
0.984
0.984
0.985
0.9&5
0.9&5
0.985
0.985
0.985
0.986
0.986
0986
0.986
0.986
0.986
0.98^
0.98"*
0.98"
0.98"
0.98"
098"
098"
0.98"
0.988
0.988
0.98S
0.98 -
1.000
0.996
0.991
0.986
0.985
0.984
0.984
0.983
0.984
0.984
0.984
0.984
0.984
0.985
0.985
0.986
0.986
0.986
0.987
0.987
0.987
0.987
0.988
0.988
0.988
0.988
0.988
0.988
0.988
0.988
0.989
0.989
0.989
0.989
0.989
0.989
0.989
0.989
0.989
0.989
0.990
0.990
0.990
0.990
0.990
a|8
*S8$L-
lOOt
•-SSlS;1
0.9®
tfi-^7**
0.99,3%
0.98||
0.98ft
0.987^
0.986f
0.986 t
0.986
0.986
0.986
0.986
0.987
0.987
0.987
0.988
0.988
0.988
0.989
0.989
0.989
0.989
0.989
0.989
0.990
0,990
0.990
0.990
0.990
0.990
0.990
0.990
0.990
0.990
0.990
0.990
0.991
0.991
0.991
0.991
0.991
0.991
0.991
0.991
0.991
iTaken from Conover, 7980.
330
-------
[3. TEST FOR HOMOGENEITY OF VARIANCE
£ '•' :'
;3.1 For Dunnett's Procedure and Bonferroni's T-test, the variances of the
data obtained from each toxicant concentration and the control are assumed
be equal. Bartlett's Test is a formal test of .this assumption. In using
this test, it is assumed that the data are normally distributed.
i
,3.2 The data used in this example are growth data from a Sheepshead Minnow
|Larval Survival and Growth Test, and are the same data used in Appendices
•C and D. These data are listed in Table B.7, together with the calculated
standard deviation for the control and each toxicant concentration.
;3.3 The test statistic for Bartlett's Test (Snedecor and Cochran, 1980) is
'as follows:
B =
Z V, In S }
i
I V. In S.
1
Where: V
C
In
= Degrees of freedom for each toxicant concentration and control
= Number of levels of toxicant concentration including the
control
= The average of the individual variances.
= 1 + [l/3(a-l)][S 1/V1 - 1/Z V.]
"
= Loge
3.4 Since B is approximately distributed as chi-square with a - 1 degrees
of freedom when the variances are equal, the appropriate critical value is
obtained from a table of the chi-square distribution for a - 1 degrees of
freedom and a significance level of 0.01. If B is less than the critical
value then the variances are assumed to be equal.
_2
3.5 For the data in this example, v-j = 2, a = 5, S = 0.0158, and
C = 1.2. The calculated B value is:
B =
2 [5{ln 0.0158) - I In Si
1.2
2[5(- 4.1477) - (- 22.1247)]
1.2
= 2.3103
331
-------
I
I 3.5 Since B is approximately distributed as chi-square with a - 1 degrees
? f™edoni when the variances are equal, the appropriate critical value
tor the test is 13.3 for a significance level of 0.01. Since B < 13 3
the conclusion is that the variances are equal. * *
TABLE B.7. SHEEPSHEAD LARVAL GROWTH DATA (WEIGHT IN MG) USED FOR
BARTLETT'S TEST FOR HOMOGENEITY OF VARIANCE
Replicate
Control
Effluent Concentration (%)
37F10.0 32"
1 1 1.017
1 2 0.745
i
I 3 0.862
i
I Mean 0.875
i
1 ^ ' 0.14
i i
§
1.157
0.914
0.992
1.021
0.12
2
0.998
0.793
1.021
0.937
0.13
3
0.837
0.935
0.839
0,882
0,05
4
0.715
0.907
1.044
0.889
0.17
5
|| 4. TRANSFORMATIONS OF THE DATA
f-^SJ.^
fl-^i^3~^
|| 4.1 When the assumptions of normality and/or homogeneity of variance are
Ijnot met, transformations of the data may remedy the problem, so that the
61 ata can be ana^yzed by parametric procedures, rather than a
P| non-parametric technique such as Steel's Many-one Rank Test or Wilcoxon's
BjKank Sum Test. Examples of transformations include log, square root arc
|| .sine .square root, and reciprocals. After the data have been transformed,
||Shapiro-Wilks and Bartlett's tests should be performed on the transformed
m observations to determine whether the assumptions of normality and/or
M homogeneity of variance are met.
^^3'-
04.2 Arc Sine Square Root Transformation^
4.2.1 For data consisting of proportions from a binomial (response/no
response; live/dead) response variable, the variance within the i-th
treatment is proportional to P^ (1 - PJ), where P, is the expected
proportion for the treatment. This clearly violates the homogeneity of
I _ , __ :
^rom: Peltier and Weber (1985).
332
-------
variance assumption required by parametric procedures such as Dunnett's or
Bonferroni's, since the existence of a treatment effect Implies different
values of Pi for different treatments, i. Also, when the observed
proportions are based on small samples, or when Pi is close to zero or
one, the normality assumption may be invalid. The arc sine square root
Urcsin - P) transformation is commonly used for such data to stabilize the
variance and satisfy the normality requirement.
4.2.2 Arc sine transformation consists of determining the angle (in
radons) represented by a sine value. In the case of arc sine square root
transformation of mortality data, the proportion of dead (or affected)
organisms is taken as the sine value, the square root of the sine value is
determined, and the angle (in radians) for the square root of the sine value
is determined. Whenever the proportion dead is 0 or 1, a special
modifica^on of the arc sine square root transformation must be used
3rC Slne '<"»'•• ™* transformation
4.2,3 Calculate the response proportion (RP) at each effluent
concentration, where:
RP = (number of dead or "affected" organisms)/ (number exposed),
Example: If 8 of 20 animals in a given treatment die:
RP = 8/20
= 0.40
4.2.4 Transform each RP to arc sine, as follows.
4.2.4.1 For RPs greater than zero or less than one:
Angle (radians) = arc sine (RPJ0.5.
Example: If RP = 0.40: /
Angle = arc sine (0.40)0-5 ^/[ /):
= arc sine 0.6325
= 0.6847 radians
333
-------
4.2.4.2 Modification of the arc sine when RP = 0.
Angle (in radians) = arc sine (1/4NJ0.5
Where: N = Number of animals/treatment
Example: If 20 animals are used:
Angle = arc sine (1/80)°«5
= arc sine 0.1118
= 0.1120 radians
4.2.4,3 Modification of the arc sine when RP = 1.0.
Angle - 1.5708 radians - (radians for RP = 0)
Example: Using above value:
Angle = 1.5708 - 0.1120
= 1.4588 radians
334
-------
APPENDIX C
DUNNETT'S PROCEDURE
li. MANUAL CALCULATIONS!
:;.l Dunnett's Procedure is used to compare each concentration mean with the
ontrol mean to decide if any of the concentrations differ from the
Control. This test has an overall error rate of alpha, which accounts for
multiple comparisons with the control. It is based on the assumptions
lat the observations are independent and normally distributed and that the
iriance of the observations is homogeneous across all concentrations and
introl. (See Appendix B for a discussion on validating the assumptions).
Stinnett's Procedure uses a pooled estimate of the variance, which is equal
|p the error value calculated in an analysis of variance. Dunnett's
•ocedure can only be used when the same number of replicate test vessels
fave been used at each concentration and the control. When this condition
not met, Bonferroni's T-test is used (see Appendix D).
12 The data used in this example are growth data from a Sheepshead Minnow
arval Survival and Growth Test, and are the same data used in Appendices B
:aiid D. These data are listed in Table C.I. One way to obtain an estimate
jf the pooled variance is to construct an ANOVA table including all sums of
quares, using the following formulas:
TABLE C.I. SHEEPSHEAD LARVAL GROWTH DATA (WEIGHT IN MG)
USED FOR DUNNETT'S PROCEDURE
1
Effluent
Cone (%)
Control
1.0
3.2
• 10.0
32.0
i
1
2
3
4
5
Replicate
1
1.017
1.157
0.998
0.873
0.715
Test
2
0.745
0.914
0.793
0.935
0.907
Vessel
3
0.862
0.992
1.021
0.839
1.044 .
Total
TT
2.624
3.063
2.812
2.647
2.666
Mean
Yi
0.875
1.021
0.937
0.882
0.889
^Prepared by Ron Freyberg, Florence Kessler, John Menkedick and Larry
Wymer, Computer Sciences Corporation, 26 W. Martin Luther King Drive,
Cincinnati, Ohio 45268; Phone 513-569-7968.
335
-------
1.3 One way to obtain an estimate of the pooled variance is to construct an
ANOVA table including all sums of squares, using the following formulas:
Total Sum of Squares: SST = z Y?. - G2/N
ij 1J
Between Sum of Squares: SSB = Z T?/n. - G2/N
j.i i
Within Sum of Squares: SSW = SST - SSB
Where: G = The grand total of all sample observations; G = I T.
N = The total sample size; N = I n. 1
n.j = The number of replicates for concentration "i".
TJ = The total of the replicate measurements for concentration ''i".
Y.-.J = The jth observation for concentration "i".
• j
1.4 Calculations:
Total Sum of Squares: SST = l Y2. - G2/N
13.812'
= 12.922 -
= 0.204
letween Sum of Squares: SSB = I T?/n. - G2/N
|fithin Sum of Squares:
= 12.763 - (13.812)/15
= 0.045
SSW = SST - SSB
= 0.204 - 0.045
= 0.159
336
-------
5 Prepare the ANQVA table as follows:
TABLE C.2 GENERALIZED ANOVA TABLE
Bliource DF Sum of
B| Squares (SS)
if
IB: *
^Between b - 1 SSB
SSm;
fflBI-
•iithin N - b SSW
HmfP
Mean Square (MS)
(SS/DF)
Sp = SSB/(b-l)
D
$5 = SSW/{N-b)
w
Bfotal N - 1 SST
= Number of different concentrations, including the control
1.6 The completed ANOVA table for this data is provided below;
TABLE C.3. COMPLETED ANOVA TABLE FOR DUNNETT'S PROCEDURE
• " —
•source DF SS
•
jHiJjBi
IfBetween 5-1=4 0.045
• Within 15 - 5 = 10 0.159
mi
W
Mean Square
0.011
0.016
Total
14
0.204
337
-------
jl.7 To perform the individual comparisons, calculate the t statistic for
[each concentration and control combination, as follows:
- ,.
+ (1/n.)
Where: Yj = Mean for each concentration
Y] = Mean for the control
Sw ~ Square root of the within mean square
n-| = Number of replicates in the control.
n-j = Number of replicates for concentration "i".
P.8 Table C.4 includes the calculated t values for each concentration and
;ontrol combination.
TABLE C.4. CALCULATED T VALUES..
Effluent
Concentration
1.0
1 3*2
I 10.0
m
1 32.0
2
I 3
4
5
- 1.414
- 0.600
- 0.068
- 0.136
338
-------
1.9 Since the purpose of the test is only to detect a decrease in growth
!from the control, a one-sided test is appropriate. The critical value for
(the one-sided comparison (2.47), with an overall alpha level of 0.05,
HO degrees of freedom and four concentrations excluding the control is read
rfrom the table of Dunnett's "T" values (Table D.5; this table assumes an
Jequal number of replicates in all treatment concentrations and the
[control). Comparing each of the calculated t values in Table C.4 with the
Ibritical value, no decreases in growth from the control were detected. Thus
She NOEC is 32.0%.
.10 To quantify the sensitivity of the test, the minimum significant
lifference (MSD) may be calculated. The formula is as follows:
MSD = d Sw7(l/n1) + (l/n)
Where: d = Critical value for the Dunnett's Procedure
Sw = The square root of the within mean square
n = The number of replicates at each concentration,
assuming an equal number of replicates at all
treatment concentrations
n-j = Number of replicates in the control
For example:
MSD = 2.47 (0.126) 7(1/3) + (1/3) = 2.47 (0.126) 72/3
= 2.47 (0.126H0.816)
= 0.254
|1.11 For this set of data, the minimum difference between the control mean
|and a concentration mean that can be detected as statistically significant
s 0.254 mg. This represents a decrease in growth of 29% from the control.
.11.1 If the data have not been transformed, the MSD (and the percent
Decrease from the control mean that it represents) can be reported as is.
.11.2 In the case where the data have been transformed, the MSD would be
In transformed units. In this case carry out the following conversion to
[determine the MSD in untransformed units.
339
-------
jl.11.2.1 Subtract the MSO from the transformed control mean. Call this
^difference 0. Next, obtain untransformed values for the control mean and
iithe difference, D.
/here:
MSDU = Controlu - Du
MSDU = The minimum significant difference for untransformed data
Controlu = The untransformed control mean
Du = The untransformed difference
|.n.2.2 Calculate the percent reduction from the control that MSDU
represents as:
MSD,
Percent Reduction =
X 100
Controlu
11.11.3 An example of a conversion of the MSD to untransformed units, when
|the arcsin square root transformation was used on the data, follows.
Step 1. Subtract the MSD from the transformed control mean. As an
example, assume the data in Table C.I were transformed by the
arc sine square root transformation. Thus:
0.875 - 0.254 = 0.621
Step 2. Obtain untransformed values for the control mean (0.875) and the
difference {0.621} obtained in Step 1, above.
[Sin(0.875)]2 = 0.589
[Sin(0.621)]2 = 0.339
Step 3. The untransformed MSO (MSDU) is determined by subtracting the
untransformed values obtained in Step 2.
MSDU = 0.589 - 0.339 = 0.250
In this case, the MSD would represent a 42% decrease in survival from
the control [(0.250/0.589H100)].
340
-------
•1.12 Table of Dunnett's "t" values.
TABLE C.5. DUNNETT'S "T" VALUESl
(One-tailed) d
$$&K
•5k
mrap
HSU?
MHliiDz
HHH9&
Hi8
H|p
HE;10
m&&n
v&m™
HK?3
ffiHp4
«HP5
iffll16
IB"
IHh8
m&jLw
H20
mm2*
r^K30
mm, 40
1^60
fflE120
ire^Bf
B?£
t
2.02
1.94
1.89
1.86
1.83
1.81
1.80
1.78
1.77
1.76
1.75
1.15
1.74
1.73
1.73
1.72
1.7J
1.70
1.68
1.67
1.66
1.64'
2
2.44
2.34
2.27
2.22
2.18
2.15
2.13
2.11
2.09
2.08
2.07
2.06
2.05
2.04
2.03
2.03
2.01
1.99
1.91
1.85
1.93
1.92
3
2.68
2.56
2.46
2.42
2.37
2.34
2.31
2.29
2.27
2.25
2.24
2.23
2.22
2.21
2.20
2.19
2.17
2.15
2.13
2.10
2.08
2.06
4
2.85
2.71
2.62
2.55
2.50
2.47
2.44
2.41
2.39
2.37
2.36
2.34
2.33
2.32
2.31
2.30
2.28
2.25
2.23
2.11
2.18
2.16
a = .05
5
2.98
2.83
2.73
2.66
2.60
2.56
2,53
2.50
2.48
2.46
2.44
2.43
2.42
2.41.
2.40
2.39
2.36
2.33
2.31
2.28
2.26
2.23
6
3.08
2.92
2.82
2.74
2.68
2.64
2.60
2,58
2.55
2.53
2.51
2.50
2.49
2.46
2.47
2.46
2.43
2.40
2.31
2.35
2.32
2.29
7
3.16
3.00
2.89
2.81
2.75
2.70
2.67
2.64
2.61
2.59
2.57
2.56
2.54
2.53
2.52
2.51
2. 48
2.45
2.42
2.39
2.37
2.34
8
3.24
3.07
2.95
2.87
2.81
2.76
2.72
2.69
2.66
2.64
2.62
2,61
2.59
2.58
2.57
2.56
2.53
2.50
2.47
2.44
2.41
2.38
9
3*. 30
3. 12
3.01
2.92
2.86
2.81
2.77
2.74
2.71
2.69
2.67 '
2.65
2.64
2.62
2.61
2.60
2.57
2.54
2.51
2.48
2.45
2.42
a- .01
1
3.37
3.14
3.00
2.90
2.62
2.76
2.72
2.68
2.65
2.62
2.60
2.58
2.57
2.55
2.54
2.53
2.49
2.46
2.42
2.39
2.36
2.33
3
3.90
3.61
3.42
3.29
3.19
3.11
3.06
3.01
2.97
2.94
2.91
2.88
2.86
2.84
2.83
2.81
2.77
2.72
2.68
2.64
2.60
2.5e
3
4.21
3.88
3.66
3.51
3.40
3.31
3.25
3.19
3.15
3.11
3.08
3.05
3.03
3.01
2,99
2.97
!.92
2.87
2.82
2.78
2.73
2.66
4
4.43
4.07
3.63
3.67
3.55
3.45
3.38
3.32
3.27
3.23
3.20
3.17
3.14
3.12
3.10
3.08
3.03
2.97
2.92
2.87
2.82
2.77
5
4.60
4.21
3.96
3.19
3.66
3.56
3.48
3.42
3.37
3.32
3,29
3.26
3.23
3.21
3.18
3.17
3.11
3.05
2.99
3.94
2.89
2.84
6
4.73
4.33
4.07
3.88
3.75
3,64
3.56
3.50
3.44
3.40
3.36
3.33
3.30
3.27
3.25
3.23
3.17
3.11
3.05
3.00
2.94
2.60
7
4.85
4.43
4.15
3.96
3.82
3.71
3.63
3.56
3.51
3.46
3.42
3.39
3.36
3.33
3.31
3.29
3.22
3.16
3.10
3.04
2.99
2.93
8
4.94
4.51
4.23
4.03
3.89
3.78
3.69
3.62
3.56
a. si
3.47
3.44
3.41
3.38
3.36
3.34
3.27
3.21
3.14
3.08
3.03
2.97
9
5.03
4.59
4.30
4.09
3.94
3.83
3.74
3.67
3.61
3.56
3.52
3.48
3.45
3.42
3.40
3.38
3.31
3.24
3.18
3.12
3.06
3.00
Vrom: Miller, 1981
341
-------
:. COMPUTER CALCULATIONS
This computer program incorporates two analyses: an analysis of
nce (ANOVA), and a multiple comparison of treatment means with the
:ontrol mean (Dunnett's Procedure). The ANOVA is used to obtain the error
alue. Dunnett's Procedure indicates which toxicant concentration means (if
|iny) are statistically different from the control mean at the 5% level of
significance. The program also provides the minimum difference between the
Control and treatment means that could be detected as statistically
lignificant, and tests the validity of the homogeneity of variance
Assumption by Bartlett's Test. The multiple comparison is based on Dunnett,
W., 1955, "Multiple Comparison Procedure for Comparing Several Treatments
nth a Control," J. Amer. Statist. Assoc. 50:1096-1121.
1.2 The source code" for the Dunnett's program is structured into a series
)f subroutines, controlled by a driver routine. Each subroutine has a
[specific function in the Dunnett's Procedure, such as data input,
ransforming the data, testing for equality of variances, computing P
values, and calculating the one-way analysis of variance.
|2.3 The program compares up to seven toxicant concentrations against the
[controls and can accommodate up to 50 replicates per concentration.
12.4 If the number of replicates at each toxicant concentration and control
[are not equal, Bonferroni's t-test is performed instead of Dunnett's
procedure (see Appendix D).
|2.5 The program was written in IBM-PC FORTRAN (XT and AT) by D, L. Weiner,
^Computer Sciences Corporation, 26 W. Martin Luther King Drive, Cincinnati,
45268. A compiled version of the program can be obtained from Computer
^Sciences Corporation by sending a diskette with a written request.
Data Input and Output
(2.6.1 Data on the proportion of surviving mysids (Mysidopsis bahia), from a
.survival, growth and fecundity test, listed in Table C.6, below, are used to
[illustrate the data input and output for this program.
[2.6.2 Data Input
6.2.1 When the program is entered, the user has the following options:
1. Create a data file
2. Edit a data file ,
3. Perform ANOVA (analysis) on existing data set
4. Exit the program
342
-------
TABLE C.6 SAMPLE DATA FOR DUNNETT'S PROGRAM.
MYSIDS.
PROPORTION OF SURVIVING
Replicate
Treatment
| Control
I 50-
I TOO.
f 210.
450.
0
0
0
0
0.
0.
0.
1.
0.
80
80
60
00
00
0.
1.
1.
0.
0.
80
00
00
80
20
1.00
0.80
1.00
0.20
0.00
1.00
0.80
1.00
0.80
0.20
1.00
1.00
1.00
0.60
0.00
1.00
1.00
0.60
0.80
0.00
1.00
0.80
0.80
0.80
0.00
0.80
1.00
0.80
0.80
0.40
2.6.2.2 When Option 1 (Create a data file) is selected, the program prompts
the user for the following information:
1. Number of groups, including control
2. For each group:
- Number of observations
- Data for each observation
2.6.2.3 After the data have been entered, the user may save the file on a
disk, and the program returns to the main menu (see below).
2.6.2.4 Sample data input is shown below.
343
-------
MAIN MENU AND DATA INPUT
l) Create a data file
2) Edit a data file
3) Perform aNWA on existing data set
4) Stop
Your choice ? l
Nurrber of observations for group 1 ? 8
Biter the data for group 1 one observation at a time.
NO. 1? 0.80
NO, 2? 0.80
NO. 3? 1.00
NO, 4? 1.00
NO. 5? 1.00
NO. 6? 1.00
NO. 7? 1.00
NO. 8? 0.80
Niirtoer of observations for group 2 ? 8
Do you wish to save the data on disk ?y
Disk file for output ? sanple
344
-------
2.3.3 Program Output
2.3.3.1 When Option 3 (Perform ANOVA on existing data set) is selected from
jthe main menu, the user is asked to select the transformation desired, and
indicate whether they expect the means of the test groups to be less or
greater than the mean for the control group (see below).
1) Create a data file
2} Edit a data file
3) Perform AHOVA on existing data set
4) Stop
Your choice ? 3
File name ? sample
Available Transformations
l) no transform
2) square root
3) loglO
4) arcsine square root
Your choice ? 4
Dunnett's test as implemented in this program is
a one-sided test. You must specify the direction
the test is to be run; that is, do you expect the
means for the test groups to be less than or
greater than the mean for the control group mean.
Direction for Dunnetts test : L=less than, G=greater than ? 1
345
-------
12.3.3.2 Summary statistics for the Yaw and transformed data, if.
pplicable, the ANOVA table, results of Bartlett's Test, the results of
Ithe multiple comparison procedure and the minimum detectable difference
are included in the program output.
Stannary Statistics for Raw Data
Group
Mean
s.d.
cv%
1
= control
2
3
4
5
8
8
8
8
8
.9250
.9000
.8500
.7250
.1000
. 1035
.1069
.1773
.2375
.1512
11.2
11.9
20.9
32.8
151.2
Group
Suimary Statistics and ANCWA
TransfornBtion = Arcsine Square Root
n Msan s.d. cv%
1
= control
2
3
4*
5*
8
8
8
8
8
1
1
1
1
.3969
.3390
. 2837
. 0570 .
.2015
.2400
.2478
.3181
.3066
.2863
17.
18.
24.
29.
142.
2
5
8
0
1
*) the mean for tnis group is significantly less than
the control mean at alpha = 0.05 (l-sided) by IXtnnett's test
Minununt detectable difference for Dunnett's test = -.316663
This corresponds to a difference of -.192003 in original units
Tnis difference corresponds to -19.79 percent of control
Between groins sum of squares « 7.826581 with 4 degrees of freedom.
Error mean square = .079230 with 35 degrees of freedom.
Bartlett's test p-value for equality of variances = .934
346
-------
12.4 Listing of Computer Program for Dunnett's Procedure.
Sstorage:2
c
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c
c
c
c
o
c
c
c
c
c
c
c
c
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c
c
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EPA Dunnett's test program. : Version 1.1 by D.L.Weiner, 9/10/87
Written for IBM PC and full compatibles. May require modifications
for other systems. This version compiled using Microsoft FORTRAN
compiled, V3.3.
Driver program for D.exe
This program does the following :
1) creation and/or editing of ascii files in the following
format (data are for example purposes only):
The first column denotes the group and
the second column the data value. Note
that it is assumed that group 1 is the
control. Delimiters can be commas or
blanks. Groups can have unequal sample
sizes.
1, 23.4
1, 17.6
1, 59.0
2, 44.1
2, 50
2, 51.7
3, 49.8
3, 39.0
3, 56.2
4, 73.4
4, 64.9
2) temporary transformation of the data for analysis purposes
the transformed data are not permanently saved
3) a one-way ANOVA
4) Bartlett's test for equality of variances
5) Dunnett's test to compare the comtrol mean vs. each of the
test group means if the sample sizes are equal; otherwise
simple t-tests (using a pooled error term) are done with
Bonferroni adjustment of p-value.
PROGRAM RESTRICTIONS
* number of groups must be between 2 and 8 (inclusive)
* number of observations per group must be between l and 50
Version 1.1 : D.L.Weiner, July,1987
program d
implicit real*8 (a-h,o-z) .
real*8 mdd
character*79 title
character*! ans
dimension wk(2000), n(20), y(400), ip(20)
dimension wkt(2000), nt(20), yt(400)
data n/20*0/, nt/20*0/
variables : ng=number of groups
n(g)=array of untransformed sample sizes
ntot=sura of n(i), i=l,g
y(ntot)=array of response data
347
-------
4 Listing of Computer Program for Dunnett's Procedure (Continued).
iunit=unit number for output
nt(g)=array of sample sizes for transformed data
yt(ntotal)=array of transformed data
ntott=sum of nt(i), i=l,g
title=user specified title for output
ssb,ssw=between and within group sum of squares
sst=total corrected sum of squares
ems=error mean square with idf degrees of freedom
. wk()=work array - contains means and variances
wkt()=work array - contains transformed means and va
work arrays are also used for other purposes als
mdd=minimum detectable difference
see source code for individual subroutines for additional documenta
call input(ng,n,ntot,y,iunit,title)
call trans(ng,n,ntot,y,nt,yt,ntott,inum)
summarize raw data if transformation requested in addition
to summarizing raw data
idf = ntott - ng
if(ng.lt.2.or,idf-It.5) then
write(*,'(/a/)'} ' Not enough data values for analysis,'
goto 10
endif
if(ng.gt.8) then
write(*,'(/a/)') ' Too many groups for analysis.'
goto 10
endif
if(inum.ne.1) call oneway(ng,n,ntot,y,sst,ssb,ssw,wk)
cal1 oneway(ng,nt,ntott,yt,sst,ssb,ssw,wkt)
ems = ssw / idf
call eqvar(ng,nt,wkt(ng+l),p)
p is p value for Bartlett's test : if p > 1 then the test couldn't
be run as one or more of the variances are zero
call dunnet (ng, idf,ems,wkt (1) ,nt,wkt (2*ng+l) , iside, ip,utdd)
call summary to summarize raw data if transformation requested
in addition to summarizing raw data : next to last arg = 0
means no ANOVA summary - n, mean, sd only
summary is called twice - once for screen output and once for
printer or disk output
call els
summarize raw data here (if analysis is on transformed data)
note that ssb,ssw,p,ip,iside are not used in this call (dummy)
348
-------
,4 Listing of Computer Program for Dunnett's Procedure (Continued).
i f ( inura . ne . 1 ) then
call summary (ng,n,ntot,wk(l) ,wk(ng-H) , ssb,ssw,p, ip, iside,
& title, 0,0, mdd)
pause ' *
call summary (ng,n,ntot,wk(l) ,wk(ng+l) , ssb,ssw,p, ip, iside,
& title, iunit.o, add)
endif
c
c summarize transformed data here
c
call summary (ng,nt,ntott,wkt (1) ,wkt (ng+1) , ssb, ssw,p, ip, iside,
& title, 0, inum, mdd)
call summary (ng,nt,ntott,wkt(l) ,wkt(ng+l) , ssb, ssw.p, ip, iside,
& ti tie, iunit, inum, mdd)
10
write(iunit, ' (lx,al) ' ) char(12)
close(iunit)
write (*,' (/a\) ') ' Do you wish to restart the program ? '
read(*, ' (al) ') ans
if (ans.eq. 'Y ' .or. ans. eg. 'y ' ) goto 1
if (ans.ne. 'Nf .and. ans. ne. 'n') goto 10
stop 'Normal ending.1
end
349
-------
;2.4 Listing of Computer Program for Dunnett's Procedure.
data input routine
variable type description
g
ntot
n(g)
y(ntot)
iunit
title
i-2
12
12
r8
12
a79
number og groups
total | of obs.
| obs. per group
data values
unit for output
title
$storage:2
c
c input.for
c
c on output
c
c
c
c
c
c
c
c
subroutine input(g,n,ntot,y,iunit,title)
implicit real*8 (a-h,o-z)
dimension y(l),n(l)
integer*2 g
character*64 fname
character*79 title
character*! ans
logical iochk
c
call els
call gotorc(8,l)
write(*.'(a/,a/,a/,a/,a)')
& *******
& \ * EPA
& , *
& , *
& t ******
write(*,'(/a\)') ' Title ?
read(*,•(a79)') title
2 write(*,'(/a\)') ' Output to printer or disk file ?
read(*,•(al)') ans
if (ans.ne.'p1.and.ans.ne.'P1.and.ans.ne
Dunnett''s
Version 1.1
Program
*
*'
* i
d'.and.ans.ne.'D') then
write(*,*) ' Please respond with a p or a d '
pause
call els
goto 2
end if
if(ans.eq.'p'.or.ans.eg.'P') then
iunit =20
open(iunit,file='prn')
goto 5
endif
iunit = 10
write(*,'(/a\)') ' Disk file for output ? '
read(*,'(a64)') fname
inquire(file=fname,exist-iochk)
if(iochk) then , _ .
write (*,'(/a\)') ' File already exists, overwrite it ?
read(*,'(al)') ans
if(ans.eq.'N'.or.ans.eg.'n') goto 3
if(ans.ne.'Y1.and.ans.ne.'y') then
350
-------
£.4 Listing of Computer Program for Dunnett's Procedure (Continued).
c
5
6
call cl
write (*
write ( *
write (*
write (*
write (*
3
*)
*>
*)
*)
'(
C
c
c
15
16
22
20
write(*,*) ' Please answer yes or no. '
goto 4
endif
endif
open(iunit,file=fname,access='sequential',status='new'}
1} Create a data file1
*} ' 2) Edit a data file'
3) Perform ANOVA on existing data set1
4) Stop'
1 (/a\)') ' Your choice ? '
read(*,'(al)') ans
i f(ans.ne.'1'.and.ans.ne.' 2'.and.ans.ne.'3'.
& and.ans.ne.'4') then
write(*,'(/a/)') ' Please enter a number 1,2 or 3*
goto 6
endif
if(ans.eq.'4') stop 'Normal Ending.1
if(ans.eg.'3'} goto 30
if(ans.eg.'2') goto 100
input from keyboard here
call inkb(g,n,ntot,y)
call els
write(*,*(/a\)') • Do you wish to save the data on disk ?'
read(*,'(al)') ans
if (ans.eq. fKr .or. ans. eq.'^n1) then
write(*( »(/a,a\) ') • Are you sure ? Data will Jse lest
& * (Y or N) ? '
read(*,'(al)') ans
if(ans.eq.'Y'.or.ans.eq.'y') goto 5
goto 16
endif
if(ans.ne.'y'.and.ans.ne.'Y') then
write(*,•(/a)') • Please respond yes or no.1
goto 16
endif
write(*,'(/a\)') ' Disk file for output ? '
read(*,'(a64)') fname •
inquire(file=fname,exist=iochk)
if(iochk) then
write (*,'(/a\)') ' File already exists, overwrite it ? '
read(*,'(al)') ans
if(ans.eq.'N1.or.ans.eg.'n') goto 16
endif
iunitl = 11
open(iunitl,file=fname,access='sequential1,status='new')
1 = 0
do 20 j=l,g
do 22 k=l,n(j)
1 = 1+1
write(iunitl,'(lx,i4,2x,a,2x,f!8.6)') j, ',*
continue
351
-------
2.4 Listing of Computer Program for Dunnett's Procedure (Continued)
25
c
c
c
30
100
10
20
22
25
28
close(iunitl)
goto 5
input from disk file here
continue
call readf(g,n,ntot,y,iflag,fname}
if(iflag.eq.O) return
goto 5
continue
call readf(g,n,ntot,y,iflag,fname)
if(iflag.eq.O) call edit(g,n,ntot,y,fname)
goto 5
end
inkb.for
on output
. keyboard input
variable type
description
g
ntot
n(g)
y(ntot)
i2
i2
i2
re
number og groups
total f of obs.
# obs. per group
data values
subroutine inkb(g,n,ntot,y)
implicit real*8(a-h,o-z)
dimension y(l),n(l)
integer g
call els
write(*,*') ' Number of observations for group ',
s i,' ? '
read(*,*,err=25) n(i)
if(n(i).le.0.or.n(i),gt.50) then
write(*,*) ' The number of observations per group must be '
& '1 to 50* * '
goto 22
endif
goto 28
write(*,»(/a/)') ' Invalid number. Please reenter.1
goto 22
write(*/'(/a,i2)a) ') ' Enter the data for group M,
& ' one observation at a time.'
do 100 j=l,n(i)
352
-------
,4 Listing of Computer Program for Dunnett's Procedure (Continued)
30
35
100
200
30
write(*,'(/a,i2,a,\)') ' NO. ',;),'? '
read(*,*,err=35) ynum
1=1+1
y(l) « ynum
goto 100
write(*('(/a/)') ' Invalid number. Please reenter.•
goto 30
continue
continue
ntot m i
return
end
readf.for
on output :
read a data file
variable
type
description
g
ntot
n(9)
y(ntot)
iflag
fname
i2
i2
12
r8
12
a64
number og groups
total # of obs.
# obs. per group
data values
0 = ok read, 1 = not
file that was read in
ok
c
c
c
c
c
c
c
c
c
c
c
c
subroutine readf(g,n,ntot,y,iflag,fname)
implicit real*8 (a-h,o-z)
integer g
character*64 fname
character*! ans : ' '••
logical iochk x
dimension y(l),n(l)
call els
iflag = o
write(*,'(/a\)') ' File name ? '
read(*,'(a64)') fname
if(fname.eg.' ') goto 31
inguire(file=fname, exist=iochk)
if(iochk) goto 50
31 write(*,*) * The file you specified does not exist, or
you need1
write(*,*J » to specify a different disk as part of the name
write(*,'(/a\)') ' Do you wish to reenter the name ? •
read(*,'(al)') ans
if (ans,eg.fY'.or.ans.eg.'y') goto 30
iflag = 1
return
50 continue
c begin file read
iunit - 30
open(iunit,file-fname,access='seguential',status='old'
readtiunit^^end^lOO) igrpr x
c i is obs#, ig is group*, nn counts #obs per group
ig~- 1
nn = 1
ilag = ig
353
-------
I
2.4 Listing of Computer Program for Dunnett's Procedure (Continued).
60
iglag = igrp
read(iunit,*,end=100,err=150) igrp, x
if(iglag.eg.igrp) nn = nn + 1
if(iglag.ne.igrp) then
n(ig) - nn
ig = ig + 1
iglag = igrp
nn = 1
end if
100
150
y(i) = x
if (nn.gt.50) then
write (*, ' (\a,i2,a\) ') ' Too many observations for croup
1 Max = 50 '
iflag = l
pause
return
endif
goto 60
continue
n(ig) = nn
ntot = i
g «• ig
close(iunit)
return
continue
write (*, l (a,i2,a,a) ') ' There is an error on line (,
pause
iflag = l
return
end
edit.for
on input
'your data file. Please correct it.'
of
file edit routine
variable
type
description
g
ntot
n(g)
y(ntot)
fname
12
12
12
r8
364
number og groups
total # of obs.
# obs. per group
data values
file to be edited
subroutine edit(g,n,ntot,y,fname)
implicit real*8(a-h,o-z)
dimension y(l),n(l)
integer g
character*64 fname
call els . ;:'
fuzz = l.e-20
iunit «= 30
open(iunit,file=fname,access='sequential'.status='old()
wnte(*,'(/a\)') ' Edit values for which group ? '
read(*,*(err=10) ig
354
-------
2.4 Listing of Computer Program for Uunnett's Procedure (Continued).
10
100
102
c
105
110
120
130
140
150
') * The following values are for group ',ig
if(ig.ge.l.and.ig.le.g) goto 100
writef*,'(//a,i2,/)') ' Please respond 1 - ' g
pause
goto 1
continue
call els
call gotorc(0,o)
writef*, ' (a,i:
call gotorc(5,6)
loff m o
if (ig.eq.l) goto 105
compute offset
do 102 i=l,ig-l
loff = loff 4 nfi)
do 110 j=l,nfig)
irow =5+ (j-i) / 4
k = mod(j,4)
iffk.eq.l) icol = 0
if(k.eq.2) icol = 20
if(k.eq.3) icol = 40
iffk.eq.oj icol = 60
call gotorc(irow,icol)
writef*,'(fis.6,\)') y(loff 4 j)
call gotorc(23,0)
write(*,'
-------
|2.4 Listing of Computer Program for Dunnett's Procedure (Continued)
200 continue
write(*,'(/a\)') ' Do you wish to save the changes ? '
read(*,'(al)') ans
if(ans.eg.'n1.or.ans.eg.'N') then
close(iunit)
return
endif
if(ans.ne.'y1.and.ans.ne.*Y') goto 200
close(iunit)
open(iunit,file=fname,access**'seguential',status='new')
1-0
do 250 j«l,g
do 252 k«l,n(j)
1 = 1 + 1
252 write(iunit,'(Ix,i4,2xla(2x,f18.6)') j, ',' ,y{l)
250 continue
close(iunitl)
return
end
356
-------
2.4 Listing of Computer Program for Dunnett's Procedure (Continued)
$storage:2
c
c cursor positioning, goto (irow,icol}
c
subroutine gotorc (irow,icol}
character*! dummy
if (irow.lt.0.or.irow.gt.24) irow = 0
if (icol.It.0.or.icol.gt.79) icol «* 0
read (dummy,'(Ix)')
call locate (0,0,ier)
write (*,'(\)'J
call locate (irow,icol,ier)
read (dummy,'(Ix)')
return
end
0 ... 79
24
357
-------
2.4 Listing of Computer Program for Dunnett's Procedure (Continued).
Sstorage:2
c
c trans. for - computes transformed data
c
c on input : variable type description
C g
c n()
c ntot
1 ° y()
1 c
I c on output : variable
! c
c nt()
c yt()
c ntott
c inum
12
12
i2
r8
type
12
r8
r8
12
number of groups
n values for each group
total # of obs.
data values
description k
n values after transformati It
data values after transform Jj|
ntot after transformations jm
transformation number i$|
subroutine trans(g, n,ntot,y,nt,yt,ntott,inum)
implicit real*8(a-h,o-2)
integer g
dimension n(l), y(l), nt(l), yt(l)
c
iflag = 0
5 call els
write(* *) Available Transformations'
write(* *) l) no transform1 - ,
write(* *) 2) square root'
write(* *) 3) logio1
write(* *) 4) arcsine square root'
write(* l(/a\)'} « Your choice ? •
read(*,*,err=50) inum
if(inum.It.l.or.inum.gt.4) goto 50
goto 60
50 write(*,*) • Please answer 1-4 •
pause ' *
goto 5
60 k = 0 T "V
kk « 0 : f-i "-?•
ntott «= 0 :
do 52 1=1, g )'
nt(i) = o
do 54 j=l,n(i)
k = k + l
goto(70,72,74,76),inum
70 temp = y(k)
goto 53
72 if (y(k).lt.O.dO) then
iflag - 1
goto 54
endif
temp m dsgrt(y(k))
goto 53
74 if (y(k).le.o.dO) then
iflag « l
358
-------
Listing of Computer Program for Dunnett's Procedure (Continued).
goto 54
endif
temp = dloglO(y(k))
goto 53
76 if (y(k).lt.O.dO.or.y(k).gt.l.dO) then
iflag - 1
goto 54
endif
temp = dasin(dsqrt(y(k}))
53 kk - We + 1
nt(i) - nt(i) + 1
ntott - ntott + 1
yt(kk) - temp
54 continue
52 continue
c
if(iflag.gt.O) then
write(*,'(/a)')
& ' One or more data values could not be transformed. These
write(*,'(a/)r) ' values will not be included in the analyses.
pause ' '
endif
c
c check to see if each group has at least 1 observation
c
do 100 i«l, g
100 if(nt(i).le.O) goto 110
return
110 call els
write(*,'(a,a,i2J') • After transformation, all of the values',
& « are missing for group ', i
write(*,'(/a)'} ' ANOVA cannot be performed. Program ending,
stop ' l
end
359
-------
2.4 Listing of Computer Program for Dunnett's Procedure (Continued).
$storage:2
c
c oneway. for
c
c on input :
c
c
c
c
c
c
c on output :
I c
c
c
c
c
c
c
computes
variable
g
"0
ntot
y()
wk()
variable
wk(l)~wk(g)
wk(g+l)-wk(g+g)
sst
ssb
ssw
oneway
type
12
12
12
r8
r8
type
r8
r8
r8
r8
rs
anova
description
number of groups
n values for each group
total sample size
data values (possible tr
work array (dimensioned
. description
group means
group variances
corrected total sum o
between group sum of
within sum of squares
ans
2*g
f s
sgu
10
c
30
C
c
c
c
c
c
20
c
subroutine oneway(g,n,ntot,y,sst,ssb,ssw,wk)
implicit real*8 (a-h,o-z)
integer*2 g
dimension n(l), y(l), wk£l)
sy = 0.0
syy = 0.0
sst ~ 0.0
ssb = 0.0
ssw =0.0
k = 0
temp =0.0 '•••:
do 10 i=l, 2*g
wk(i)=0.0
do 20 1=1, g
do 30 j=l,n(i)
k = k + 1
sy = sy + y{k)
syy = syy + y(k) * y(k)
wk(i) » wk(i) + y(k)
wk(g-t-i) = wk(g+i) + y(k)*y(k)
compute and store 1th group variance in wk(g+i)
wk(g+l) - wk(g+i) - wk(i) * wk£i) / n(i)
if(n(i).gt.l) wk£g+i) * wk(g4i) /
temp = temp + wk(i) * wk(i) / n£i)
compute and store ith mean in wk(i)
wk(i) - wk(i) / n(i)
sst = syy - sy * sy / ntot
ssb = temp - sy * sy / ntot
ssw •= sst - ssb
return
end
360
-------
,4 Listing of Computer Program for Dunnett's Procedure (Continued).
Sstorage:2
c
c eqvar.for
10
computes tests for equality of variances
on input :
variable
g
var(g)
variable
P
type
12
12
12
r8
type
r8
description
number of groups
n values for each group
array of variances
data values (possible trans
description
Bartlett's test p-value
on output
subroutine eqvar{g,n,var,p)
implicit real*8(a-h,o-z)
integer g
dimension var(l), n(l)
vmin = var(l)
vmax = var(l)
imin « 1
imax «= 1
vsum - var(l)
sse « (n(l)-l) * var(l)
idf » n(l) - l
cl - O.do
c2 = O.dO
if(var(l).le.l.d-10) goto 100
cl = (n(l)-l) * dloglO(vard))
if ((n(i)-l).gt.O) c2 = l.dO / (n(l)-l)
do 10 i=2,g
vsum « vsum + var(i)
sse = sse + (n(i)-l) * var(i)
idf = idf + (n(i) - 1) : . :.
if(var(i).le.l.d-10) goto 100
cl - cl + (n(i)-l) * dlogiofvar(i))
ifUn(i)-l).gt.O) c2 = c2 + l.dO / (n(i)-l)
if (var(i).le.vmin) then
vmin = var(i)
imin = i
endif
if (var(i).gt.vmax) then
vmax = var(i)
imax = i
endif
continue
f = vmax / vmin
idfl - n(imax) - l
idf2 = n(imin) - 1
call pvalue (3,2,f,idfl,idf2,pi)
note pi = p-value for F max test
361
-------
2.4 Listing of Computer Program for Dunnett's Procedure (Continued)
C - l.dO + (l.dO / (3*(g-l))J * (c2 - l.dO/idf)
chi » 2.303 * (idf * dloglO(sse/idf) - cl)
chi = chi / c
idfl = g-l
idf2 - 0
call pvalue (4,2,chi,idfl,idf2,p)
return
100 continue
c set p to 2 (a flag) if l or more variances = 0
p = 2.dO
return
end
362
-------
•
[2.4 Listing of Computer Program for Dunnett's Procedure (Continued).
variable
itype
value
idfl
idf2
variable
P
type
i2
12
r8
12
i2
type
r8
description
1-t, 2=z, 3=f , 4=chi square
1=1 sided, 2=2 sided
value of test statistic
1st degrees of freedom t,z,
2nd degrees of freedom f
description
p-value
Sstorage:2
c
c subroutine pvalue.for - compute p values
c
c
c on input :
-C
c
c
c
c
c
c
o on output :
c
c
c
subroutine pvalue(itype,i!2,value,idfl,idf2,p)
implicit real*8 (a-h,b-z)
goto (10,11,12,13) itype
'10 t = value
idf « idfl
aa=idf/2.do
bb=0.5dO
xx-l.dO/(l.d(H(t**2)/idf)
bta=beta(xx,aa,bb)
if(i!2.eq.l.and.t.gt.0.dO) p-bta/2.dO
if(i!2.eq.l.and.t.lt.0.dO) p=(l.do-bta/2.dO)
if(i!2.eq.2) p = bta
return
11 z = value
aa=l.dlO/2.dO
bb*=0.5do
xx=l.dlO/(l.dl(H(z**2))
bta=beta(xx,aa,bb)
if(il2.eq.l.and.z.gt.0.dO) p=bta/2.dO
if(i!2.eq.l.and.z.lt.0.dO) p=(l.dO~bta/2.dO)
if(i!2.eq.2) z = bta
return
12 f - value
aa=idf2/2.dO
bb=idfl/2.dO
xx=l.dO/(l-dO+(idfl*f)/idf2)
p=beta(xx,aa,bb)
return
13 chi » value
idf = idfl
aa=l.dlO/2.dO
bb=idf/2.dO
xx=l.dlO/(1.dlO+chi) ;
p-beta(xx,aa,bb)
return
stop
end
363
-------
Ri
K.4 Listing of Computer Program for Dunnett's Procedure (Continued)
10
11
12
13
14
double precision function beta(xx,aa,bb)
implicit real*8(a-i,k-z)
integer*2 j
ier » 0 .
BETA=1.0
IF (XX - 1.0) 1,30,30
BETA=0.0
IF (XX) 30,30,4
A=AA
B=BB
x=xx
LO=DLOG(X)
Ll-DLOG(l.O-X)
M=DLGAMA(A) + DLGAKA(B) - DLGAMA(A+B)
IF (A-1.5) 6,7,7
BETA=BETA+DEXP(A*LO+B*L1-M)/A
M=M+DLOG(A)-DLOG(A+B)
GO TO 5
IF (8-1.5) 8,9,9
BETA=BETA-DEXP(A*LO+B*L1-M)/B
M=M+DLOG(B)-DLOG(A+B)
B-B+1.0
GO TO 7
Y-1.28155156553942DO
L=(Y*Y-3.0)/6.0
H=(2.0*A-1.0)*(2.0*B-1.0)/(A+B-1.0)
Z=(L+(5.0*H-4.0)/(6.0*H))*(A-B)/(A+B-1.0}*2.0/H
L=DSQRT(K+L)/H
CUT=-V*L-Z
CUT=A/ (A+B*DEXP(2. Q*CUT) )
IF (CUT-0.5) 12,12,10
CUT=Y*L-Z
CUT=A/ (A+B*DEXP(2.0*CUT) }
IF (CUT-0.5) 11,12,12
CUT=0.5
H-1.0
IF (X-CUT) 14,14,13
H=LO .
LO=L1
Ll-H
x-i.o-x-
H=A
A=B
B=H
BETA-BETA+1.0
H— 1.0
EPS=1.0D-16
M=DEXP (A*LQ+ (B-l . 0) *L1-M)/A
X=X/(1.0-X)
I>=0.0
Y=l,0
2=1.0
DO 18 J=l,100
I=J
364
-------
,4 Listing of Computer Program for Dunnett's Procedure (Continued).
15
20
16
18
19
30
L0=(I-B)*(A+I-1.0)/(A+2.0*1-2.0)*X/(A+2.0*1-1.0)
L1«(A+B+I-1. 0)*!/(A+2.0*1)*X/(A+2.0*1-1.0}
L=L*LO+M
Z=Z*LO+Y
M=M*L1+L
Y=Y*L1+Z
IP (Z) 15,18,15
S=L/Z
10
IF (T) 16,20,16
IP (S) 18,19,18
IF (DABS(S/T-1.0)-EPS) 19,19,18
CONTINUE
BETA-BETA+H*T
RETURN
RETURN
END
DOUBLE PRECISION FUNCTION DLGAMA(XX)
DOUBLE PRECISION XX,ZZ,TERM,RZ2,DLNG
IER=0
zz=xx
IF (XX-1.D10) 2,2,1
IF (XX-1.D35) 8,9,9
IF (XX-l.D-9) 3,3,4
IER—1
DLNG=-1.D38
GO TO 10
TERM=1.DO
IF (ZZ-18.DO) 6,6,7
TERM=TERM*ZZ
ZZ=ZZ+1.DO
GO TO 5
RZ2=1.DO/ZZ**2
DLNG =(ZZ-0.5DO)*DLOG(ZZ)-ZZ +0.9189385332046727 -DLOG{TERK}+
1(1.DO/ZZ)*(.8333333333333333D-1-(RZ2*(.2777777777777777D-2+(RZ2*
2(.7936507936507936D-3-(RZ2*(.5952380952380952D-3)))))))
GO TO 10
DLNG-ZZ*(DLOG(ZZ)-1.DO)
GO TO 10
IER=+1
DLNG=1.D38
DLGAHA»DLNG
RETURN
END
365
-------
;2.4 Listing of Computer Program for Dunnett's Procedure (Continued).
$storage:2
c
c subroutine dunnet.for - compute p values
c
10
20
C
c
c
22
on input i
variable
type
description
on output :
ng
idf
ems
mean(ng)
n(ng)
t<8,50)
iside
variable
ip(ng)
12
12
rs
ra
12
r8
12
type
12
number of groups 2<=ng<=8
degrees of freedom for erro
error mean square
array of means
n per each group
work array
0*trts lower, l=trts higher
description
0=NS, l=sig @ alpha=0.05
HDD
r8
ip(l) = 0 => Dunnetts te
ip(l) = 1 => Bonferroni
min. detectable diff. in
original units
note : the calling program must check to see that 2<=ng<=8 and
that idf is >« 5
subroutine dunnet(ng,idf,ems,mean,n,t,iside,ip,mdd)
implicit real*8 (a-h,o-z)
real*8 mean(l), mdd
character*! ans
logical iochk
dimension t(7,49), ip(l), n(l)
read in Dunnett's t values
inquire(file=(dunnet.fil',exist=iochk)
if(iochk) goto 10
write(*,*} ' The file containing Dunnett t values is not on the'
write(*,*) ' default drive. The file name is DUNNET.FIL '
write(*,*) * Please copy it over to the default drive and rerun1
write(*,*) ' this program. '
stop ' '
open (97,file-'dunnet.fil',status='old')
do 20 j-1,49
read(97,'(7f5.2)') (t(i(j),i=l,7)
close(97)
read in direction for the test
call els
write(* *)
write(*
write(*
write(*
write(*
*)
*)
*)
*)
Dunnett''s test as implemented in this program is
a one-sided test. Vou must specify the direction
the test is to be run; that is, do you expect the
means for the test groups to be less than or
greater than the mean for the control group mean.
366
-------
30
c
c
c
c
write(*,'(/a\)')
& read^aVranr16"8 tCSt : ^leSS than' Greater than 7 .
"&£:£^S£M-tI't-"*-™-<»-'*'
' Please respond L or G. '
endif
ifjans.eq.'I'.or.ans.eq.'L') iside=o
if(ans.eq.'g'.or.ans.eq.'G') iside=l
cmean « mean(l)
check to see if sample sizes are equal :
do 30 i=2,ng
if(n(i)-n(i-i)) 100, 30, 100
continue
xn = i.do * n(l)
denom = dsqrt(2,dO * ems / xn)
recover Dunnett's t value
icol « ng - i
tficol
if not, do Bonferroni
iffi
dunt = t(icol , 49)
ip(l) = 0
do 50 i=2,ng
ip(i}=0
if (iside.eq.O) diff
if (iside.eq.l) diff
stat = diff / denom
if (stat.gt.dunt) ip(i)=i
cmean - mean(i)
meanfi) - cmean
50
c
c compute MDD
c ••...'•';
mdd = dunt * denom
o *< if(iside.eq.O) mdd = -i.do * mdd
c fixup if transformed is done by summary
return J
100 continue
c Bonferroni adjustment here
alpha - 0.05do / (ng - i
pctile « i.do - alpha
tval - tinv (pctile, idf)
nl « n(l)
do iso i-2,ng
ni
367
-------
2.4 Listing of Computer Program for Dunnett's Procedure {Continued}
denom - dsqrt(ems * (l.do/nl + l.do/nij )
if (iside.eq.O) diff = cmean - mean(i)
if (iside.eq.l) diff = mean(i) - cmean
stat « diff / denom
150 if (stat.gt.tval) ip(i)=l
c
c compute HDD
c
denom = dsqrt(2.dO * ems / nl)
mdd = tval * denom
if(iside.eq.O) mdd = -l.dO * mdd
c fixup if transformed is done by summary
return
end
368
-------
'.4 Listing of Computer Program for Dunnett's Procedure (Continued).
I $storage:2
1 °
I c summary . for
§ c
1 c on input :
Bj C
I C
1 C
I °
I- c
1 c
I c
I' <=
i c
1 <=
I c
1 c
1 c
1 c
I c
1 c
I c
[ c
I c
c
c
computes
variable
g
n()
ntot
mean ( )
var()
ssb
ssw
P
lp()
iside
title
iunit
inum
MDD
oneway
type
12
12
12
r8
r8
r8
r8
r8
12
12
a?9
12
12
rs
anova
description
number of groups
n values for each group
total sample size
data values (possible trans
work array (dimensioned 2*g
between group sum of squ
within sum of squares
Bartlett's test p-value
flag for Dunnett's test res
0=ns, l=sig
ip(l) - 0 => Dunnetts test
ip(l) = 1 => Bonferroni t-t
direction of Dunnett's test
0=lower, l=upper
title
unit # for output
0 means summarize raw data,
l=no trans, 2=sqrt,
3=loglO, 4=arcsine
min. detectable diff. for
Dunnett ' s test
subroutine summary(g,n,ntot,mean,var,ssb,ssw,p,ip,iside,title,
& iunit,inum,mdd)
implicit real*8 (a~h,o-z)
real*8 mean(l), mdd, mddl
Integer*2 g
character*79 title
character*20 tran(4)
character*12 direct
character*! pstar
dimension n(l), var(l), lp(l)
if(inum.eq.0} goto 2
tran(l)=' None '
tran(2)=' Square Root '
tran(3)=' LoglO '
tran(4)-'Arcsine Square Root'
convert mdd to original units
if (inum.eq.1) then
tempc = mean(l)
tempt = mean (1) -f mdd
mddl = tempc - tempt
end if
if (inun>,eq.2) then
tempc = mean(l) ** 2
tempt = (mean(l) •+• mdd) ** 2
mddl = tempc - tempt
endif
369
-------
2.4 Listing of Computer Program for Dunnett's Procedure (Continued)
30
if (inura.eq.3) then
tempo = 10.0 ** (mean(l))
tempt - 10.0 ** (mean(l) + radd)
mddl * tempo - tempt
endif
if (inum.eq.4) then
tempo = (dsin(aean(l)})**2
tern = (mean(l) + mdd)
tempt = (dsin(tem) )**2
mddl = tempo - tempt
endif
mddl = (dabs(mdd)/mdd) * dabs(mddl)
pctrl = 100. do * mddl / dabs (tempo)
check to Bee if all sample sizes are equal
iegn = 0
do 3 i = 2, g
continue
goto 5
ieqn = 1
4,3,4
if (iunit.gt.O) write(iunit, ' (lx,al) ') char(12)
write(iunit, ' (/,lx,a/) ') title
if (inum.eq.O) write(iunit, • (/,15x,a//) ')
1 Summary Statistics for Raw Data1
if (inum.ge. 1) then
writefiunit, l (/(17x,a) f)
1 Summary statistics and AKOVA*
writefiunit, • (/,13xfa, a/} ') * Transformation = '(tran{inum)
endif
write(iunit,*)
1 Group n Mean s.d. cv% '
writefiunit,*)
if (var(l) .gt.O.dO) then ~
sd = dsqrt(var(l))
else
sd = o.dO
endif
if (mean(l) .ne.O.dO) then
cv = dabs(100.dO * sd / mean(l))
else cv = O.dO
endif
write (iunit,30) n(l) ,mean(l) ,sd,cv
format (' 1 * control • ,lx, i2, 3x,fl2.4, lx,f 12. 4, 9x, f6. 1)
do 10 i»2,g
if (var(i).gt.O.dO) then
sd - dsqrt(var(i))
else
sd = O.dO
endif
if (mean(i) .ne.O.dO) then
370
-------
2.4 Listing of Computer Program for Dunnett's Procedure (Continued).
cv - dabs(100.dO * sd / mean(i))
else
cv - o.do
endif
pstar=' '
if(ip(i).eq.l) pstar-'*'
if(inum.ne.0}
write (iunit,'(4x,i2,al,6x,i2,3x,fi2.4,lx,fl2.4,9x,f6.i)')
i,pstar,n(i),raean(i),sd,cv
c don't write out pstar if inum « o - summarize raw data
c
if(inum.eq.0)
& write (iunit,'(4x,i2,7x,i2,3x,fi2.4,lx,fl2.4,9x,f6.1)')
& i,n(i),mean(i),sd,cv
10 continue
write(iunit,*)
jt »
if(inum.eq.0) return
if (iside.eq.O) then
direct='less than1
else
direct='greater than'
endif
if(ipfl).lt.l) then
write(iunit,•(/a,a,/,a,a/)<)
& ' *) the mean for this group is significantly 'direct,
& the control mean at alpha = 0.05 (l-sided) by Duwiett'-s'
& * test' '
else
'
) the mean for this group is significantly 'direct,
the control mean at alpha « 0.05 (1-sided) by a t - test1
with Bonferroni adjustment of alpha level* '
endif
if (iunit. eq.O) pause ' •
idf 1 = g - i
idf2 = ntot - g
f = (ssb/idfi) / (ssw/idf2)
call pvalue(3,2,f,g-l,ntot-g,pval)
if (pval.lt. 0.001) pval = 0.001
writefiunit, ' (//) ')
if(ipd).lt.l) then
m Actable difference for',
else
write(iunit,'(a,/,a,fl5.6)») ' Minumum detectable difference for'
& t-tests with Bonferroni adjustment « • mdd
endif
371
-------
'.4 Listing of Computer Program for Dunnett's Procedure (Continued).
if(inum.gt.l) write(iunit,'(a,f15.6,a)»)
1 This corresponds to a difference of ',mddl,' in original units
write(iunit,'(a,f8.2,a//)') ' This difference corresponds to ',
100
& pctrl, ' percent of control'
if(ieqn.eq.l) then
write(iunit,*j
write(iunit,*)
write(iunit,*)
writefiunit,*)
writefiunit,*)
write(iunit,*)
write(iunit,*)
writefiunit,*)
write(iunit,*
end if
* Note - the above value for the minimum *
* detectable difference is approximate as *
* the sample sizes are not the same for all of *
* the groups. *
*
write(iunit,'(a,f!6.6,a,i2,a/J')
r Between groups sum of squares =l,ssb,' with
degrees of freedom.
p
', pval
ssw/idf2, • with ',idf2,
write(iunit,'(a,f6.3,/)'
write(iunit,'(a,fl6.6,a,
' Error mean square -
* degrees of freedom,'
if(p.gt.l.dO) goto 100
if(p,It.0.001) then
p «= 0.001
write(iunit,*(a,f6.3,/)•)
1 Bartletf'e test p-value for equality of variances <=
else
write(iunit,'(a,f6.3,/J r)
' Bartletf's test p-value for equality of variances = '
endif
return
if(p.gt.0.01)
write(iunit,*)
write(iunit,*)
write(iunit,*j
write(iunit,*)
write(iunit,*)
writefiunit,*)
write(iunit,*)
write(iunit,*)
return
write(iunit,*)
write(iunit,*)
write(iunit,*)
write(iunit,*)
write(iunit,*)
write(iunit,*)
write(iunit,*)
return
end
* *
* Warning - the test for equality of variances *
* is significant (p less than O.bl). The
* results of this analysis should be inter-
* preted with caution.
*
'* *
'* Warning - the test for equality of variances *
1 * could not be computed as 1 or mere of the *
'* variances is zero. *
'* *
372
-------
I
12.4 Listing of Computer Program for Dunnett's Procedure (Continued).
$storage:2
REAL*8 FUNCTION TINV(P,NDF)
IMPLICIT REAL*8(A-H,0-Z)
DF=NDF*1.DO :
Z-GAUINV(P)
T=Z
T=T+(Z**3+Z)/(4.DO* DF)
T=T4(5.DO*Z**5+16.DO*Z**3+3.DO*2)/(96.DO* DF**2)
T=T+(3.DO*Z**7+19.DO*Z**5+17.DO*Z**3-15.DO*Z)/(384.DO* DF**3)
T=T+(79.DO*Z**9 + 776.DO*Z**7-t-1482.DO*Z**5-1920.DO*Z**3-945.DO*Z)/
$(92160.DO* DF**4)
TINV=T
RETURN
END
REAL*8 FUNCTION GAUINV(P)
IMPLICIT REAL*8(A-H,0-Z)
D=P
IF(D.GT..5DO) D=1,-D
T2=DLOG(1./(D*D)J
T=DSQRT(T2)
GAUINV=T-(2.515517DO-t-0.802853DO*T+0.010328DO*T2)/
* (1.0D04l.432788DO*T+0.189269DO*T2+.001308DO*T*T2)
IF(P.LT..5DO) GAUINV^-GAUINV
RETURN
END
373
-------
2.4 Listing of Computer Program for Dunnett's Procedure (Continued).
$ include:'speedy.fil'
c 0 ... 79
c cursor positioning, goto (irow,icol) :
c 24
subroutine gotorc (irow,icol)
character*! dummy
if (irow.lt.0.or.irow.gt.24) irow = 0
if (icol.lt.0,or.icol.gt,79) icol = 0
read (dummy,'(Ix)')
call locate (0,0,ier)
write <*,'(\)')
call locate (irow,icol,ier)
read (dummy,'(Ix)')
return
end
c clears the screen, returns to text mode if not already in text mode,
c and puts cursor in upper left corner
subroutine clrscr
call qrmode (im,i)
if (im.ne.2) call qsmode(2)
call gclear (0,7)
call gotorc (0,0)
write (*,'(\)')
return
end
c clears to end of line from current cursor position, does not move
c cursor
subroutine clreol
call gcpos (icol,irow) .
if (icol.eg.79) then
if (irow.ne.24) write (*,'(al)') * '
else
call qstext (32,0,7,(79-icol))
end if
return
end
c gotorc + clreol
subroutine goclrc (irow,icol)
call gotorc (irow,icol)
call clreol
return
end
374
-------
2.4 Listing of Computer Program for Dunnett's Procedure {Continued}
c converts a character (ascii value) to upper case (if lower case)
character*! function upchar (ch)
character*! c,ch
equivalence (ich,c)
c = ch
if (ich.ge.97.and.ich.le.122) ich
upchar = c
return
end
ich - 32
c converts a fortran string of length len to uppercase
subroutine upstr (str.len)
character*! str(l)
character*! upchar
do 10 i=l,len
10 str(i) - upchar(str(i)}
return
end
c back up (move left) one text position on the screen
subroutine backup
call qcpos (icol,irow) .
call qcmov ((icol-1),irow)
return
end
c pauses for idelay seconds
subroutine delay (idelay)
call qtime (ihr, iinin, isec, ihun)
10 call qtime (ihr,imin,nsec,ihun)
if (isec.gt.nsec) then
iexp = 60 - isec + nsec
else
iexp = nsec - isec
endif
if (iexp.gt,idelay) return
goto 10
return
end
c get a string from the keyboard, echo it to the screen, but handle
375
-------
12.4 Listing of Computer Program for Dunnett's Procedure (Continued).
c each character separately, so there is no scrolling, etc.
c if user hits escape, str(l) = ESC (char(27)), then return.
c if string is of length zero, str(l) » char(13J.
c maximum length of string accepted is len.
subroutine getstr (str,len)
character*! str(1),gstr(80)
equivalence (gstr(l),ifirst)
ilen « 0
10 call qinkey (iext.key)
if ((iext.eq.l).and.((key.eq.13).or.(key.eq.27))) goto 100
if (iext.eq..Land.key.ge. 32. and.Key. le.126.and.ilen.lt. len) then
write (*,'(al,\)') key
ilen = ilen + l
gstr(ilen) = key
endif
if (iext.eq.Land.key.eq.8.and.ilen-.gt.O) then
call backup
write (*,'(al,\) ') ' '
call backup
ilen = ilen - l
end if
goto 10
100 if (key.eq.27) then
ifirst = 27
ilen = 1
else
do 105 k=ilen+l,len
105 gstr(k) = • *
end if
if (ilen.eq.O) ifirst = 13
do lio k=l,len
110 str(k) = gstr(k)
return
end
c this routine gets a password for a protected data set.
c it works about the same as getstr, but does not echo the input
c characters to the screen, maximum length is 10 characters.
subroutine gpwrd (gstr)
character*! gstr(10)
10
ilen = o
call qinkey (iext,key)
if (iext.eq,0) goto 10
if (key.eq.27) goto 27
if (key.eq.13) goto 13
if (key.ge.32.and.key.le.126.and.ilen.lt.10) then
write (*,'(a\)') * '
ilen « ilen + 1
376
-------
1.4 Listing of Computer Program for Dunnett's Procedure (Continued)
13
27
gstr(ilen) - key
end if
if (key.eq.S.and.ilen.gt.O) then
call backup
ilen = ilen - 1
endif
goto 10
if (ilen.eq.O) goto 27
call pad (gstr,ilen,10)
return
gstr(l) - char(key)
return
end
c this routine decodes an encrypted password stored in the header
c file and returns the original ascii string.
subroutine dpwrd (pw)
character*! pw(10), n(10)
call copy (pw,
pw(l)
pw(2)
pw(3)
pw(4)
pw(5)
pw(6)
pw(7)
pw(8)
pw(9)
pw(10)
BE
*
=
=
as
t*
*
*
=
=
char
char
char
char
char
char
char
char
char
char
n,10)
(ichar(n(6))
(ichar (n (3) )
(ichar(n(8) )
(ichar(n(4) )
(ichar(n(10))
(ichar(n(7) )
(ichar(n(5) )
(ichar(n(2) )
(ichar (n(9))
(ichar(n(l))
return
end
2 +
2 +
2 +'
2 +
2 +
2 +
2 +
2 +
2 +
2 4
6)
3)
8)
5)
9)
4)
2)
1)
0)
10
20
finds length of a string (str) of max length mien (position of last
non-blank character)
function length (str(mlen)
character*! str(mien)
k - mien 4 1
k = k - l
if (k.eq.O) goto 20
if (str(k).eq.• ') goto 10
length - k
return
end
c centers a string (str) in a field of len characters, padded on both
c sides by blanXs. strips away leading blanks, then pads it back out,
377
-------
2.4
Listing of Computer Program for Dunnett's Procedure (Continued)
10
30
40
subroutine center (str,len)
character*! str(l)
if (length(str,len).eq.O) return
kl = 0
kl - kl + 1
if (str(kl).eg.' '} goto 5
k2 - length (str,len}
ilen - k2 - kl + 1
do 10 k-kl,k2
str(k-kl-H) * str(k)
call pad (str,ilen,len)
imov * (len-ilen)/2
do 30 k=ilen,l,-l
strfk+imov) = str(k)
do 40 k=l,imov
str(k) - ' *
return
end
10
left justifies a string, pads with blanks to the right
subroutine leftj (str,len)
character*! str(l)
if (length(str,len).eq.O) return
kl = 0
kl - kl + l
if (str(kl).eq.' ») goto 5
k2 = length (str,len)
ilen - k2 - kl + l
do 10 k=kl,k2
str(k-kl-t-i) = str(k)
call pad (str,ilen,len)
return
end
10
right justifies a string of length len, pads with blanks at left
subroutine rightj (str,len)
character*! str(l)
if (length(str,len).eq.O) return
kl « 0
kl = kl + 1
if (str(kl).eq.' ') goto 5
k2 «= length (str,len)
ilen « k2 - kl + l
do 10 k«k2,kl,-l
str(k-k2+len) « str(k)
call pad (str,0,len-ilen)
return
end
378
-------
;
Listing of Computer Program for Dunnett's Procedure (Continued)
c strips the dollar sign (col 1) from a fortran string of length len
c pads with a blank at the right. *««gtn ien,
subroutine stripp (str,len)
character*! str(l)
if (str(l).eq.'$') then
do 10 k=l,len-l
10 str(k) = str(k+!)
str(len) = ' '
end if
return
end
c copies LEN characters from fortran string FROM to fortran string TO
subroutine copy (from,to,len)
character*! from(len),to(len)
do 5 k=l,len
5 to(k) » from(k)
return
end
c pads fortran string of length LEN to length NEWLEN with blanks
subroutine pad (str, len,newlen)
character*! str(newlen)
do 5 k=len-n,newlen
5 str(k) m ' "
return
end
c forces user to press a function key between Fl and Fn.
c ESC is considered equivalent to Pi.
10
20
function ifnkey (n)
call qinkey (i,k)
if (i.eq.o.and.k.ge.59.and.k.le.(584n)} goto 20
if (i.eq.l.and.k.eq.27) then
ifnkey = 1
return
end if
goto 10
ifnkey - k - 58
return
end
379
-------
2.4 Listing of Computer Program for Dunnett's Procedure (Continue^)
c tests whether the first len characters of two strings are
c identical.
logical function equal (sl,s2,len)
character*! sl(l),s2(l)
equal - .true.
do 5 k=l,len
5 if (sl(k).ne.s2(k)) goto 10
return
10 equal » .false.
return
end
c tests for "same1* col name - upcase, stripp
function same (a,b,len)
character*! a(len),b(len),al(80),a2(80)
logical same,equal
call copy (a,al,len)
call copy (b,a2,len)
call upstr (al,len)
call upstr (a2,len)
call stripp (al,len)
call stripp (a2,len)
if (equal(al,a2,lenj) then
sane = .true.
else
same = .false.
endif
return
end
tests for upper-case equality of strings - capitalizes, then tests,
function uequal (a,b,len)
character*! a(len),b(len),al(80),a2(80)
logical uequal,equal
call copy (a,al,len)
call copy (b,a2,len)
call upstr (al.len)
call upstr (a2,len)
if (equal(al,a2,len)J then
uequal = .true.
else
uequal « .false.
endif
return
end
c prompts user to press any key to continue.
c at the bottom of the screen.
subroutine retcon
message is centered
call goclrc (23,27)
write (*,'(a\)') 'press any key to continue'
call gotorc (23,27)
call qinkey (ji,ji)
return
end
380
-------
APPENDIX D
BONFERRONI'S T-TEST
1. Bonferroni's T-test Is used as an alternative to Dunnett's Procedure
[when the number of replicates is not the same for all concentrations. This
[test sets an upper bound of alpha on the overall error rate, in contrast to
•Dunnett's Procedure, for which the overall error rate is fixed at alpha.
[Thus, Dunnett's Procedure is a more powerful test.
. Bonferroni's T-test is based on the same assumptions of normality of
distribution and homogeneity of variance as Dunnett's Procedure (See,
[Appendix B for testing these assumptions), and, like Dunnett's Procedure,
uses a pooled estimate of the variance, which is equal to the error value
calculated in an analysis of variance.
3. An example of the use of Bonferroni's T-test is provided below. The
data used in the example are the same as in Appendix C, except that the
third replicate from the 32% effluent treatment is presumed to have been
lost. Thus, Dunnett's Procedure cannot be used. The weight data are
presented in Table D.I.
TABLE D.I. SHEEPSHEAD LARVAL GROWTH DATA (WEIGHT IN MG)
USED FOR BONFERRQNI'S TEST
Effluent i
Cone {*)
Replicate Test Vessel
1 2 3
Total
Mean
Control
1.0
3.2
10.0
32.0
1
2
3
4
5
1.017
1.157
0.998
0.873
0.715
0.745
0.914
0.793
0.935
0.907
0.862
0.992
1.021
0.839
(Data lost)
2.624
3.063
2.812
2.647
1.622
0.875
1.021
0.937
0.882
0.811
^Prepared by Ron Freyberg, Florence Kessler, John Menkedick and Larry
Wymer, Computer Sciences Corporation, 26 W. Martin Luther King Drive,
Cincinnati, Ohio 45268; Phone 513-569-7968.
381
-------
*.,in ?? estimate of the P°oled variance is to construct an
table including all sums of squares, using the following formulas:
Total Sum of Squares: SST = I Y? . - G2/N
Between Sum of Squares: SSB = Z T?/n . - G2
i 7 7
Within Sum of Squares: SSW = SST - SSB
/N
Where: G = The grand total of all sample observations; G
N = The total sample size; N = E n.
E T.
1
n. - The number of replicates for concentration "i".
Ti = The total of the replicate measurements for concentration "i"
Yij = The ^th observation for concentration "i".
3.2 Calculations:
Total Sum of Squares: SST = I Y?. - G2/N
i -i J
- 11.832 -
= 0.188
12.768'
14
Between Sum of Squares: SSB = £ T?/n. - G2/N
= 11.709 - (12.768}2/14
= 0.064
[Within Sum of Squares: SSW = SST - SSB
= 0.188 - 0,064
= 0.124
382
-------
3.3 Prepare the ANOVA table as follows:
TABLE D.2. GENERALIZED ANOVA TABLE
Source
DF Sum of
Squares {SS)
Mean Square (MS)
(SS/DF) .
Between b - 1
Within N - b
SSB
SSW
= SSB/(b-l)
= SSW/(N-b)
Total
N - 1
SST
*b = Number of different concentrations, including the control.
3.4 The completed ANOVA table for this data is provided below;
TABLE D.3. COMPLETED ANOVA TABLE FOR BONFERRONI'S TEST
Source
DF
SS
Mean Square
Between 5-1=4 0.064
Within 14 - 5 = 9 0.124
0.016
0.014
Total
13
0.188
383
-------
3.5 To perform the individual comparisons, calculate the t statistic for
each concentration and control combination, as follows:
(yi -V
[S
w
+ (l/n.J]
Where:
w
nl
ni
= Mean for each concentration
= Mean for the control
= Square root of the within mean square
= Number of replicates in the control.
= Number of replicates for concentration "i"
3.6 Table D.4 includes the calculated t values for each concentration and
control combination.
TAB.E 3.4. CALCULATED T VALUES.
Effluent
Concentration i
1.0 2
3.2 3
10.0 4
32.0 5
11
- 1.511
- 0.642
- 0.072
- 0.592
384
-------
3.7 Since the purpose of the test is only to detect a decrease in growth
from the control, a one-sided test is appropriate. The critical value for
the one-sided comparison (2.686), with an overall alpha level of 0.05, nine
degrees of freedom and four concentrations excluding the control, was
obtained from Table D.5. Comparing each of the calculated t values in
Table D.4 with the critical value, no decreases in growth from the control
were detected. Thus the NOEC is 32.0%.
385
-------
TABLE 0.5. CRITICAL VALUES FOR BONFERRGNI'S "T"
P = 0.05 CRITICAL LEVEL, ONE TAILED
i
D.F.
2
f £
I 5
i $
i i
1 !
i ,2
? 10
i u
£ 12
1 1!
I JJ
f 16
? ,17
1 8
L I9
20
21
23
24
25
?*
2 7
28
29
30
31
22
33
34
35
26
3?
39
39
40
50
60
70
£0
SO
103
110
120
IMF.
D.F. =
K =
K
6
2
- 1 K = 2
.314 12.707
.920 4,303
2. 354
2.132
4
i
i
:
;
i
i
]
]
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
t
i
.016
.94*
.895
. 660
.834
.6)13
. 796
.783
.771
. 762
. 754
.746
. 740
.735
.730
. 725
.721
. 718
. 714
.711
.709 .
. 706
. 704
. 702
. 700
.6*8
.696
.694
.693
.691
.690
.689
.688
.686
.685
.684
.676
.671
.66?
.665
.662
.661
.659
658
.645
Degrees
Number
3.183
2.777
2.571
2.447
2.365
2.307
2.263
2.229
2.201
2. 179
2.161
2. 145
2. 132
2.120
2. 110
2. 101
2.394
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.049
2.046
2.043
2.040
2.037
2.035
2.033
2.031
2.029
2.027
2.025
2.023
2.022
2.009
2.001
1.995
1.991
1.967
1 . 5 64
1.9&2
1.980
1.960
of
K = 3
19.002
5.340
3. 741
3.187
2.912
2. 750
2,642
2.567
2. 510
2.4(6
2.432
2.404
2,380
2.360
2.343
2.329
2.316
2. 3C5
2.295
2.206
2.278
2.271
2.264
2.258
2.253
2.246
2.243
2.239
2.235
2.231
2.228
2.224
2. 221
2.219
2.216
2.213
2.211
2.209
2,207
2.205
2.189
2. 179
2.171
2.166
2. 162
2,158
2.156
2.153
2.129
freedom
K = 4
25.452
6.206
4. 177
3.496
3.164
2.969
2. 842
2.752
2.686
2.634
2.594
2.561
2. 533
2.513
2.490
2.473
2.459
2.446
2.434
2.424
2.414
2.406
2 .398
2,391
2.385
2.579
2.374
2.369
2.364
2. 360
2.356
2.352
2. 349
2.346
2.342
2. 340
2.33?
2.334
2.332
2.329
2.311
2. 3UO
2. 291
2.285
2.260
2. 276
2.273
2.270
2.242
for MSE
of concentrations to
K = 5
31.821
6.965
4.541
3. 747
3.365
3. 143
2.998
2.697
2.822
2. 764
2.719
2.661
2.651
2.625
2.603
2.584
2.567
2.553
2.540
2.526
2.518
2. 5C9
2.500
2.493
2.486
2.479
2.473
2. 468
2,463
2.458
2. 453
2.449
2.445
2. 442
2.436
2.435
2, 432
2.429
2.426
2. 424
2.404
2.391
2. 361
£•3 ?^
2.369
2.365
2. 361
2. 353
2. 327
(Mean
K = 6
38. 189
7.649
4.657
J.961
3.535
3.288
3.128
J.016
2.934
2.871
2.821
2.780
2. 746
2.718
2.6^4
2.674
2.655
2.64C
2.626
2.613
2.'592
2.583
2.574
2.566
2.559
2.553
2.547
2.541
2 .536
2. 531
2.527
2.523
2. 519
2.515
2.512
2.508
2.505
2.502
2.499
2.476
2.463
2.453
2^440
i. '35
21*29
2.354
Square
be compared
K = 7
44.556
8. 277
5.138
4.148
3.681
3.412
3.239
3.118
3 .029
2.^61
2.907
2.S63
2. 827
2.797
2.771
2. 749
2. 729
2.712
2.697
2.684
2.672
2. 661
2.651
2.642
2.634
2.627
2.620
2.613
2.607
2.602
2.597
2.592
2.587
2.583
2.579
2.575
2.572
2.560
2.565
2.562
2.539
2.524
2.513
2. 5-C5
2.495
i .494
2 . *• 9 D
2.4g7
2.453
Error)
to the
X = 8
50.924
8. 661
5.392
4. 315
3. 811
3.522
3.336
3. 206
3.111
3.039
2. 981
2 .935
2. 897
2.844
2 .33 7
2.814
2. 793
2.775
2. 759
2. 745
2.732
2. 721
2. 710
2.7C 1
2.692
2. 464
2.677
2.670
2. 664
2.658
2 .652
2. 647
2.643
2.633
2.C34
2.63D
2 .626
2. 623
2.619
2. 616
. 592
.576
. .564
.5*9
C44
.* \ 4 0
2.536
2 .458
K = 9
57.290
9.406
5.626
4.466
3.927
3.619
3.422
3. 285
3. 185
3.108
3. 047
2.998
2.958
2.924
2.C95
2.871
2.849
2.830
2.61 3
2. 798
2. 785
2.773
2. 762
2.752
2.743
2. 734
2. 727
2.720
2.713
2.707
2.701
2. 696
2. 691
2.686
2. 682
2. 678
2.674
Z. 67C
2. 667
2.663
2. 638
2.621
2.609
2. 6CC
2. 593
2.588
2. 583
2. 580
2.540
K = 10
63.657
9. 925
5.841
4 .605
4. 033
3.708
3 .500
3.356
3.250
3.170
3. 106
3.055
3.013
2.977
2.94?
2 .921
2 . 899
2 . 879
2 .861
2. 846
2. 832
2 .819
2. 808
2 . 797
2.788
2.779
2.771
2.764
2.757
2. 750
2.745
2 . 739
2.734
2 .729
2. 724
2. 720
2.716
2.712
2.708
2.705
2.678
2. 661
2.648
2. 639
2. 632
2 .626
2. 622
2.618
2.576
from ANQVA.
control .
386
-------
APPENDIX E
• STEEL'S MANY-ONE RANK TESll
11. Steel's Many-One Rank Test is a nonparametric test for comparing
^treatments with a control. This test is an alternative to the Dunnett's
Procedure, and may be applied to the data when the normality assumption has
not been met. Steel's Test requires equal variances across the treatments
;and the control, but it is thought to be fairly insensitive to deviations
|from this condition (Steel, 1959). The tables for Steel's Test require an
[equal number of replicates at each concentration. If this is not the case,
.use Wilcoxon's Rank Sum Test, with Bonferroni's adjustment (See Appendix F).
12. For an analysis using Steel's Test, for each control and concentration
[combination, combine the data and arrange the observations in order of size
'from smallest to largest. Assign the ranks to the ordered observations (1
to the smallest, 2 to the next smallest, etc.). If ties occur in the
ranking, assign the average rank to the observation. (Extensive ties would
invalidate this procedure.) The sum of the ranks within each concentration
and within the control is then calculated. To determine if the response in
a concentration is significantly different from the response in the control,
the minimum rank sum for each concentration and control combination is
compared to the critical value in Table E.5. In this table, k equals the
number of treatments excluding the control and n equals the number of
replicates for each concentration and the control.
3. An example of the use of this test is provided below. The test employs
survival data from a mysid 7-day, chronic test. The data are listed in
Table E.I. Throughout the test, the control data are taken from the site
water control. Since there is 0% survival for all eight replicates for the
32% concentration, it is not included in this analysis and is considered a
qualitative mortality effect.
4. For each control and concentration combination, combine the data and
arrange the observations in order of size from smallest to largest. Assign
the ranks (1,2,3, ... 16) to the ordered observations (] to the smallest,
2 to the next smallest, etc.). If ties occur in the ranking, assign the
average rank to the observation.
5. An example of assigning ranks to the combined data for the control and
0.32% effluent concentration is given in Table E.2. This ranking procedure
is repeated for each control and concentration combination. The complete
set of rankings is listed in Table E.3. The ranks are then summed for each
effluent concentration, as shown in Table E.4.
^Prepared by Ron Freyberg, Florence Kessler, John Menkedick and Larry
Wymer, Computer Sciences Corporation, 26 W. Martin Luther King Drive,
Cincinnati, Ohio 45268; Phone 513-569-7968)
387
-------
jj6. For this set of data, we wish to determine if the survival in any of the
jef fluent concentrations is significantly lower than the survival of the
|control organisms. If this occurs, the rank sum at that concentration would
fbe significantly lower than the rank sum of the control. Thus, we are only
Iconcerned with comparing the rank sums for the survival at each of the
Ivarious effluent concentrations with some "minimum" or critical rank sum, at
[or below which the survival would be considered to be significantly lower
fthan the control. At a probability level of 0.05, the critical rank sum in
test with four, concentrations and eight replicates per concentration,
|is 47 (see Table F.4).
Of the rank sums in Table E.4, none are less than 47. Therefore, due to
fthe qualitative effect at the 32% effluent concentration, the NOEC is 10%
[effluent and the LOEC is 32% effluent.
388
-------
TABLE E.I. EXAMPLE OF STEEL'S MANY-ONE RANK TEST-
SURVIVAL DATA FOR MYSID 7-DAY CHRONIC TEST
Effluent
Concentration
Control
(Site Hater)
Control
(Brine «
Dilution water)
0.32?
1.0?
3.2%
10.0*
32. 01
Replicate
Chamber
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7 •
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
Number of
My s Ids at
Start of Test
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
• 5
5
5
5
5
5
5
5
5
5
5
Number of
Live Mysids
at End of Test
4
4
5
4
5
4
4 '
5 ;
3
5
3
3
4
4
3
3
4
4
4
5
4
4
5
3
3
4
5
4
4
4
5
5
5
4
5
3
5
4
4
3
5
5
5
5
3
5
4
4
0
0
0
0
0
0
0
0
389
-------
TABLE E.2. EXAMPLE OF STEEL'S MANY-ONE RANK TEST: ASSIGNING
RANKS TO THE CONTROL AND 0.32% EFFLUENT CONCENTRATIONS
Rank Number of Live
Mysids
Control or 0.32% Effluent
1
6.5
6.5
6.5
6.5
6.5
6,5
6.5
6.5
6.5
6.5
14
14
14
14
14
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
0.32%
Control
Control
Control
Control
Control
0.32%
0.32%
0.32%
0.32%
0.32%
Control
Control
Control
0.32%
0.32%
TABLE E.3. TABLE OF RANKS
1 It Replicate
ml Lnamber
as I
ill 4
H2 4
H3 5
H4 4
I6 4
1 l
Control 1
" i —
{6.5,6,6.
(6.5,6,6.
(14,13.5,
(6.5,6,6.
£14,13.5,
(6.5,6,6.
(6.5,6,6.
(14,13.5,
~ •
5,5}
5,5)
13.5,12.5}
5,5}
13.5,12.5)
5,5)
5,5)
13.5.12.5}
U
4
4
4
5
4
4
5
3
Effluent Concentrating (%}
.32
^ ^-^— *™^
(6.5)
(6.5)
(6.5)
(14)
(6.5)
(6.5)
(14)
(1)
1
3
4
5
4
4
4
5
5
.0
, — __
(1)
(6)
(13.5)
(6)
(6)
(6)
(13.5)
(13.5)
3
5
4
5
3
5
4
4
3
.2
— — •
(13.5)
(6.5)
(13.5)
(1.5)
(13.5)
(6.5)
(6.5}
(1.5)
10.0
* i .
5 (12.5)
5 (12.5)
5 (12.5)
5 (12.5)
3 (1)
5 (12.5)
4 (5)
4 (5)
°rder °f the Concentration with which they
390
-------
TABLE E.4. RANK SUMS
Effluent
Concentration
Rank Sum
0.32
1.00
3.2
10.0
61.5
65.5
63.0
73.5
TABLE E.5. SIGNIFICANT VALUES OF RANK SUMS: JOINT CONFIDENCE
COEFFICIENTS OF 0.95 (UPPER) and 0.99 (LOWER) FOR
ONE-SIDED ALTERNATIVES
n
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
k =
2
11
18
15
27
23
37
32
49
43
63
56
79
71
97
87
116
105
138
125
161
147
186
170
213
196
241
223
272
252
304
282
339
315
number
3
10
17
—
26
22
36
31
48
42
62
55
77
69
95
85
114
103
135
123
158
144
182
167
209
192
237
219
267
248
299
278
333
310
of treatments
4 5
10
17
—
25
21
35
30
47
41
61
54
76
68
93
84
112
102
133
121
155
142
180
165
206
190
234
217
264
245
296
275
330
307
10
16
• —
25
21
35
30
46
40
60
53
75
67
92
83
111
100
132
120
154
141
178
164
204
188
232
215
262
243
294
273
327
305
(excluding
6 7
10
16
_
24
_
34
29
46
40
59
52
74
66
91
82
110
99
130
119
153
140
177
162
203
187
231
213
260
241
292
271
325
303
-
16
_
24
_
34
29
' 45
40
59
52
74
66
90
81
109
99
129
118
152
139
176
161
201
186
229
212
259
240
290
270
323
301
control )
8 9
-
16
_
24
_
33
29
45
39
58
51
73
65
90
81
108
98
129
117
151
138
175
160
200
185
228
211
257
239
288
268
322
300
_ ' ' -
15
23
33
29
44
39
58
51
72
65
89
80
108
98
128
117
150
137
174
160
199
184
227
210
256
238
287
267
320
299
1959.
391
-------
APPENDIX F
WILCOXON RANK SUM TEST
1. Wilcoxon's Rank Sum Test is a non-parametric test, to be used as an
nl 'thP ^ t0t Ste6 'S Many-°ne Rank "est whe" the n^ber of replica?es are
not the same at each concentration. A Bonferroni's adjustment of the
W<0T°r rate f°J comPa^°n °f each concentrat o vTtVcon rol is
Ma" Ter b°Und of a]Pha on the overall error rate, in contrast
Ih "an£0n',Ra?k T«t. f°r "hich the overall error rate Is fixed Jt
Thus, Steel's Test is a more powerful test.
e in
hsev r^ice
wl'th reproduction data from the
Observation
L,n°I tea^?^n!ra.t.!°,n.a!;d "zlrfrrs^ne^to^ar"6 ^ "** • ^
in rank occur, assign the average rank to the
effl^f^L^fL5:9"1',"!/?^?,10 the combined data for the control and
5. For this set of data, we wish to determine if the fertility in anv of
?s thCrra%npraJh°nS VS S1'9"jfl'Cantly lo«er than in the contro . When
contro! i5?i K!'- thVankJUtn1for that """ntration compared to the
control W111 be significantly lower than the rank sum given by the averaae
frank over both concentrations times the number of replicates at that test
f Teacher ^^r^ WUh C0m"ar1n thfrank sum V S
crit rlnt, Inn, VhS ft1"6^.00"06"^3110"5 W1'th some '"Inimum" or
[critical rank sum, at or below which the fertility would be considered to he
sigmncantly ower than the control. At a probability level of 0 OS the
critical rank in a test with four concentrations and seven repllcates'in the
|control is 44 for those concentrations with eight replicates and 34 for
jthose concentrations with seven replicates (sel Table F?5. fSr R - 4).
rn t °f th!! ^ank s™s 1n Tab]e F'4> only ^e 10% effluent concentration does
fnot exceed _ its critical value of 44. Therefore, the LOEC for ?he test on
fertilTty 1S 10% effluent, and the NOEC is 3.2% effluent
L P r by Ron Freyberg, Florence Kessler, John Menkedick and Larry
Wymer, Computer Sciences Corporation, 26 W. Martin Luther Kina Drive
Cincinnati, Ohio 45268; Phone 513-569-7968) 9 '
392
-------
TABLE F.I. EXAMPLE OF WILCOXON'S RANK SUM TEST-
FECUNDITY DATA FOR MYSID 7-DAY CHRONIC TEST
Effluent
Concentration
Control
(Site Water)
Control
(Srine &
Dilution water)
0.32?
1 fW
. ire-
3.2$
10.0?
32.0%
Replicate
Chamber
1
2
3
4
5
6
7
8
1
2
3
4
5
6
_ 7
8
1
2
3
4
5
6
7
8
1
3
4.
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
•3
4
5
6
7
8
Number of
Hysids at
Start of Test
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5 -'•; '•
5
5
5
5
5 ..-.
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
Number of Proportion
Live Mysids • of Females
at End of Test With Eggs
4 0.50
4
5 0.75
4 0.67
5 0.67
4 0.50
4 1.00
5 1.00
3 1.00
5 1.00
3 1.00
3 1.00
4 1.00
4 0.50
3 0.50
3 0.50
4 1.00
4 0.50
4 0.67
5 1.00
4 0.50
4 1.00
5 1.00
3 0.00
3 0.50
4 0.00
5 0.75
« 1 . 00
4 l . 00
.. '* 1.00
' -' 5 0.67
i! 5. 0.67
5 0.33
4 0.50
5 1.00
3
5 1.00
4 0.00
4 0.33
3 0.50
5 0.00
5 0.50
5 0.33
5 0.00
3 0,50
5 0.00
4 0.50
4 Q.50
. •• 0
0
0
0
0
0
0
0
393
-------
TABLE F.2. EXAMPLE OF WILCOXON'S RANK SUM TEST: ASSIGNING
RANKS TO THE CONTROL AND EFFLUENT CONCENTRATIONS
Rank Proportion of
Females W/Eggs
Site Water Control
or 32% Effluent
1
3.5
3.5
3.5
3.5
7
7
7
9
12.5
12.5
12.5
12.5
12.5
12.5
0.00
0.50
0.50
0.50
0.50
0.67
0.67
0.67
0.75
1.00
1.00
1.00
1.00
1.00
1.00
0.32%
Control
Control
0.32%
0.32%
Control
Control
0.32%
Control
Control
Control
0.32%
0.32%
0.32%
0.32%
I TABLE F
I Site Water
j 1 Rep Proper- Control Rank
i i
1
I
I ;
i |
|| :
•' i
1
1
2
3
4
5
6
7
8
tion
0.50 (3.5,3,5.5,7,5)
- - - -
0.75 (9,9.5,10,13)
0.67 (7,6.5,8.5,11.5)
0.67 (7,6.5,8.5,11.5)
0.50 (3.5,3,5.5,7.5)
1.00 (12.5,13,12.5,14.
1.00 (12.5,13,12.5,12.
aControl ranks are given in
.3. TABLE OF
Effluent
0.32
1
0
0
1
0
1
5) 1
5) 0
the
.00
.50
.67
,00
.50
.00
.00
.00
(12.5)
(3.5)
(7)
(12.5)
(3.5)
(12.5)
(12.5
(1)
order of the
RANKS 1
Concentration (%)
.,1.0
0.50
0.00
0.75
1.00
1.00
1.00
0.67
0.67
(3)
(1)
(9.5)
(13)
(13)
(13)
(6.5)
(6.5)
3.2
0.33
0.50
1.00
--
1.00
0.00
0.33
0.50
(2.5)
(5.5)
(12,5)
(12.5)
(1)
(2.5)
(5.5)
concentration with which
10.0
0.00
0.50
0.33
0.00
0.50
0,00
0.50
0.50
they
(2)
(7.5)
(4)
(2)
(7.5)
(2)
(7.5)
(7.5)
K were ranked.
394
-------
TABLE F.4. RANK SUMS
Effluent
Concentration
(*)
0.32
1.00
3.2
10.0
Rank Sum
65
65.5
42
40
No. of
Replicates
8
8
7
8
Critical
Rank Sum
44
44
34
44
TABLE F.5. CRITICAL VALUES FOR WILCOXON'S RANK SUM TEST WITH
aONFERRONI'S ADJUSTMENT OF ERROR RATE FOR COMPARISON
OF "K" TREATMENTS VS A CONTROL FIVE PERCENT CRITICAL
LEVEL (ONE-SIDED ALTERNATIVE: TREATMENT CONTROL)
K No. Replicates No.
in Control
1 3
4
5
6
7
8
9
10
2 3
4
5
6
7
8
9
10
3
6
6
7
8
8
9
10
10
_ _
_-
6
7
7
8
8
9
of ReplicatesrEffluent Concentration
4
10
11
12
13
14
15
16
17
— —
10
11
12
13
14
14
15
5
16
17
19
20
21
23
24
26
15
16
17
18
20
21
22
23
6
23
24
26
28
29
31
33
35
22
23
24
26
27
29
31
32
7
30
32
34
36
39
41
43
45
29
31
33
34
36
38
40
42
8
39
41
44
46
49
51
54
56
38
40
42
44
46
49
51
53
9
49
51
54
57
60
63
66
69
47
49
52
55
57
60
62
65
10
59
62
66
69
72
72
79
82
58
60
63
66
69
72
75
78
395
-------
TABLE F.5. CRITICAL VALUES FOR WILCOXON'S RANK SUM TEST WITH
BONFERRONI'S ADJUSTMENT OF ERROR RATE FOR COMPARISON
OF "K" TREATMENTS VS A CONTROL FIVE PERCENT CRITICAL
LEVEL (ONE-SIDED ALTERNATIVE: TREATMENT CONTROL)(CONTINUED)
m K No. Replice
mm in Control
mm.
H — _
BESc o i
H ?
1
1
1
I z
H| o
m 10
II 10
H8|
1 4 2
i
i
1
i
I 9
B 10
msms
KBBy
1 5 2
H 4
1 i
i
1 0
I Q
1 •,»
B 10
B
Ii 6 J
i ; r-
1
i 8
i 9
i 10
i
tes No. of Replicates:Effluent Concentration
3 4
— —
10
11
6 11
7 12
7 13
7 13
8 14
- -
--
10
6 11
6 12
7 12
7 13
7 14
_ _ __
--
10
11
6 11
6 12
7 13
7 13
— - _„
--
10
11
6 Tl
6 12
6 12
7 13
5
_ _
16
17
18
19
20
21
22
— _
15
16
17
18
19
20
21
_ _
15
16
17
18
19
20
21
_ _
15
16
16
17
18
19
20
6
21
22
24
25
26
28
29
31
21
22
23
24
26
27
28
30
— —
22
23
24
25
27
28
29
— —
21
22
24
25
26
27
29
7
29
30
32
33
35
37
39
41
28
30
31
33
34
36
38
40
28
29
31
32
34
35
37
39
28
29
30
32
33
35
37
38
8
37
39
41
43
45
47
49
51
37
38
40
42
44
46
48
50
36
38
40
42
43
45
47
49
36
38
39
41
43
45
47
49
9
46
48
51
53
56
.58
61
63
46
48
50
52
55
57
60
62
46
48
50
52
54
56
59
61
45
47
49
51
54
56
58
60
10
- 57
59
62
65
68
70
73
76
56
59
61
64
67
69
72
75
56
58
61
63
66
68
71
74
56
58
60
63
65
68
70
73
i
i 396
-------
TABLE F.5. CRITICAL VALUES FOR WILCOXON RANK SUM TEST WITH
, uu... u>t-tu
-------
APPENDIX G
PROBIT ANALYSIS
1.1 This program calculates the LC50, LC15, LC10, LC5, and LCI values, and
associated 95% confidence intervals.
2. The program is written in IBM PC Basic.for the IBM compatible PC by
D. L. Weiner, Computer Sciences Corporation, 26 W. Martin Luther King Drive,
Cincinnati, Ohio 45268. A compiled version of the program can be obtained
;from Computer Sciences Corporation by sending a diskette with a written
^request.
j2.1 Data input is illustrated by a set of mortality data from a sheepshead
.minnow embryo-larval survival and teratogenicity test. The program begins
;with a request for the following information:
1. Output designation (P = printer, D = disk file).
2. Title for the output.
3. A selection of model fitting options {see sample output
for a detailed description of options). If Option 2 is
selected, the theoretical lower threshold needs to be entered.
If option 3 is selected, the program request the number of
animals responding-in the control group and the total number
of original animals in the control group be entered.
:, 4. The number of test concentrations.
2.2. The program then requests information on the results at each
concentration, beginning with the lowest concentration.
1. Concentration.
2. Number of organisms responding.
3. Total number of exposed organisms.
2.2.1. See sample data input on the next page.
398
-------
2.2.1 Sample Data Input.
uuuuuuuuuuuuuuuuuuuuuuuuuuuw
u u
ij EPA PRCBIT ANALYSIS PROGRAM U
ij USED FOR CAIXIJLATING DC VALUES U
U Version 1.4 U
UUUiJUUUUUUTOJUU^^
Output to printer or disk file (P / D)? p
Title ? Probit Analysis of Sheepshead Minnow Rnbryo-Larval Data
Model Fitting Options Which Are Available
1) Fit a model which includes two parameters: an intercept and a
slope. This model assumes that the spontaneous response
(in controls) is zero. No control data are entered if this
option is specified.
2) Fit a model which includes three parameters: an intercept, a
slope and a theoretical lower threshold which represents the
level of spontaneous response (in controls). This option
requires the user to input the theoretical lower threshold
(the value must be between 0.0 and 0.99). No control data is
entered if this option is specified.
3) Fit a model which includes three parameters, an intercept, a
slope and a lower threshold. The lover threshold is estimated
based on control data which are input by the user. If the number
responding in the control group is zero, then this option is
indentical to option two (above).
Your choice (1, 2, or 3)? 3
Number of responders in the control group = ? 2
Number of animals exposed in the. concurrent control group = ?
Number of administered concentrations ? 5
20
399
-------
[2.2.1 Sample Data Input (Continued).
Input data starting with the lowest concentration
Concentration = ? 0.5
Number responding = ? 2
Number exposed = ? 20
Concentration - ? 1,0
Number responding = ? 1
-Number exposed - ? 20
Concentration = ? 2.0
Number responding = ? 4
Number exposed = ? 20
Concentration = ? 4.0
Number responding = ? 16
Number exposed = ? 20
Concentration = ? 8.0
Number responding - ? 20
Number exposed = ? 20
Number
1
2
3
4
5
Cone.
0.5000
1 . 0000
2.0000
4.0000
8.0000
Number
Resp.
2
1
4
16
20
, Number
Exposed
20
20
20
20
20
Do you wish to modify your data ? n
The number of control animals which responded
The number of control animals exposed = 20
Do you wish to modify these values ? n
— 2
400
-------
2.3 Sample Data Output
2.3.1 The program output includes the following:
A table of the observed, adjusted (using Abbott's formula)
and predicted proportions responding at each concentration.
Chi-square statistic for heterogeneity. This test is one
indicator of how well the data fit the model.
Estimates of the mean (mu) and standard deviation (sigma)
of the underlying tolerance distribution.
Estimates and standard errors of the intercept and slope of
the fitted probit regression line.
Estimate and standard error of the lower threshold (if
requested - requires control data on input).
A table of estimated EC values and 95% confidence limits.
Please note that EC, effective concentration, is a broad term
and applies to any response, such as fertilization, death or
immobilization. If mortality data is entered in the program
as the response, the EC estimates are equivalent to LC
(lethal concentration) estimates.
A plot of the fitted probit regression line with observed
data overlaid on the plot.
401
-------
[2.3.2 Probit Statistics Output
Probit Analysis of Sheepshead Minnow Embryo-Larval Data
Cone.
Number
Exposed
ftfumber
Resp.
Observed
Proportion
Responding
Adjusted
Proportion
Responding
Predicted
Proportion
Responding
Control
0.5000
1.0000
2,0000
4.0000
8.0000
20
20
20
20
20
20
2
2
1
4
16
20
0.1000
0.1000
0.0500
0.2000
0.8000
1.0000
Chi - Square Heterogeneity = 0.441
Mu
Sigma
Parameter
0.479736
0.150766
Estimate Std. Err.
intercept
Slope
1.818003 0.976915
6.632814 1.804695
Spontaneous 0.084104 0.036007
Response Rate
0.0000
0.0174
-.0372
0.1265
0.7816
1.0000
0.0841
0.0000
0.0007
0.1179
0.7914
0.9975
95% Confidence Limits
( -0.096749,
( 3.095611,
( 0.013529,
3.732756)
10.170017}
0.154678)
Estimated EC Values and Confidence Limits
Point
EC 1.00
EC 5.00
EC10.00
EC15.00
SC50.00
EC85.00
EC90.00
EC95.00
EC99.00
Cone.
1.3459
1.7051
1.9343
2.1061
3.0181
4.3250
4.7093
5.3423
6.7680
Lower Upper
95% Confidence Limits
0.4533
0.7439
0.9654
1.1484
2.2676
3.5656
3.8443
4.2566
5.0712
1.9222
2.2689
2.4871
2.6523
3.6717
6.3827
7.5099
9.6486
15.6871
402
-------
J2.3.3 Plot of Adjusted Probits and Predicted Regression Line.
PLOT OF ADJUSTED HABITS AND PREDICTED RH3*ESSICN LINE
Probit
10-*-
2+
0+0
EC01
H 1 1 h
EC10 EC25 EC50 HT75 EC90
EC99
403
-------
[2.4 Listing of Computer Program for Probit Analysis.
10
20
30
40
50
60
70
80
90
100
1 10
120
130
140
150
160
1 70
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
output is p r o b i t
pv a Iues
t er a t i on
'EPA PROB1T analysis program : Version 1.4 by ti.L.Weiner, 3/24/88
'Written for IBM PC and full compatibles. May requ'ire minor
'modifications for other systems.
DIM NDOSE(20),N8ESP(20),DOSE(20),LDOSE(20),CH1SO(18),T05(18) OP<14>
QY( 14 ) '
DIM UT(20>, YPROB(20), WKY(20), XPR]ME(20), Y(20)
DIM PK4) , 01 (4>,P2(8) ,02(8), P3(5),03<5), PLTT$(51,71)
B1GC=0! : PI = 3.1415926535*
GOSUB 720 ' input dat a
GOSUB 320 ' check for valid data file type
CLS : LOCATE 12,35 : PRINT "Working ...» ...
GOSUB 1970 ' read in t and chisq values
1 sub 1950 is used to compute probits : input is no.r
' sub 2270 is used to compute area under normal curve
FOR I = 1 TO K
W T < 1 ) = 1 ! ' initialize weights to 0 or 1 fcr first
If NRESP(I) = 0 OR NRESP( I ) = NDOSE( I ) THEN UT(I) = 0!
IF BIGC >= NRESP< 1 }/HDOSE< I } THEN WT(I)=0?
XPR 1ME( ! ) = 0!
NEXT I
ITER = 0 ' begin leroth iteration
GOSUB 3180 ' model fitting
GOSUB 3500 ' compute predicted probits , working profaits (wky)
1 and weights (wt>
OK = 0
GOSUB 3640 '
IF OK=1 TKEM
ITER = ITER'
GOTO 210
REH - subroutine to force form feeds
PRINT #2, CHR$(12)
RETURH
REM - check for valid data files , wt
N1=1 : N2=1 : N3=0 : WT( 1 ) =DOSE<1>
FOR I = 2 TO N
FOR J = 1 TO N2
THEN GOTO 390
check for convergence
GOTO 3950 ' convergence achieveo,
• 1 ' begin next iteration
f
is used as a work array here
I = 2
J = 1
1 F DOSE( J ) = WT(J)
NEXT J
N1 = N1 + 1 : UT(N1 ) = DOSE ( I ) : N2 = ti1
NEXT I
FOR 1=1 TO K
IF KRESP(I)>0 AND NRESPf I ) TKEN
WEXT I
IF N3<=1 THEN GOTO 620
N2 = N3
FOR 1 = 1 TO N3 - 1
FOR J=J+1 TO N3
IF UT(1)=WT(J) THEN N2=N2-1
NEXT J
NEXT I
N3 = N2
IF N1 >= 3 AND N3 >= 2 THEN RETURN
IF N1 >= 3 THEN GOTO 620
CLS :PRINT " ":PRINT " "
UT (N3)=DOSE( I )
404
-------
2.4 Listing of Computer Program for Probit Analysis (Continued).
550 PRINT "
560 PRINT »
570 PRINT "
580 PRINT "
590 PRINT »
600 PRINT "
610 IF N3>=2 THEN GOTO 5550
620 CLS: PRINT " ":PR1NT
630 PRINT "
640 PRINT "
650 PRINT »
660 PRINT "
670 PRINT "
680 PRINT "
690 PRINT "
700 PRIKT "
I I £ £ E E E E E E E E E I t E E E E E [ [E[ [ E E E E £ E IE £ E [ E £ E E E £ [£ £[ [ £ £ [ £ E E £ f E E E E E £'
['
[ Note : data file must contain at least three [i
I unique concentration levels. ,,
C ['
t t U til t£E££ [££££££[ EEEEEEEE££[tEEE££[E£f [£[[[£££[ E [£££££££££'
II E f EE E E £ £ EE E EE EEEIE E££E EEf EEEEEE EEEEEEfE £ EUI ' I E £ EEEE [ £'EEEE'
V
t Note : data filemust containat ieest t we ri
I concentrations for K h i c ,h t^epercert r'
E responding is between OX arc 10C% M
E 11 E E E f m E E E E i r n .m E M ; [ E E £ i E E E i; i r i E E : M : E :: E : E E E E E E E £ E m •
: P R I N T " "
710 GOTO 5550
720 REH • Data Input subroutine
730 PR!(JT " I tEEEEEEEEIEEEEEEEEUtEE EMCEE £[[[[[ EEICEMd; ME E£E£EEEEEEE'
740PRINT"[
750 PRINT " [ EPA PROSIT ANALYSIS PROGRAM [.
760PRINT" E USED FOR CALCULATING EC VALUES p
7 7 0 P R I N T » [ V e r s * o n 1 . 4 £,
780 PR!"T " (EEEEEEUEi £E I t £ I E E £ £ £ E £ t £ £ E I E £ £ [ [ £ E E E £ £ IE £ E M : I E t E I £ £ E E E £ E E £'
790 PRINT " " : PR I NT " "
800 INPUT "Output to printer or dis-k file (P / D)";ANS$
810 IF AWS$='"" TS*EV G 07 0 8CD
820 ANS$ = LEFTt(AKSS( 1 >; I F ASC(ANS$}>96 THEN ANS$ = ChRS{ASC"P" AND ANS$<>U'D" GOTO 800
840 IF ANS$="P" THEN F 1 L E S ="Ip t1 :"
850 IF ANS$ = »D" THEN INPUT "File ns-ne for outpLt"; FILES
860 INPUT "Title ";TITLE$
870 OPEN FILES FOR OUTPUT AS #2
880 PRINT #2," »
890 PRINT #2," EPA PROSIT ANALYSIS PROGRAM"
900 PRIHT #2," USED FOR CALCULATING EC VALUES"
910 PRINT 32," Version 1.4"
920 PRINT #2," ": PRINT #2," " : P R I N T it 2, " ": CLS
Model Fitting Options Which Are Available ni:PRIHT " "
1) Fit a model which includes two parameters: a-i intercept and
930 PRINT '
940 PBINT "
a"
950 PRINT »
960 PRINT "
970 PRINT »
980 PRINT "
a"
990 PRINT "
the"
1000 PRINT "
1010 PRINT »
1020 PRINT »
is"
1030 PRINT "
1040 PRINT "
a"
slope. This model assumes tKat the spontaneous response"
(in controls) is lero. No control data are entered if this"
option is specified,";PRINT " "
2) Fit a model which includes three parameters: en intercept
slope and a theoretical lower threshold which represents
level of spontaneous response (in controls). This option"
requires the user to input the theoretical lower threshold"
(the value must be between 0.0 and 0.99). No control data
entered if this option is specified.":PRINT " "
3) Fit a model which includes three parameters, an intercept,
405
-------
2.4 Listing of Computer Program for Probit Analysis (Continued).
1 070
1080
1090
1100
1110
1 120
1 130
1140
1 150
1 160
1 170
1 ISO
1 190
1200
1210
1220
1230
124C
1250
1260
1270
1280
1290
1300
1310
1320
1330
1340
1350
1360
1370
1380
1390
1400
1410
1420
1430
1440
1450
1460
1470
1480
slope and a lower threshold. The lower threshold is
responding in the control group is zero, then this opti
1050 PRINT "
est imated"
1060 PRINT " based on ^ntrol data which are input by the user. If the
number"
PRINT "
i s "
PRINT " indenttcal to option two (above).":PRINT " "
INPUT » Tour choice <1, 2, or 3 ) » ; C H 0 S
IF CHOI <> "I" AND CHCS <> •' 2 '• AND CHOJ <> » 3 » THEN CLS : GOTO 930
IF CMOS = "1" THEN CLS : GOTO 1240
•IF C H Q $ = •' 3 " THEN CLS : GOTO 1160
CLS : INPUT "Spontaneous response rate ";BIGC
IF B1G01I OR BJGC<0. THEN PRINT "Value must be between 0 a-d 1 » : G 0 T 0
GOTO 1240
INPUT "Number of responders in the control group = " - N R C T R i.
IT NRC7RL<=0 THEN PRINT "Number must be greater than 0, please reenter"
GOTO 1160
INPUT "Number of animals exposed in the concurrent contrcl group - ...
NCTRL '
IF NCTRL < 0 THEN PRINT » I n v a I i d numbe r , please r e e n t e r -• : G 0 T 0 1180
IF NRCTRL>NCTRL THEN PRINT "The number of responders must be no greater"
IF NRCTRL>NCTRL THEN PRINT "than the number exposed, please r e e n t e r'- -
GOTO 1160
C = NRCTRL / NCTRL ' empirical control resp
B1GC = C '^itiaE predicted control resp
1VPUT "'Number of administered concent rat icr-s "' • N
* 1 = N : I f NCTRL > 0 THEN N1 = Ni + f
IF N> = 3 THEN GOTO 1290
CLS
PRINT "Sot enough concert rat i on levels to fit s mode I"' : GO' C 55-50
3F N1>20 THEN PRINT '-Maximum number of concentration levels exceeded'"
GOTO 5550
CLS
PRINT:PRINT»lnput data starting with the lowest cone entration"•PR INT
DOSE(O) = 0 ' dummy value
FOR J = 1 TO N
INPUT"Concentrations " ; D 0 S E ( J )
IF DOSE(J)<=0 THEN PRINT "Invalid concentration - please ree-ter» • GOT 0
1340
IF DOSE(J> > DOSE(J-1) THEN GOTO 1390
PRINT :PRINT "Concentrstions must be entered in ascending o^der - tow to
h i g h . »
PRINT "Please reenter the data.":GOTO 1310 '-
LDOSE(J) = LOG(OOSE(J ) )/2.3025851* MoglO dose
INPUT "Number responding = ";NRESP(J>
IF NRESP(J)<0 THEN PRINT "Invalid number - please r e en t er •': GO T 0 1400
INPUT "Number exposed = ";NDOSE(J)
IF NRESP(J)>NOOSE(J) THEN PR I NT"Number responding can't be greater than
number exposed • please reenter": GOTO 1340
PRINT
NEXT J
CLS
PRINT " Number Number
PRINT " Number Cone. Resp. Exposed "
406
-------
2.4
Listing of Computer Program for Probit Analysis (Continued).
1 490
1500
1510
1520
1530
1540
1550
1560
1570
i1580
ft 590
;1600
1610
1620
1630
1640
1650
1660
1670
1680
1690
1700
1710
1720
1730
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1750
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1780
1790
1800
1810
1820
1830
1840
1850
1S60
•1870
|
[1830
[1890
j1900
-1910
,1920
|1930
1940
i1950
ntfan
####";I;DOSE{I),
: GOTO
PRINT "
FOR 1 = 1 70 N
PRINT USING" # #
NRESP( I ),NDOSE( I )
NEXT 1
PRINT: INPUT "Do you wish to modify your data " ; A N S S
IF A N S * = " " THEN GOTO 1530
ANS$ = LEFT$(ANSS, 1 } : I F ASC(ANS$)>96 THEN ANS$ = CHRJ(ASC(ANS$) - 32>
IF ANS$<>"N" AND ANS$<>"T" THEN GOTO 1530
IF ANS$="N" THEN GOTO 1680
INPUT "Observation Number to be modified "; 10 B
IF I08< = 0 OR IOB>N THEN PRINT" Invalid Kumber":GOT 0 1535
INPUT "Concentration = ";DOSE{IOB>
IF OOSE(10B}<=0 THEN PRINT "Invalid concentration - p esse -eenter
1600
LDOSE( IOB) = LOG(COSE( I 0B})/2.302585 1 # 'IcglC dcse
INPUT "Number responding = ";KRESP96 T H E H A S S 1 = C ri R S C A S C ( A *, S S 3 - 3 2 >
IF ANSS<>"N" AND ANS4<>"'Y" THEN GOTO 1710
IF ANS$="N» THEN GOTO 1950
INPUT "Spontsneous response rate ";B1GC
IF BIG01! OR B1GC<0! THEN PRINT "Value must be between 0 and l "-GOTO
1760
GOTO 1950
PRINT "The number of control animals which responded = ";kRCTRL
PRINT "The number of control animals exposed = " ; KCTRL
INPUT "Do you wish to modify these values ";ANS$
IF ANSt="» THEN GOTO 1680
ANS$ = LEFT$(ANS$, 1): If ASC(ANS$)>96 THEN ANS$ = CHR$tASC(ANSS3 - 32)
IF ANSSo»N" AND ANSS<>"Y" THEN GOTO 1680
IF ANS$="N" THEN GOTO 1950
INPUT "Number of responders in the control group = ",-NRCTRL
IF NRCTRL< = 0 THEN PRIVT "Number must be greater th3r. 0, piease reenter"
GOTO 1860
INPUT "Number of animals exposed in the concurrent control group =
NCTRL
IF NCTRL < 0 THEN PRINT "Invalid number, please reenter":GOTO 1880
IF NRCTRL>NCTRL THEN PRINT "The number of responders must be no greater"
IF NRCTRL>NCTRL THEN PRINT "than the number exposed, please reenter":
GOTO 1860
C = NRCTRL / NCTRL ' empirical control resp
BIGC 3 C ' initial predicted control resp
GOTO 1680
CLS
RETURN
407
-------
,4 Listing of Computer Program for Probit Analysis (Continued).
1970
1980
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
2110
2120
2130
2140
2150
2160
2170
2180
2190
2200
2210
2220
2230
2240
2250
226C
227G
2280
2290
2300
2310
2320
2330
2340
2350
2360
2370
2380
2390
2400
2410
2420
2430
2440
2450
2460
2470
2480
2490
2500
2510
subroutine to toad in op, o y, t 0 5 , chisq
FOR I = 1 TO 9
READ OP( 1 ) ' op
NEXT 1
DATA .01 , . 05, . 1
values are percent i I e s for predicted curve
.15, .5, .85, .9, .95, .99
oy values are probits corresponding to Op values
6.0364
( a I pha = O.C5 t wo- s
c f freedom
( df )
FOR I = 1 TO
READ OY( I )
NEXT I
DATA 2.6737,3.3551,3.7184,3.9636,5.
DATA 6,2816,6.6449,7.3263
' TOS values are 97.5 pereentiles
for a t-distributio.n. I denotes the degrees
1 and runs from Idf to 18df
FOR I = 1 TO 18
READ T 05 (.1 }
NEXT I
DATA 12.706,4. 303,3. 182,2, 776,2.571,2.447,2.365, 2. 3C6
DATA 2.262,2.228,2.201 ,2. 179,2.16,2.145,2. 131 ,2! 12,2. 11,2. 101
CHISQ values are 95 pereentiles (alpha =C,05 two sided)
1 for a chi-squa'e distribution. I denotes the degrees of freedom
' (df) and runs from Idf to ISdf.
FOR I = 1 70 18
READ CM I S0< I )
NEXT I
DATA 3.841,S.991,7.815.9.488,11.07,12.592,14. fl'67, 15.5:7
DATA 16.919, 18.307,19.675.21.026,22.342.23.685,24.9
DATA 27.587,28. 869
RETURN
' subroutine to co-put p r o b •" t s
' input is nd,r * h e r e nd = *exposed and
1 output = pr ob i t
•6 , 2* . 296
precision equals that of BASIC
P = R/ND
PPP=PP
If R=0 AND 1TER=0
IF R = ND AND I TER = 0
IF BIGC >= P THEN
PP= (P - BIGC >/( 1 !
BIGC)
= #respor.din3
Abbotts
THEN XP = - 105 : GOTO 2570
THEN XP= 105 : GOTO 2570
XP=- 1 05 : GOTO 2570
•nfinfty if
nf i rit y 'f
P0=-.322232431088*
P1 = - 1 ! : P2=-.342242088547*
P4=-.0000453642210148*
Q0=.099348462606* : Q1=.588581570495*
02 = .531103462366* : 03=.10353775285*
04= .0038560700634*
XP = 0
IF PPP > .5 TKE» PP = 1 • PP
IF PP=.5 THEN GOTO 2570
Y = SQR(IOG<1/(PP*PP»)
P3=- .02C423121G24S*
M
T2
T3
T4
U1
(T*P4
(T1 +
*
PI ) «
PO )
+ Q3)
408
-------
12.4 Listing of Computer Program for Probit Analysis (Continued).
2520
2530
2540
2550
2560
2570
2580
2590
2600
2610
2620
2630
2640
2650
2660
2670
2680
2690
2700
2710
2720
2730
2740
2750
2760
2770
. 2780
279C
2SOO
2810
2823
2830
2840
2850
2860
2870
2880
2890
2900
2910
2920
2930
2940
2950
2960
2970
2980
2990
3000
3010
3020
3030
3040
3050
3060
U2
U3
U4
XP
1 F
= ( U1
= (U2
= (U3
U4 )
XP=-XP
integral
pvaIue
of normal distribution
PU2)»21 .97926161894152*
PU4) = -3.56098437CT815390
Q1(2)=91 . 1649054C45T49*
02)
01)
00 )
= r + = 0 THEN 2= Z/SOR(2)
P1< 1 ) = 242.6679552305318* :
P1(3)=6.996383488619135# :
OK 1 } = 215.0588758698612* :
01 (3) = 15. 08279763040779* :
P2< 1 ) = 300.4592610201616* ;
P2<3)=339.3208167343437* ;
P2<5 )=43. 16222722205673* :
P2(7)=.564195517478974* :
G2<1) = 300.4592609569833*
Q2(3)=931.354094S506096#
02(5}=277.5854447439876*
Q2{7)=12.78272731962942*
P3(1)=-2.996107077035422D
P3<3) = - .2269565935396869* :
P3(5) = -2. 23192459734 1.847S-02
03C}=1.062C92305284679D-C2 : C3(2)».19T3C89261G782SB*
fl3(3)=1.051675107C67932# : Q3<4>=1.98733201817T3<3*
Q3(5 } = 1#
CONST*.3939422804014327*
1 F 2 > 4 # G 0 T 0 3 0 1 0 ...
IF Z >= .46875* GOTO 2920
TOP=P1(1):BOT=01(1)
FOR 1 = 2 TO 4 '.'•'•".
1 1 = 2 * ( I - 1 ) : z 2 = Z ' I 1 •; :';
TOP = TOP + P1(I) « 22
BOT=BOT+01(I)*Z2
NEXT! • •' • -
R 1 = TOP / BOT : ERFX =-2 ' fi 1
TOP = P2( 1 ) : BOT = Q2( 1 )
FOR I = 2 TO 8
22 = 2 * I 1
P2( I ) * ZZ
02(I) * 22
02
P2(2)=451.9189537118729*
P2{4)=152.9892850469404*
P2(6)=7.21T758250883094*
P2(8) = -1.3686485 73 S27U7D-07
02(2 ) = 790.950925327898*
02(4)=638.9802644656312*
C2(6)=77.00015293522947*
02(8)=1#
03 : P3(2)=-4.947309t06232507D
P3(4}=-.27S6613CS6C9647S*
02
GOTO 3MO
It = 1-1
TOP = TOP
BOT = BOT
NEXT !
R2 = TOP / BOT : EHFCX = 0*
IF 2 < 13.038* THEN ERFCX = EXP(
ERFX = 1* - ERFCX : GOTO 3110
22 = 1* / (2*2) : TOP = P3(1> : BOT
FOR I = 2 TO 5
2*2)
R2
= 03( 1 )
11 = 2 *
TOP=TOP
NEXT 1
R3 = TOP
(I - 1 ) : 22
• P3
-------
1.4 Listing of Computer Program for Probit Analysis (Continued).
1
1
I
1
i
1
1
i 3070
1 3080
i 3090
1 3100
1 3110
• 3120
iEm 3i3°
mm 3i4G
H 315°
Hi 316°
asm 3170
HR 3180
I^BHB
Hg| 3190
|BJE 3200
ffiS 3210
II 3220
ra| 3230
IH 3240
SlU 3250
iBBB
OH 326°
IH 32?°
EH 3230
IH 329°
IB 330°
HH 3310
IM 3320
I
»ffl
i
P
i
i
1
1
1
(81
1
I
I
L
3330
3340
3350
336C
3370
3380
3390
3400
3410
3420
3430
3440
3450
3460
3470
3480
3490
3500
3510
3520
3530
3540
3550
• 3560
I 3570
I 3580
1 359°
1 3600
W
i 3610
CONST = COHST * SQR<2#) : El = COHST * X2 • R3
ERFCX = Q#
IF 2 < 13.038* THEN ERFCX = ( E X P ( - Z * Z > / 2 ) * E1
E R f X = 1 # - E R F C X
E R F D U = E R F X - ,
IFZ1=OTHENPVALUE=(1+ERFDy)/2!
Z=Z1'recoverz
IF RVALUE <=0 THEN RVALUE =. 000001
IF RVALUE >=1 THEN RVALUE = .999999 : '
RETURN ,
1 subroutine to fit probit model
SNW = Ot : SNUX=0! : SNUY=0! : SNWXY=C! : SNUXX=Q! : SNWYY=G!
SNUXP = 0 > : SKWXPP = 0! : SNUXPY = 0! : SNWXXP = 0!
FOR I s 1 TO M
ND = NDOSE(I) : W = WT{!) : X = LDCSEC1) ; fi = NRESP(I)
NW = ND*W : XPR = XPRIME(l)
IF 1TER <=0 THEN GOSUB 2270 : YPROB(!}=PROBIT : Y=TPKOB 0 THEM Y = WKY(I) ' working probit if not 0 iteration
SNUY = SNWY + NU»Y : SHUYY = SNWYY + KU*Y*Y : SNWXY = SWWXY + N U * X - Y
SVW = SNW '+ NW : SNWX = SKUX + KW*X : SMUXX = SNWXX + KW»X*X
SNUXP = SNWXP + NU-XPR : SMWXPP = SNUXPP + MW*XPR*XPR
SNWXPY = SNWXPY + MW'XPR*Y : SVWXXP = SNUXXP + KW * X * XPft
NEXT 1
X8AR = SNWX/SNH ; YBAR = SNUY/SNU ; XPBAR = SHWXP / SNW
SYY = SNWYY • SNWY * SNWY / SKW : SXX = SNWXX • SKUX * SNWX / SNU
SX.Y = SNWXY - iKWX * SNWY / SNU : SXPXP = ShWXPP - SNJXP * SNWXP / SNU
SXXP = SNWXXP • SWWX * SNUXP / SNU
SXPY=SMWXPY-SNUXP»S«UY/SNU
I f SXX = 0 T KEN GOTO 5610
SLOPE = SXY /SXX
1STCPT = YBAR - SLOPE * XBAR
IF NCTRL <= 0 THEN RETURN ' otherwise adjust for natural response rate
SXPXP = SXPXP + NCTRL * (1! - BIGO/BIGC
SXPY = SXPY + NCTRL * (C • BIGO/BIGC
NUK = (SXY/SXX) • ((SXXP " SXPY) / (SXPXP * SXX})
DEN - 1' • ((SXXP * SXXP) / (SXPXP * SXX))
SLOPE = NUH / DEN
TEMP = SXY / SXX ;
DELC = (1! • BIGC) * ((SXPY - TEMP * SXXP) / (SXPXP • ( S X X => * S X X P ) / S X X ) )
BIGC = BIGC + DELC
INTCPT = YBAR - SLOPE * XBAR - (DELC * XPBAR / (If - BIGC))
RETURN
1 subroutine to compute y, wky, w, zv : input is n, tdose, intcpt, stope
FOR K = 1 TO N
Y(K) = INTCPT + LDOSE(K) * SLOPE ' predicted probit
2 = Y(K) - 5) : ' § 0 S U B 2590 ' get p value ,
2V = <1!/(SOR(2)*PI)))*EXP(-. 5*2*2)
I F 2V< = 0 THEN 2V= .000001
P = NRESP(K)/NDOSE
-------
2.4 Listing of Computer Program for Probit Analysis (Continued).
3620
3630
3640
3650
3660
3670
3680
3690
3700
3710
3720
3730
3740
3750
376C
3770
3780
3790
3800
3810
3820
3830"
3840
3850
3860
3870
3880
3890
3900
3910
3920
3930
3940
3950
3960
3970
3980
3990
4000
4010
4020
4030
4040
4050
NEXT K
RE TURN
1 subroutine to check for- convergence
IT MER > 25 THEN GOTO 3750 - modify here if more iteratlons required
IF 1TER>0 THEN GOTO 3690
OLDINT = 1NTCPT ; OLDSLO = SLOPE
GOTO 3940
IF {OLD1NT=0> OR
-------
2.4 Listing of Computer Program for Probit Analysis (Continued).
4060 RATIO = NRESP(L) / NDOSEU) :ARATIO = (RAT 10 -B1GCw, i , .1
4070 PRIHT #2. USING «*«**#.*#„ „,„ ( R" 1 0 B , 6C ,/ 1 , . B , cc j.
#S##
4080 NEXT L
4090 CHIHET = STY - SLOPE * SXY
4100 IF NCTRL>0 THEN CHIHET = CHIHET - DELC
4110 PRINT #2, '• »: PRINT #2, PRINT
4120 PRINT #2, USJNG "###.###";CHIHET - PRJ
4130 NDF = N - 2 : T •= 1.96 : HET = 1 ! '
4140 IF CHIHET <= CHISQ THEN GOTO 4240
4150 T = T05 C ,,E, SES B ,, J (SX)(
4^6_ G= HET » T*T * SEB / C S L 0 P £ * S L CP E )
4270 If G < 1 ' THEN GOTO 4350
4280 PRINT 82 , ""*"-"'»''***»•»****»«»*
4290 PRINT H2, "*
* 11
4300 PRINT #2, "*
4310 PRINT »2, "«
* it
4320 PRINT *2, »*
* n
4330 PRINT it 2, ''*<
Slope not ifgBlMe.nt|y -Hffr.Bt
EC fiducial limits cannot be computed.
4340 PRINT #2, » »
4350 IF NCTRL > 0 THEN SEC = (1! - BIGC)*2 / (SXPXP
4360 SEI = (11/SNW) + (X8AR * XBAR * SEB)
4370 IF NCTRL > 0 THEN SEI = SEI *
-------
j2.4 Listing of Computer Program for Probit Analysis (Continued).
4440 PRINT #2, USING "Intercept ####.#*####
4450
4460
4470
4480
4490
4500
4510
4520
4530
4540
4550
4560
4570
4580
4590
4600
4610
4620
4630
4640
4650
4660
4670
46SO
4690
4700
4710
4720
4730
4740
4750
4760
4770
4780
4790
4600
4810
4815
4820
4830
4840
4850
4860
4870
4880
4890
4900
4910
4920
SCR{SEC*H£ T >
XL = SLOPE - T * SQRCSEB»HET) : XU = SLOPE + T * SGR(SEB-HET)
PRINT #2, USING "Slope ####.###### #«#*.##*### <#####.######
*«###.######)»;SLOPE,SOHCSEB*KET),XL,XU
F R I N T * 2 , " "
IF NCTRL <=0 THEN GOTO 4530
XL = B1GC • T * SQH(SEC*HET) : XU = B1GC
PRINT #2, USING "Spontaneous *###.#*##»«
#####.#*####)";BIGC,SOR(SEC«HET),XL,XU
PRINT #2, "Response Rate"
GOTO 4550
PRINT #2,
PRINT #2,
GOSUB 290
PRINT #2,
PRINT #2,'
PRINT
"Theoretical Spontaneous Response Rate =
USING "#,####"; B I C C
#2 . «
PRINT #2, "Point
PRINT * 2 , "' "
PRINT #2, TITLES ; PRINT 32, " «
Estimated EC Values and Confide nee L ' SIM s
L owe r
Cone .
95% Confidence
PRINT #2,
Upper"
Limits"
FOR I
H = (
IF G> =
= 1 TO '
OY{ I ) -
1 ! THEN
IF NCTRL >
T EKP = H +
SE = SGR (
XL = TEMP
XU = TEMP
0!
(G
< 1
T
• T
1NTCPT } / SLOPE
GOTO 4900
THEN GOT 0 4730
/ < 1 ! - G»*CH •
• G >/SKW * £(K-
* SE / (SLOPE *
* SE / (SLOPE *
XBAR )
XBAR }*2 )*SE8
'M » ' G ) }
(1 » - GM
SE = SE
SCR ( HET )
IF XL<-10 THEM XL = • 1 0
IF XU> 20 THEN XU= 20
GOTO 4920
1 fixup formulas if a threshold (spontaneous response) was estimated
C11 = SEB
TEHPC = «1! - BIGC) " (1! - BIGC»
C22 = SE C / T EKPC
C12 = 11 / (SXXP - (SXX * SXPXP)/SXXP>
R1 = H + 20 THEN XLM 20 :
IF G<1I THEN GOTO 4920
PRINT 02,USING "EC##.##
GOTO 4930
PRINT #2,USING "EC##.##
10-H
########.####
##########.####>
4930 NEXT I
100*0P(I ) ; 10'M; 10*XL; 10"XU
413
-------
(2.4
Listing of Computer Program for Probit Analysis (Continued).
4940 IF HSG=1 THEN PRINT #2, -' --: PRINT #2,» NOTE
or equal to 1.E20 are really infinite"
GOSUB 290
'subroutine to do the probit plot
4950
4960
4970
4980
4990
5000
5010
5020
5030
5040
5050
5060
5C70
5080
. 5090
51CO
5110
5120
5130
5140
5150
5 160
5170
5132
5 190
52CO
5210
5220
5230
5240
5250
5260
5270
5280
5290
5300
5310
5320
5330
5340
5350
5360
5370
5380
PRINT
PRINT
L IKE
PRINT
# 2, TITLES :
#2, »
: PRINT #2,
ft 2 , "Probit"
PRINT # 2, » «
PLOT OF ADJUSTED PROBITS AND PREDICTED REGRESSIONS
LLD99 =
D R 0 W = 1 0 > : RADJ = .2
LLD01 = (2.6732-INTCPT)/SLOPE
ADJ = CLLD99 • LLD01 )/ 68
DCOL = LLDQ1 : CADJ = ADJ
FOR J=1 TO H
RDIFF = DROU - YPROB(J)
i RQWX = RDIFF/RADJ + 1
CD I F F = LOOSE( J ) • DCOL
1 COLX = CD I F F/ CADJ -*• 1
IF YPROB(J) < 0 THEN IROWX=51
IF YPROB(J) > 10 THEN IROUX=1
IF LOOSE(J)LLD99 THEN ICOLX=71
PLTT$<]R0yX,ICOLX)=»o» • change plotting
KEXT J
NO= 1 00 ' number cf points on
FOR 1=1 TO 99
R= I
. C T fi E H G-0 T 0 5 3 C 0
c e » p u t e p r c fc ; t
i NT CF ! } /SL CP E
PROB r T
1
<7.327- IN7CPT}/S,OPE
if desired
predicted curve
i e
P is negative
EC value
IF I / », D < = £
G3S.JB 2270
L CGD=( PRGB1T
RDIFF = DRCW
IROUX = RD! F F/RADJ
CD I F F = L 0GB • DCOL
ICOLX = CD I FF/CADJ + 1
IF PROBIT < C THEN IROUX=51
IF PROBIT > 10 THEN !ROWX=1
IF LOGO < LLD01 THEN ICOLX=1
IF LOGO > LLD99 THEM JCOL%=71
IF PLTTt(IROWX,ICOLX) <>»o» THEN PLTT$(1ROWX,IC0LX}-
plotting symbols here if desired
NEXT I
FOR 1=1
change
( 5 * J J X )
USING »
5390
5400
5410
5420
5430
5440
TO 51
11=1-1
J J X = ( I I - 2 ) / 5 : J J X = I I -
3 F JJS = 0 THEN PRINT #2,
IF JJXoO THEN PRINT #?, »
FOR J = 1 TO 71
IF < P t T T $ < 1 , J ) <> " o •• AND P L T T $ < I , J ) < >
plotting symbols here if desired
JJ=J-1-LAG : IF JJ <= 0 THEN GOTO 5430
FOR K=1 TO JJ
PRINT #2, " ";
NEXT K
PRINT #2, PLTTS{I,J);
LAG = J
PRINT #2,"*";;lfUH =
"." ) THEN GOTO 5450 ' change
'print blanks out to next symbol
414
-------
G.4 Listing of Computer Program for Profait Analysis (Continued).
5450 NEXT J
5460 PRINT #2, " "
5470 LAG=0
5480 NEXT I
5490 BOT$="•+-----
5500
5510
5520
5530
5540
5550
5560
5570
558G
5590
5600
5610
5620
5630
5640
5650
5660
5670
5675
5680
569D
57CO
5710
5720
5730
5740
5750
5760
5770
5780
5790
5800
5810
5820
5830
PRINT tf 2 , "
BOT$=»EC01
" ; B 0 T $
EC 10
EC 99"
";BOT$
EC25
EC50
EC75
EC90
PRINT # 2,"
GCSUB 290
IF FlLES-o-Mptl :" THEN LOCATE 12,30 : PRINT "Output stored in ",-FILES
LOCATE 15,1 ;IN.PUT "Fit another data set ";AKS$
IF ANSS-"" THEN GOTO 5550
AVSS = LEfT$(ANSS, 1 ) : 1 F ASCCANS$)>96 THEN AKS$ = CHR$(ASC"S" AND ANS$«>"Y" THEN GOTO 5550
IF ANS$="Y" THEN CLEAR : CLOSE #2 : CIS : GOTO 4C
GOTO 5910
CL S
P R ! K T " " ; P R I H T » »
PRINT" [
PRINT" [
PRINT" [ Mote
PRINT" {
PRINT" E
PRINT" E
P R I K T " [
EEC [ [[ [[ [[[ECEUEEEE [mm [[[[ E [[I E mmt [I
iterations are not converging. This usually
means that only one concentration is on the
linear portion of the concentration response
curve.
f S I N T
E :: f m E m E E E m E i E m m m E i; m H m m :
1 1 1 tu t
IF WCTRL = G ThEN GOTO 5S10
P.RINT:PRINT -it may be possible to fit the data assuiti^g the spontaneous"
PRINT "control rate is zero.":PRlKT
INPUT "Would you like to try";ANS$
IF ANSS="" THEN GOTO 5740
ANS$ = LEFT$(ANS$, 1): J F ASC(ANS$»96 THEN A N S $ = C K R $ ( A S C ( A K S J ) - 3 2 )
IF ANS$o»N" AND AKSSo"Y" THEN GOTO 5740
IF ANS$="N" THEN GOTO 5810
NCTRL=0:NRCTRL=0:BIGC=0
CLS : LOCATE 12,35 :PR!NT "Working ..."; GOTO 140
PRINT #2, TITLES: PRINT *2, ""
PRINT #2," ":PftINT #2," "
PRINT #2," **»"**"»««•««****»»»***«**»**«*»**...»«,*,,,..***,.,*»*.,.,
; 5840 PRINT #2,"
* ii
5850 PRINT #2,"
* ii
15860 PRINT #2,"
5870 PRINT #2,"
* N
5875 PRINT #2,"
5880 PRINT #2,"
* it
Note : Iterations ere not converging. This usually
means that only one concentration is on the
linear portion of the concentrstfon response
415
-------
2.4 Listing of Computer Program for Probit Analysis (Continued)
5890 PRINT fl2,
5900 PRINT
5910 END
: P R I N T " " : GOTO 5550
416
-------