EPA-650/4-74-022
COLLABORATIVE STUDY
OF
METHOD FOR THE DETERMINATION OF PARTICULATE
MATTER EMISSIONS FROM STATIONARY SOURCES
(MUNICIPAL INCINERATORS)
by
Henry F. Hamil
Richard E. Thomas
EPA Contract No. 68-02-0626
SwRI Project No. 01-3462-002
Prepared for
Methods Standardi/ation Branch
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Environmental Protection Aj^ncy
Research Triangle Park, N. C. 27711
Attn: M. Rodney Midgett, Research Chemist
Section Chief, Stationary Source Methods Section
July 1, 1974
SOUTHWEST RESEARCH INSTITUTE
SAN ANTONIO CORPUS CHRISTI HOUSTON
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This report has been reviewed by the Office of Research and Development, EPA, and approved for pub-
lication. Approval does not signify that the contents necessarily reflect the views and policies of the Environ-
mental Protection Agency, nor does mention of trade names or commercial products constitute endorsement
or recommendation for use.
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SOUTHWEST RESEARCH INSTITUTE
Post Office Drawer 28510, 8500 Culebra Road
San Antonio, Texas 78228
COLLABORATIVE STUDY
OF
METHOD FOR THE DETERMINATION OF PARTICULATE
MATTER EMISSIONS FROM STATIONARY SOURCES
(MUNICIPAL INCINERATORS)
by
Henry F. Hamil
Richard E. Thomas
EPA Contract No. 68-02-0626
SwRI Project No. 01-3462-002
Prepared for
Methods Standardization Branch
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Environmental Protection Agency
Research Triangle Park, N. C. 27711
n
Attn: M. Rodney Midgett, Research Chemist
Section Chief, Stationary Source Methods Section
App roved:
John T. Goodw in
Director
Department of Chemistry
and Chemical Engineering
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SUMMARY AND CONCLUSIONS
This report presents the results obtained from a collaborative test of Method 5, a test procedure promul-
gated by the Environmental Protection Agency for the determination of particulate emission levels from station-
ary sources. Method 5 specifies that particulate matter be withdrawn isokinetically from the source and its
weight be determined gravimetrically after removal of uncombined water.
The test was conducted at a municipal incinerator using four collaborative teams. A total of 12 runs were
made over a two week period, and 47 individual concentration determinations made by the four collaborators.
From these, the values which conformed to the standards of 60 scf of gas collected and ±10% of isokinetic
sampling were used in the analysis. The resultant working sample was 11 runs and a total of 32 individual
observations. These were submitted to statistical analysis to obtain precision estimates for Method 5.
The precision is expressed in terms of within-laboratory, between-laboratory and laboratory bias compo-
nents. For purposes of statistical treatment, the determinations are grouped into blocks. Two separate furnace
trains were used at the incinerator, the No. 1 unit during the first week of testing, and the No. 2 during the
second week. The values obtained from each stack were grouped as a block for this test. The statistical analysis
is based on the assumption that the true emission concentration remains essentially constant over the course
of each week's runs. No independent method for determining the concentration was available during the test
to substantiate this assumption, but a preliminary statistical test on the determinations detected no significant
differences among the runs that would indicate a changing mean value over the test period.
The precision components are estimated in terms of standard deviations, which are shown to be propor-
tional to the mean of the Method 5 determinations, 8, and can be summarized as follows.
(a) Within-laboratory: The estimated within-laboratory standard deviation is 25.3% of 5 and has
24 degrees of freedom associated with it.
(b) Between-laboratory: The estimated between-laboratory standard deviation is 38.7% of 5, with
3 degrees of freedom.
(c) Laboratory bias: From the above, we can estimate a laboratory bias standard deviation of 29.3%
of6.
The above precision estimates reflect not only operator variability, but, to an extent, source variability
which cannot be separated from these terms. Since the results summarized above were obtained from a single
test, further testing would, of course, be necessary to obtain conclusive results.
Recommendations are made for the improvement of the precision of Method 5, and considerations given
for the use of the method in field testing.
in
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TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS vi
LIST OF TABLES vi
I. INTRODUCTION 1
II. COLLABORATIVE TESTING OF METHOD 5 2
A. Collaborative Test Site 2
B. Collaborators 6
C. Philosophy of Collaborative Testing 6
III. STATISTICAL DESIGN AND ANALYSIS 8
A. Statistical Terminology 8
B. Collaborative Test Plan 9
C. Collaborative Test Data 9
D. Precision of Method 5 10
IV. COMPARISONS WITH OTHER STUDIES 13
V. RECOMMENDATIONS 14
APPENDIX A-Method 5-Determination of Particulate Emissions From Stationary Sources 15
APPENDIX B-Statistical Methods 19
B.1 Preliminary Analysis of the Original Collaborative Test Data 21
B.2 Significance of the Port Effect 21
B.3 Transformations 23
B.4 Empirical Relationship Between Mean and Standard Deviation 23
B.5 Unbiased Estimation of Standard Deviation Components 25
B.6 Weighted Coefficient of Variation Estimates 27
B.7 Estimation of Precision Components .... 29
LIST OF REFERENCES 33
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LIST OF ILLUSTRATIONS
Figure Page
1 Flow Diagram of Holmes Road Incinerator Plant 3
2 Sampling Port Configuration 4
3 Average Velocity Profiles 5
4 Holmes Road Incinerator Test Site 6
5 Control Console Operation 7
6 Impinger Train Operation 7
B.I Interlaboratory Run Plot 24
B.2 Intralaboratory Collaborator Block Plot 25
LIST OF TABLES
Table Page
1 Test Site Data 6
2 Particulate Collaborative Test Data Arranged in Blocks, Ib/scfX 107 10
B.I Original Particulate Concentrations, Ib X scfX 107 21
B.2 Significance of Port Effect 22
B.3 Data Transformation To Achieve Run Equality of Variance 23
B.4 Interlaboratory Run Summary . . 24
B.5 Intralaboratory Collaborator Block Summary 25
B.6 Run Beta Estimates and Weights 30
B.7 Collaborator Block Beta Estimates and Weights 30
VI
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I. INTRODUCTION
This report describes the work performed and results obtained on Southwest Research Institute Project
No. 01-3462-002, Contract No. 68-02-0626, which includes collaborative testing of Method 5 for particulate
emissions as given in "Standards of Performance for New Stationary Sources."^*
This report describes the collaborative testing of Method 5 at a municipal incinerator, the statistical analysis
of the data from the collaborative tests, and the conclusions and recommendations based on the analysis of the
data.
*Superscript numbers in parentheses refer to the List of References at the end of this report.
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I. COLLABORATIVE TESTING OF METHOD 5
A. Collaborative Test Site
Arrangements were made for collaborative testing of Method 5 at the Holmes Road Incinerator of the
Division of Solid Waste Management, Department of Public Works, City of Houston, Texas. Facilities were in-
stalled to provide for simultaneous sampling by four collaborators, each collaborative team working on separate
ports on a platform on the stack.
The incinerator was visited in November, 1972, to inspect the facilities and conduct preliminary sampling
to determine site suitability. At that time, details of site preparation, including addition of platform extensions
and additional sampling ports were made. Site modifications were completed in May,1973, and another site
visit was made to assure suitability for collaborative testing.
The 5-yr old facility consists of two parallel furnace trains, with a capacity of 400 tons of refuse per furnace
per day. The furnaces are a triple grate continuous feed design. Refuse is transferred from the storage bins to the
furnace-charging hoppers by two traveling bridge cranes.
From the charging hoppers, the refuse feeds continuously through water-cooled chutes onto traveling
grate stokers in the furnaces. When the residue reaches the end of the combustion grate, it drops through a chute
to either of t\vo ash conveyers. The residue is quenched and conveyed to rotating screen separators, which dis-
charge into loading-out hoppers for trucking to the disposal area adjacent to the incinerator plant.
Gases leaving the furnaces are cooled in water spray chambers and then enter the flue gas scrubbers to
remove the fly ash. The gases then pass through the induced draft fans and out the stacks. A flow diagram of
one of the incinerator units is shown in Figure 1.
Four sampling ports were available on both the Number 1 (east) and Number 2 (west) units. The sample
ports were at 90 deg to each other and were offset 6 in. vertically from port to port to avoid probe interference.
Access to the sample ports was from a 360-deg platform around the stacks, which were 6.5 ft inside diameter
and 148 ft high. The sample ports were 102 ft above grade and 57 ft (8.8 diameters) above the nearest upstream
flow disturbance. This allowed the use of 12 traverse points, 6 on each diameter traverse. Sample port layout
is shown in Figure 2, and a velocity profile is shown in Figure 3. The velocity profiles were obtained by averaging
the velocities obtained at each traverse point by two laboratories on all velocity traverses. A view of the test site
and Number 1 stack is in Figure 4.
Pertinent information concerning stack dimensions, sample poit location with respect to flow disturbance,
and traverse point locations is tabulated in Table 1.
Traversing for the test itself was accomplished as follows (see diagram p. 6): Sampling teams at ports A and
B began sampling at points 1 and l', respectively. After ten minutes, the team at port A moved to point 2, and
the team at port C began sampling at point 1. Simultaneously, the team at port B moved to point 2' and the
team at port D moved to point l' and began sampling. This pattern was followed until the diameter traverse
was completed (it should be noted that the sampling period of the teams at ports A and B was displaced in time
by ten minutes from that of the teams at ports C and D, the assumption being that stack conditions were suffi-
ciently constant to justify this displacement in time. This displacement in time was necessary to avoid interfer-
ence from two probes sampling the same traverse point simultaneously). Each team then moved its sampling unit
to the port on its right (as one faces the stack), and the traversing procedure was repeated. These two diameter
traverses then constituted a run. Port heights were varied (see Figure 2) so that interference of the probes was
prevented.
The first week of the test was conducted on the Number 1 unit. Failure of the moving grates on that unit
necessitated testing on the Number 2 unit during the second week of the test.
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H
O
o
ft!
in
OS
u
o
a
OS
p
a
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1
6"
FIGURE 1. SAMPLING PORT CONFIGURATION
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£ 55
0
A
B
12
24
36 48
Stack Diameter, inches
Profile, East Stack
72
78
C
D
e 55
50
45
12
24
A
B
D
O
36 48
Stack Diameter, inches
Profile, West Stack
Axis through ports A, C
Axis through ports B, D
72
78
C
D
FIGURE 3. AVERAGE VELOCITY PROFILES
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TABLE 1. TEST SITE DATA
Inside stack diameter-
Distance of sampling site from downstream disturbance:
Distance of sampling site from upstream disturbance:
Number of traverse points on a diameter:
Sampling time at each traverse point:
78 inches
8.8 diameters
>2 diameters
6
10 minutes
Traverse
Point
1
2
3
4
5
6
Distance from outside wall to
traverse point, inches:
3-3/8
11-1/2
23
55
66-1/2
74-5/8
FIGURE 4. HOLMES ROAD INCINERATOR TEST SITE
B. Collaborators
The collaborators for the Holmes Road Incinera-
tor test were Mr. Mike Taylor and Mr. Rick Hohmann
of Southwest Research Institute, Houston Laboratory,
Houston, Texas; Mr. Charles Rodriguez and
Mr. Ron Hawkins of Southwest Research Institute,
San Antonio Laboratory, San Antonio, Texas;
Mr. Quirino Wong, Mr. Randy Creighton, and
Mr. Steve Byrd, City of Houston, Department of Pub-
lic Health; Mr. John Key, Mr. James Draper,
Mr. Tom McMickle, Mr. Tom Palmer, Mr. Michael Lee,
and Mr. Charles Goerner, Air Pollution Control Services,
Texas State Department of Health.*
Collaborative tests were conducted under the gen-
eral supervision of Mr. Nollie Swynnerton of Southwest
Research Institute. Mr. Swynnerton had the overall
responsibility for assuring that the test was conducted
in accordance with the collaborative test plan, and that
all collaborators adhered to Method 5 as written in
the Federal Register " '. Collaborators for the test
were selected by Dr. Henry Hamil of Southwest
Research Institute.
In Figures 5 and 6, members of the collaborative teams are shown in the operation of impinger trains
and a control console during one of the test runs.
C. Philosophy of Collaborative Testing
The concept of collaborative testing followed in the tests discussed in this report involves conducting the
test in such a manner as to simulate "real world" testing as closely as possible. "Real world" testing implies
that the results obtained during the test by each collaborator would be the same results obtainable if he were
sampling alone, without outside supervision and without any additional information from outside sources,
i.e., test supervisor or other collaborators.
*Throughout the remainder of this report, the collaborative laboratories are referenced by randomly assigned code numbers as
Lab 101, Lab 102, Lab 103, and Lab 104 These code numbers do not correspond to the above ordered listing of collaborators.
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FIGURE 5. CONTROL CONSOLE OPERATION
FIGURE 6. IMPINGER TRAIN OPERATION
The function of the test supervisor in such a testing scheme is primarily to see that the method is adhered
to as written and that no individual innovations are incorporated into the method by any collaborator. During
the test program, the test supervisor observed the collaborators during sampling and sample recovery. If random
experimental errors were observed, such as mismeasurement of volume of impinger solution, improper rinsing
of probe, etc.. no interference was made by the test supervisor. Since such random errors will occur in the
everyday use of this method in the field, unduly restrictive supervision of the collaborative test would bias the
method with respect to the field test results which will be obtained when the method is put into general usage.
However, if gross deviations were observed of such magnitude as to make it clear that the collaborator was not
following the method as written, the deviations would be pointed out to the collaborator and corrected by the
test supervisor.
While most of the instructions in the Federal Register are quite explicit, some areas are subject to inter-
pretation. Where this was the case, the individual collaborators were allowed to exercise their professional
judgement as to the interpretation of the instructions.
The overall basis for this so-called "real-world" concept of collaborative testing is to evaluate the subject
method in such a manner as to reflect the reliability and precision that would be expected of the method in
field testing.
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III. STATISTICAL DESIGN AND ANALYSIS
A. Statistical Terminology
To facilitate the understanding of this report and the utilization of its findings, this section explains the statistical
terms used in this report. The procedures for obtaining estimates of the pertinent values are developed and justified in
the subsequent sections.
We^say that an estimator, 6, is unbiased for a parameter 0 if the expected value of 0 is 0, or expressed in notational
form, E(6) = 9. Let Xj, x2,. . • , xn be a sample of n replicates from the population of method determinations.
I n
—_ \. '"^
(1) x = — 2_i xi as tne sample mean, an unbiased estimate of the true mean, 6, of the determinations, the
" «=1
center of the distribution. For an accurate method, 6 is ^, the true stack concentration.
1 "
(2) s2 = y (xj - x )2 as the sample variance,an unbiased estimate of the true variance, a2 . This term
gives a measure of the dispersion in the distribution around §.
(3) s = \fs2 as the sample standard deviation, an alternative measure of dispersion, which estimates 0, the true
standard deviation.
The sample standard deviation, s, however, is not unbiased for a,( 7) so a correction factor needs to be applied.
The correction factor for a sample of size n is an , and the product of an and s is unbiased for a. That is, E(ans) = a.
As « increases, the value of an decreases, going for example from a3 = 1.1 284, a4 = 1.0854 to a,0 = 1.0281.
We define
as the true coefficient of variation for a given distribution. To estimate this parameter, we use a sample coefficient of
variation, j3, defined by
. = ^s
X
where |3 is the ratio of the unbiased estimates of a and 6 , respectively. The coefficient of variation measures the per-
centage scatter in the observations about the mean and thus is a readily understandable way to express the precision
of the observations.
The experimental plan for this test calls for 12 runs. On each run, the collaborative teams were expected to col-
lect simultaneous samples from the stack in accordance with Method 5. Since the actual particulate emission con-
centration in the stack fluctuates, one can in general expect different true concentrations for each run. To permit
a complete statistical analysis, the individual runs are grouped into blocks, where each block has approximately the
same true emission concentration level.
We can apply the statistical terms of the preceding paragraphs both to the collaborators' values during a given
run, and to each collaborator's values in a given block. In this report, statistical results from the first situation are
referred to as run results. Those from the second situation are referred to as collaborator-block results. For example,
a run mean is the average of each collaborator's concentration level for the run as obtained by Method 5. A
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collaborator-block coefficient of variation is the ratio of the unbiased standard deviation to the sample mean for all the
collaborator's runs grouped in the block.
The variability associated with a Method 5 concentration determination is estimated in terms of the •within-
laboratory and the between-laboratory precision components. In addition, a laboratory bias component can be esti-
mated. The following definitions of these terms are given with respect to a true stack concentration, ju'-
• Within-laboratory-The within-laboratory standard deviation, a, measures the dispersion in replicate
single determinations made using Method 5 by one laboratory team (same field operators, laboratory
analyst, and equipment) sampling the same true concentration, ju. The value of 0 is estimated from
within each collaborator-block combination.
• Between-laboratory-The between-laboratory standard deviation, a^, measures the total variability in a
concentration determination due to simultaneous Method 5 determinations by different laboratories
sampling the same true stack concentration, ju. The between-laboratory variance, a\, may be expressed as
al=al+ a2
and consists of a within-laboratory variance plus a laboratory bias variance, o2L. The between-laboratory
standard deviation is estimated using the run results.
• Laboratory bias—The laboratory bias standard deviation, OL = \fa^ — a2 , is that portion of the total
variability that can be ascribed to differences in the field operators, analysts and instrumentation, and
due to different manners of performance of procedural details left unspecified in the method. This term
measures that part of the total variability in a determination which results from the use of the method
by different laboratories, as well as from modifications in usage by a single laboratory over a period of
time. The laboratory bias standard deviation is estimated from the within- and between-laboratory esti-
mates previously obtained.
B. Collaborative Test Plan
The sampling was done through the four ports on each stack described previously, with each laboratory sam-
pling from two ports during each run. At the end of the first hour of sampling, the teams rotated in a counterclockwise
direction to the next adjacent port. The starting ports for the teams during each run were chosen through a random-
ization technique, and these will be shown in Table 2.
The incinerator operated only with one stack at a time. After the first week of testing, the plant shifted their
operation from the Number 1 unit to the Number 2 unit. Thus, the first five samples were taken from stack Number 1,
and the remaining seven from Number 2. In the absence of operating characteristics or any means of determining a
true concentration level, the unit from which the determinations were made was used as the blocking factor. The
resulting design, then, was two blocks of size 5 and 7, respectively, as shown in Table 2.
C. Collaborative Test Data
The data used in the statistical analysis of the collaborative test are presented in Table 2, along with the port at
which sampling was begun. These determinations were subjected to preliminary calculation checks to ensure that all
values were determined by using the proper formulas and conversion factors. The data as presented are consistent
with the formulas prescribed in Method 5, and the details of the recalculation are given in Appendix B.I, along with
the determinations as reported by the collaborators.
No determination was reported by Lab 104 in Run 1 due to equipment malfunction. In order to evaluate
Method 5 for field testing, the analysis is done using only values which satisfy the requirements for a compliance
test result. These requirements include (1) that there be a minimum sampling volume of 60 cubic feet, and
(2) that the sample be drawn between 90 and 110 percent of isokinetic sampling. The values marked with
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TABLE 2. PARTICULATE COLLABORATIVE TEST DATA ARRANGED
IN BLOCKS, Ib/scf X 107
Tt]or\f
DIUClV
1
2
Run
IxUIl
i
,2
3
4
5
6
7
8
9
10
11
12
Lab 101
Data
219.1
230.2
202.7
278.2
298.4
267.5$
245.4
468.9
260.0*
197.2
232.2
250.4
Port
A
B
D
D
A
D
D
D
A
C
D
A
Lab 102
Data
170.6*
192.6
207.8
303.5*
236.4
183.8$
171.1*$
201.4
202.2*
121.5*$
217.4*$
205.6
Port
B
A
A
A
B
C
C
B
C
A
B
C
Lab 103
Data
93.6
163.6
157.8
183.6
151.2
125.9
137.9
179.1
157.0*
123.0
168.5
158.5
Port
C
D
B
C
C
A
A
A
B
B
C
D
Lab 104
Data
O.Of
187.6$
380.7
82.7
125.7$
187.5
171.7
249.0*$
228.5*
177.3
229.9
189.8$
Port
D
C
C
B
D
B
B
C
D
D
A
B
*Determmation was made with less than 60 ft3 of gas. corrected to standard conditions.
fNo value reported for this run.
$ Determination was not obtained between 90 and 110 percent of isokinetic.
Note:
EPA policy is to express all measurements in Agency documents in metric units.
When implementing this practice will result in undue cost or difficulty in clarity,
NERC/RTP is providing conversion factors for the particular non-metric units used
in the document. For this report, the factor is:
10'' Ib/scf = 1.6018 X 103 Mg/m3.
a double dagger are those with an unacceptable isokinetic variation factor, and those with an asterisk were samples
of less than 60 cubic feet, corrected to standard conditions.
In these cases, the values were eliminated from the analysis, and no attempt was made to adjust these or sub-
stitute for them. While a substitution would yield a larger data base, the values would not be actual Method 5 deter-
minations, and so could inordinately bias the results, particularly when such a large number of substitutions would be
needed. This leaves a total of 32 valid determinations out of a possible 48.
Although sample ports are placed in a manner to be as nearly equivalent as possible, the unknown factors of
gas flow patterns and variations can lead to a particular port showing a consistently higher or consistently lower
emission concentration level over the course of the test. A test for the significance of a port effect is performed in
Appendix B.2. Using a common rank test, no consistent tendency can be found for any of the ports to give a high
or a low emission level throughout the runs. As a result of this, and the fact that two ports were sampled on each
run, no port factor is included in any further analysis.
D. Precision of Method 5
There are no techniques currently available for determining the true particulate emission concentration level
from a stack, and thus there is no way to determine the accuracy of the method. Further, no ancillary tests can be
run to separate the analytical phase of the test from the field phase. Thus the only means available for evaluating
Method 5 is to examine the precision that can be expected from a field test result.
As a preliminary to evaluating the precision of the method, the determinations are tested for equality of vari-
ance using Bartlett's test. ' In addition, the determinations are passed through two common variance stabilizing
transformations, the logarithmic and the square root, and Bartlett's test is again applied. The use of transformation
10
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serves two purposes. First, it can put the data into an acceptable form for an analysis of variance; and second, it can
provide information concerning the true nature of the distribution of the sample points.
In Appendix B.3, it is demonstrated that for the run data, the logarithmic transform provides the best fit. As has
been demonstrated in a previous study by Hamil and Camann/4) this is a strong indication of a proportional relation-
ship between the mean and standard deviation for the run data.
To further this argument, a regression line is fit to the paired sample means and sample standard deviations for
the run data in Appendix B.4. The graph in Figure B.I shows the least squares fit to the points having been forced
through the origin. The degree of fit is measured by the coefficient of determination, r2 , which has a value of 0.85 1 5
for the run data. This indicates that over 85 percent of the variation in the magnitude of the standard deviation is
attributed to the variation in the magnitude of the mean.
The correlation coefficient, r = Vr2 . f°r the run data is 0.9228. Using tables given in Dixon and Massey/2) this
value is significant at the 5-percent level, which justifies the use of the no intercept regression line as a model for these
data points.
A similar argument is presented for the collaborator-block data. For these paired values, the relationship is not
as strong as it was for the run data. The value of r2 for the least squares fit is 0.5343, which gives a value of r of
0.7309. Again referring to significance tables for r, we can determine that this value is significant at the 5-percent
significance level.
The conclusion that we draw from the above results is that there is a proportionality between the mean and the
standard deviation for both the run data and the collaborator-block data. This implies that
and
ob =
where a and 05 are the within- lab and between-lab components respectively, C and Q, are constants, and 5 represents
the true mean determination level. This is equivalent to saying that while the standard deviations change according
to the emission concentration, the ratio of the standard deviation to the mean, the coefficient of variation, remains
constant. Thus, we may rewrite the above expressions as
i 0/6=0
and
o/,/6 = ft,
where (3 is the true within-laboratory coefficient of variation, and fo is the true between-laboratory coefficient of
variation.
On the basis of the previous argument, then, we will estimate our precision components not directly, but by
estimating the appropriate coefficients of variation and expressing the standard deviations as percentages of the mean.
In Appendices B.5 and B.6, the technique for obtaining estimates of (3 and |3^ is discussed, and it is shown that the
resulting estimates are unbiased for the standard deviation components. Our estimates of a and aj, are defined with
respect to the mean determination, S.
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and
The actual estimates of 0 and /3j are obtained in Appendix B.7 from the collaborative test data. The within-lab
coefficient of variation, taken from the collaborator-block data, is |3 = 0.253. Using this, we then estimate the within-
lab standard deviation as
a = (0.253)6,
with 24 degrees of freedom.
The between-lab coefficient of variation, 0£, is estimated from the values across any particular run. From
Appendix B.7, we have a value of 0b = (0.387), which gives an estimated between-lab standard deviation of
ab = (0.387)6
at a true determination mean, 6 . This estimate has 3 degrees of freedom associated with it.
From the formula presented in section A above, the laboratory bias standard deviation may be estimated as
= V(0.387)262 -(0.253)262
= V(0.086)52
= (0.293)6
at a true determination mean, 6.
These values indicate a lack of precision in the method, especially with regard to the laboratory bias compo-
nent. The differences between the labs in this study were of such a magnitude to suggest that each laboratory was
obtaining a value whose usual range was essentially lab dependent. If such is the case, then there is an apparent
discrepancy arising from some technique or procedure in the method which is not defined in the necessary detail.
This could include the methods for sample recovery from both the filter and the probe wash, for which more
detailed procedure should be specified and more care in handling should be recommended.
The within-laboratory precision could also be aided by such detail, since it could help to avoid the probable
causes of unusual values, namely contamination of the probe tip by scraping against the inside of the port and loss
of particulates due to probe handling and cleaning. Although not a major problem at this site, it has been a notice-
able factor in a previous test/5)
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IV. COMPARISONS WITH OTHER STUDIES
Two other collaborative tests of Method 5 have been conducted/3'5^ at a cement plant and a fossil-fuel fired
steam generator. The following comparisons can be made with the results of those tests.
• The within-laboratory standard deviation estimate for this study is lower than the values obtained in the
other studies. The difference is due in some measure to the fact that the high value phenomenon that
can effect the within-laboratory estimate is less prevalent in this test than in the other two.
• The between-laboratory standard deviation estimate for this study is comparable to that of the power
plant, and lower than the value obtained from the cement plant. However, the high values obtained in
the cement plant test were localized in a single laboratory's results. This caused an inflation of the
laboratory bias component, which accounts for the difference between that study and the other two.
• The laboratory bias standard deviation is higher than the value obtained in the power plant test. The
difference in the manner of probe cleanup and sample recovery is probably the major cause of the
variability in the results from lab to lab. In this study, the infrequency of high values led to the reduc-
tion of the within-laboratory estimate, but the between-laboratory estimate remained high. This
suggests that a solution to the high value problem will not, by itself, result in a great improvement in
the precision demonstrated for the method but that work must be done to add the details in the
technique that will enable distinct crews to perform the method in a more nearly identical manner.
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V. RECOMMENDATIONS
On the basis of the conclusions and results presented and from observations by personnel in the field, the fol-
lowing recommendations can be made concerning Method 5:
(1) Frequency of calculation errors in the collaborative test data and differences among labs in the number of
significant digits carried can be a major problem in evaluating field test results. It is recommended that a
standard Method 5 computer program be written to calculate compliance test results from raw field data.
(2) More detail should be specified in the technique for sample recovery from the probe. The probe collection
and handling are the probable causes of the extreme high and low values which greatly contribute to the
lack of precision in the method.
(3) At present, there is no standard technique for cleaning the filter apparatus, which undoubtedly is a major
contributor to the high laboratory bias. It is recommended that a detailed procedure be established and
incorporated into the method.
(4) When using the method in a stack with high moisture content, filters tend to blind off rapidly, causing
them to have to be changed during the course of the run. This has the effect of magnifying the handling and
sample recovery requirements, thus resulting in more opportunity for errors. Sampling teams using Method 5
are encouraged to utilize as large a filter as they can accomodate when working at this type of site to
minimize this problem.
14
-------
APPENDIX A
METHOD 5-DETERMINATION OF PARTICULATE EMISSIONS FROM
STATIONARY SOURCES
Federal Register, Vol. 36, No. 247
December 23, 1971
15
-------
RULES AND REGULATIONS
2.1.4 Filter Holder—Pyrex' glass with
heating system capable of maintaining mini-
mum temperature of 235" P.
2.1.5 Implngers / Condenser—Four Itnpln-
gera connected In Berles with glase boll Joint
fittings. The first, third, and fourth Impln-
gers are of the Greeniburg-Smith design,
modified by replacing the tip with a !/2-Lnch
ID glass tube extending to one-half Inch
from the bottom of the flask The second 1m-
plnger Is of the Greenburg-Smltli design
with the standard tip. A condenser may be
•used In place of the Implngers provided that
the moisture content of the stack gas can
still be determined.
2.1.6 Metering system—Vacuum gauge,
leak-free pump, thermometers capable of
measuring temperature to within 6" F., dry
gas meter with 2% accuracy, and related
equipment, or equivalent, as required to
maintain an Isoklnetlc sampling rate and to
determine sample volume.
2.1.7 Barometer—To measure atmospheric
pressure to ±0.1 Inches Hg.
2.2 Sample recovery.
2 2.1 Probe brush—At least as long as
probe.
8.2.2 Glass wash bottles—Two.
2.2.3 Glass sample storage containers.
2.2.4 Graduated cylinder—26O ml.
2.3 Analysis.
2.3.1 Glass weighing dishes.
2.3.2 Desiccator.
2.3.3 Analytical balance—To measure to
±0.1 mg.
2.3.4 Trip balance—300 g. capacity, to
measure to ± 0.06 g.
3 Reagentt.
3.1 Sampling.
3.1.1 Filters—Glaes fiber, MSA 1106 BH1.
or equivalent, numbered for Identification
and prewelghed.
3.1.2 Silica gel—Indicating type, 6-16
mesh, dried at 178' C. (360' F.) for 2 hours.
3.1.3 Water.
3.1 4 Crushed Ice.
3.2 Sample recovery.
3 2.1 Acetone—Reagent grade.
3.3 Analysis.
3.31 Water.
MP4NGER TRAIN OPTIONAL MAY BE REPLACED
BY AN EQUIVALENT CONDENSER
HEATED AREA FILTER HOLDER / THERMOMETER CHECK
^VALVE
METHOD 6—DETERMINATION or PARTXCULATC
EMISSIONS FROM STATIONARY SOURCES
1. Principle and applicability
1.1 Principle. Paniculate matter Is with-
drawn ifiokinetically from the source and Its
weight Is determined gravlmetrically after re-
moval of uncomfolned water.
1 2 Applicability This meflhod Is applica-
ble for the determination of partlculate emis-
sions from stationary sources only when
specified by the test procedures for determin-
ing compliance with New Source Perform-
ance Standards
2 Apparatus.
2 1 Sampling train The design specifica-
tions of the partlculate sampling train used
by EPA (Figure 5-1) are described In APTD-
0581. Commercial models orf this train are
available *
211 Nozzle—Stainless steel (316) with
sharp, tapered leading edge.
212 Probe—Pyrex' glass with a heating
system capable of maintaining a minimum
gas temperature of 250' F. at the exit end
during sampling to prevent condensation
from occurring. When length limitations
(greater than about 8 ft) are encountered at
temperatures less than 600* F., Incoloy 825 1,
or equivalent, may be used. Probes for sam-
pling gas streams at temperatures In excess
of 600° F. must have been approved by the
Admiiustaator.
2.1.3 Pitot tube—Type S, or equivalent,
attached to probe to monitor stack gas
velocity.
PROBE
-------
RULES AND REGULATIONS
SAMU (OIK
WTCH KM M0._
HUM *H-
AMBIENT TtMPCMTUftE
ASSUKD MOISTUV. *
HEATH KX 1ETTINQ.
ntW UNQTH.»
ntOMHtATtftSETTlNO
TUVEJtUKM
NUMB
TOTAL
lAVUm
TIM
(«(.•**
AvtnAue
CTATie
PKSSUM
(Ps|. hi Hf.
fTACX
TDKUTUM
(T^-'f
WOCtTT
HtAO
UP*).
nenuK
OtfKRBffUL
ACMM
OttfKX
wra
I* w.
ta.HjO
OA5UJMJ
VOIUW
(VnoH?
GAS SAURJ nuet**nm
AT on GAS UETEA
muT
(T« *),*»
A*fl.
OUTUT
rr.^i.'F
Ai*.
A.9-
SAMnrfeon
rtMKRATUSi,
°F
1
rEMPERATURE
orCAl
LEAVING
COHDEKSEft OR
LAST WPINGEH
•F
4.2 Sample recovery. Exercise care In mov-
ing the collection train Trom the test site to
the sample recovery area to minimize the
IOSB of collected sample or the gain of
extraneous paniculate matter. Set aside a
portion of the acetone used In the sample
recovery as a blank for analysis. Measure the
volume of water from the first three 1m-
plngers, then discard. Place the samples In
containers as follows.
Container No. 1 Remove the filter from
Its holder, place In this container, and seal.
Container No. 2. Place loose paniculate
matter and acetone washings from all
sample-exposed surfaces prior to the filter
In this container and seal. Use a razor blade,
brush, or rubber policeman to lose adhering
particles.
Container No. 3 Transfer the silica gel
from the fourth Unplnger to the original con-
tainer and seal Use a rubber policeman as
an aid In removing silica gel from the
Implnger
4 3 Analysis. Record the data required on
the example sheet shown In Figure 5-3.
Handle each sample container as follows:
Container No. 1. Transfer the filter and
any loose paniculate matter from the sample
container to a tared glass weighing dish,
desiccate, and dry to a constant weight Re-
port results to the nearest 0 6 mg.
Container No. 2 Transfer the acetone
washings to a tared beaker and evaporate to
dryness at ambient temperature and pres-
sure. Desiccate and dry to a constant weight.
Report results to the nearest 0 5 mg
Container No. 3. Weigh the spent silica gel
and report to the nearest gram.
6 Calibration.
Use methods and equipment which have
been approved by the Administrator to
calibrate the orifice meter, pilot tube, dry
gas meter, and probe heater. Recalibrate
after each test series
8 Calculations.
61 Average dry gas meter temperature
and average orifice pressure drop. See data
sheet (Figure 6-2).
6.3 Dry gas volume. Correct the sample
volume measured by the dry gas meter to
standard conditions (70° P., 29.92 Inches Hg)
by using Equation fi-1.
v».,H=v.
T
-------
APPENDIX B
STATISTICAL METHODS
19
-------
STATISTICAL METHODS
This appendix consists of various sections which contain detailed statistical procedures carried out in the analysis
of the particulate matter collaborative study data. Reference to these sections has been made at various junctures in
the Statistical Design and Analysis part of the body of this report. Each Appendix B section is an independent ad hoc
statistical analysis pertinent to a particular problem addressed in the body of the report.
B.1 Preliminary Analysis of the Original Collaborative Test Data
Preliminary recalculations were made on the originally reported data to ensure that the proper formulas were used
and that the concentrations used in the analysis were correctly computed. There is some question about the propriety
of this in light of the philosophy of collaborative testing expressed previously. However, no computation is made that
is not the direct result of the actual data obtained by the collaborator. Recalculation only ensures that there is some
consistency to the number of significant digits carried and that the concentration used in the analysis does not contain
a calculation error that will bias the results. The data originally reported are shown in Table B.I, and comparison with
Table 2 in Section III indicates the need for such a step.
TABLE B.I. ORIGINAL PARTICULATE
CONCENTRATIONS, Ib/scf X 107
Run
1
2
3
4
5
6
7
8
9
10
11
12
Collaborator
Lab 101
219.0
2300
203.0
278.0
298.0
2680
245 0
469.0
260.0
197.0
232.0
251.0
Lab 102
170.9
192.6
208.0
303.0
236.0
183.8
171.1
201.5
202.0
121.5
217.4
205.6
Lab 103
93.6
163.6
157.8
183.7
153.2
125.9
137.9
179.1
157.0
123.0
168.5
158.5
Lab 104
Missing
187.6
380.7
82.7
125.6
187.5
171.7
249.0
228.5
177.3
229.9
189.8
Each collaborator reported a concentration for all runs, with
the exception of Lab 104 in Run 1. This resulted from a malfunc-
tion in the temperature indicator which caused the collaborator to be
unable to complete the run. In numerous other cases, however, the
determinations were unacceptable with respect to the requirements
listed in the Federal Register,'*' a minimum sampling volume of 60
standard cubic feet and an isokinetic factor of 90 to 110 percent.
The end result was that of the 47 total determinations made, only
32 conformed to the definition of a replication for a compliance
test, and only these were used in the analysis.
Since there is no technique available for determining the true
particulate emission concentration, the procedure for grouping the
runs into fairly homogeneous blocks is somewhat arbitrary. The
only readily available means for establishing blocks was to divide the
runs according to the two weeks during which the test was conducted.
The assumption that is made under these circumstances is that there
is an essentially constant level of particulate emissions over each week's operation. This assumption may not be valid
due to the variety of materials burned and normal fluctuations; however, a preliminary statistical test indicated no reason
to believe there were large differences in the true emission level during the two weeks of testing. Therefore, this block-
ing scheme was accepted as suitable.
There were several values in the collaborators' data that seemed inconsistent with the remainder of the data. These
included the low values of Lab 103 in Run 1 and Lab 104 in Run 4, and the high values of Lab 104 in Run 3 and
Lab 101 in Run 8. The presence of these high and low values is a consistent problem with the use of Method 5. There
has been some discussion of the possible causes of these occurrences, with careless probe handling and probe contamina-
tion being the most likely candidates. There is not sufficient cause to eliminate these from the analysis as outlying values,
however, since their presence is apparently characteristic of the type of results one can expect from the method in field
testing.
B.2 Significance of the Port Effect
The test was designed to offset and eliminate any effect of the possible differences in observed concentration
levels resulting from the pattern of gas flow in the stack. The possibility does exist, however, that a particular port will
consistently show a higher or lower value than the others.
21
-------
A non-parametric analysis of variance is used to test the hypothesis of no port effect. The test is that of Kruskal-
Wallis/2^ and the resulting statistic is given by
12
N(N
3(/V + 1)
where
,-th
RJ- the sum of the ranks of the observations from the i port
rif- the number of valid determinations made from the r port
and
N = ^ «,—the total number of valid determinations from the test
/ = 1
k— the number of ports.
The usable data points are presented in Table B.2, by port, along with the rank of each value. The values are as-
signed rankings in the collective sample, with the highest determination in each week given rank 1. The sum of the
ranks for each port and the number of determinations are shown at the bottom of each column. Separate tests arc
performed for the four ports from the first stack and for the four from the second stack.
TABLE B.2. SIGNIFICANCE OF PORT EFFECT
Block
1
Port
*i
"z
A
219.1
192.6
207.8
298.4
(6)*
(9)
(7)
(2)
24
4
B
230.2
157 8
82.7
236.4
(5)
(12)
(15)
(4)
36
4
C
93.6
380.7
183.6
151.2
(14)
(1)
(10)
(13)
38
4
D
163.6
202.7
278.2
(11)
(8)
(3)
22
3
H = 1.5167
2
Ri
"i
125.9
137.9
179.1
229.9
250.4
(16)
(15)
(10)
(5)
(2)
48
5
187.5
171 7
201.4
123 0
(9)
(12)
(7)
(17)
45
4
197.2
168.5
205.6
(8)
(13)
(6)
27
3
2454
468.9
1773
232 2
158.5
(3)
(1)
(11)
(4)
114)
33
5
//= 1.9941
*Number in parentheses is rank of value in combined sample.
For the first week's test, the value of H was 1.517, while for the second week,//had a value of 1.994. For a
value of//to be significant, it must exceed a value taken from a table of the chi-square distribution with k — 1 =
4-1 = 3 degrees of freedom. The tabled value at a 5-percent level of significance is 7.81. Thus, the difference be-
tween the determinations due to a port effect is essentially nonexistent, and on this basis, the port factor is eliminated
from further analysis.
22
-------
B.3 Transformations
In order to gain information concerning the distributional nature of the Method 5 determinations, the observations
are passed through two common variance stabilizing transformations, the logarithmic and the square root. To determine
the adequacy of the transformations, Bartlett's test for homogeneity of variance *• •* is used to measure the degree of
equality achieved.
The results of the test are shown in Table B.3 for the two transformations, as well as for the data in their original
form (linear). Bartlett's test statistic is presented along with degrees of freedom and the associated significance level for
each transformation. The significance levels are obtained from
TABLE B.3. DATA TRANSFORMATION TO ACHIEVE a chi-square distribution with the degrees of freedom shown.
RUN EQUALITY OF VARIANCE
Clearly, at any usual significance level, all three forms of
the data provide an acceptable model from the equality of vari-
ance aspect. However, the highest degree of equality is ob-
tained through the logarithmic transformation, and this is taken
to be the appropriate model.
In a previous study by Hamil and Camann, ' this has
been shown to be an indication that there is a proportionality
between the mean and standard deviation for the run data. This same model has been shown to be appropriate for data
from particulate matter emissions in a study at a powerplant as well. '
B.4 Empirical Relationship Between Mean and Standard Deviation
In Appendix B.3, an underlying proportionality between the mean and standard deviation for the run data is indi-
cated. In this section, we will attempt to establish this relationship empirically from the determinations obtained at the
Holmes Road Incinerator study. Let
be the concentration reported during run k in block/ by lab z
Transformation
Linear
Logarithmic
Square Root
Test
Statistic
8.678
5.923
6.505
Degrees of
Freedom
10
10
10
Significance
0.56
0.82
0.77
1 P
= ~ y_]
P i= 1
xijk be the mean for run k, block/ across collaborators, forp collaborators
s,k
be the run standard deviation
Table B.4 gives the values of the sample statistics obtained at the Holmes Road site. There is a general tendency
for the standard deviation in the run data to rise as the mean level of concentration rises. To further this idea, the
paired statistics are plotted, and a least squares regression line is fit to the points. The model used is the no intercept
model, or a line forced through the origin, since a mean of zero could only occur in the event that each determination
equalled zero. The model used, then, is
s,k = b xjk
where b is a constant. The individual points and the regression line thus obtained are shown in Figure B.I. The measure
of the degree of fit obtained is the coefficient of determination, r2, which for the no intercept model is obtained by the
formula^
23
-------
TABLE B.4. INTERLABORATORY RUN
SUMMARY
Block
1
2
Run
1
2
3
4
5
6
7
8
9*
10
11
12
Mean Paniculate
Concentration,
Ib/scf
156.3
195.5
237.2
181.5
228.7
156.7
185.0
283.1
0.0
165.8
210.2
204.8
Std. Dev.,
Ib/scf
88.7
33.4
98.2
97.8
73.9
43.6
55.0
161.3
0.0
38.4
36.1
46.0
*No usable results in Sample 9.
n n
n n
*fk
i=l i=l i=l i=l
For the run data, the value of r2 is 0.8515, indicating that ap-
proximately 85 percent of the variation in the magnitude of the
standard deviation is attributed to variation in the magnitude of
the mean. The correlation coefficient, r = \/P, between x^ and
Sj/f is 0.9228. From a table of significant values of/- presented in
Dixon and Massey/2^ this value indicates that a significant amount
of correlation exists between the sample mean and sample standard
deviation for the no intercept model used.
A similar analysis can be used on the collaborator-block values.
If we let nij be the number of valid determinations in block/ by
collaborator /, then we have
Slk
200
150
100
50
X,; =
Run Standard Deviation
Ib/scf X 107
as the mean for collaborator; in block /
50
100
150
200
250
300
Run Mean, Ib/scf X 107
FIGURE B.I. INTERLABORATORY RUN PLOT
24
-------
and
Si, = „
(xijk ~ xij.y as the collaborator-block standard deviation.
k = 1
TABLE B.5. INTRALABORATORY COLLAB-
ORATOR BLOCK SUMMARY
Block
1
2
Collaborator
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Mean Participate
Concentration,
Ib/scf
245.7
212.3
150.0
231.7
278.8
203.5
148.8
191.6
Std. Dev.,
Ib/scf
40.7
22.2
33.8
210.7
108.3
3.0
23.3
26.4
The eight pairs of values obtained are shown in Table B.5.
As before, we fit a regression line through the origin to
these points and try to determine the adequacy of the fit.
For the collaborator-block data, the value of r2 is found to
be 0.5343. It is apparent from Figure E.2 that the degree of
fit is not as strong as for the run data.
The value of r is 0.7309, which is, however, still above the
critical value in the table, at the 0.05 level. Thus, we can still
say that there is evidence of a proportional relationship. This,
coupled with the results of the previous study, gives credence to
the use of this as a model for the data.
250
200
150
100
Collaborator-Block Standard Deviation
Ib/scf X 107
Collaborator- Block Mean, Ib/scf X 10'
FIGURE B.2. INTRALABORATORY COLLABORATOR-BLOCK PLOT
B.5 Unbiased Estimation of Standard Deviation Components
In Appendix B.4, an investigation into the correlation between the mean and standard deviation for the collabora-
tor-block data revealed that there was an empirical basis for accepting the model for the within-lab standard deviation of
for the data. To estimate this standard deviation, we use the relationship
Sj/ - Cx,f
25
-------
where Cis a constant, representing the proportionality. As previously discussed, Sy is a biased estimator for the true
standard deviation, a. The correction factor for removing the bias is dependent on the sample size n. and is given by
Ziegler^ ' as
n
r ~
2 \2
<*„ = —
where F represents the standard gamma function. Thus, we can say that
or
a = anE(sjj)
= 06.
so that in obtaining an unbiased estimate of 0, we can obtain an unbiased estimate of a as well. Thus, we define an esti-
mator for a, a, where
From Appendices B.3 and B.4, we determine that a suitable model for the run data is given by
Ob = fo6
where aj, = \/o\ + a2 is the between-lab standard deviation. Empirically, we have
sjk = Cbxik
and Sjk is a biased estimator for aj,. Thus, forp collaborators,
E(aps/k) = a
and we have
26
-------
Obtaining an estimate of (3^, we have a new estimator, a/,, of a^ given by
and substituting our estimates of a\, and a, we have
so that the laboratory bias standard deviation may be estimated as a percentage of the mean as well.
B.6 Weighted Coefficient of Variation Estimates
The technique used for obtaining estimates of the coefficients of variation of interest is to use a linear combi-
nation of the individual beta values obtained. The linear combination used will be of the form
7=1
where j3y is the/th coefficient of variation estimate, k is the total number of estimates, and Wj is a weight applied to
the/th estimate.
As previously discussed, the individual estimate of )3 is obtained as
for a sample of size n. This estimator is shown in B.5 to be unbiased for the true coefficient of variation. However,
since we are dealing with small samples to obtain our individual estimates, weighting is more desirable in that it pro-
vides for more contribution from those values derived from larger samples. There is more variability in the beta
values obtained from the smaller samples, as can be seen by inspecting the variance of the estimator. We have that
Var(j3) = Var
(¥)
= «,2
2n
for normally distributed samples,* ' and true coefficient of variation,/3. Rewriting this expression, we have
27
-------
and all terms are constant except for a2 and n. Thus, the magnitude of the variance changes with respect to the
factor a2/n. Now, since an decreases as n increases, the factor a2/« must decrease as n increases, and the variance
is reduced.
The weights, Wj, are determined according to the technique used in weighted least squares analysis' % which
gives a minimum variance estimate of the parameter. The individual weight, w/, is computed as the inverse of the
variance of the estimate, |3/, and then standardized. Weights are said to be standardized when
1
k
To standardize, the weights are divided by the average of the inverse variances for all the estimates. Thus, we can
write
w, = —
where
«,-=-
Var(ft)
and
Now, from the above expressions we can determine u/, u and w,- for the beta estimates. For any estimate,
1
for sample size «/, and
Ui =
Var(ft)
1 A i
= 1^-5-
7, •<--' ,,,2
+2(32)
2j32
28
-------
Thus, the /th weight, w,, is
w, = —
n,
<&,
2
L/32(l + 202)_
2
|32(1 + 202)
E
«/
4
The estimated coefficient of variation is
£«"L-f
/=] an, x
_;=!««,_
B.7 Estimation of Precision Components
In Appendices B.3 and B.4, the relationships are established for the within-laboratory standard deviation, a,
and the between-laboratory standard deviation, a/,,
a = (36
and
29
-------
where 6 is the true mean of the determinations. In Appendix B.5, it is shown that for the laboratory bias standard
deviation, ai, the above expressions imply
In Appendix B.6, the technique for obtaining an estimate of a coefficient of variation as a linear combination of
the individual values is discussed. The estimator is of the form
*/=!
where fy is the estimated beta from the/th sample, Wj is the weight given to that estimate, and k is the number of esti-
mates obtained. For the run data, this becomes
12
= -V
11
t-J
/=!
The factor 11 is used since one run had no usable determinations. In Table B.6, the individual coefficients of variation
and their corresponding weights are given. Using these in the above equation, we obtain
TABLE B.6. RUN BETA
ESTIMATES AND
WEIGHTS
Run
1
2
3
4
5
6
7
8
9*
10
11
12
Beta Hat
0.7114
0.1928
0.4494
0.6078
0.3647
0.3484
0.3353
0.6427
0.0000
0.2613
0.1940
0.2532
Weight
0.565
1.045
1.507
1.045
1.045
0.565
1.045
1.045
0.000
1.045
1.045
1.045
*No usable determinations
in this run.
TABLE B.7. COLLABORATOR-BLOCK
BETA ESTIMATES AND WEIGHTS
Block
1
2
Collaborator
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Beta Hat
0.1763
0.1182
0.2394
1.1398
0.4131
0.0183
0.1644
0.1493
Weight
1.310
0.698
1.310
0.377
1.310
0.377
1.611
1.007
fe = (0.387)
and consequently
ab=\
= (0.387)6
This estimate has 4 — 1=3 degrees of freedom for comparison of
four laboratories.
Similarly, for the within-laboratory coefficient of variation
we have
for the 8 collaborator-block combinations. The individual estimates
and their weights are shown in Table B.7. Substituting, we have
0 = (0.253)
and an estimated standard deviation of
= (0.253)5.
This estimate has 32 - 8 = 24 degrees of freedom, for the 32 determinations
divided into 8 collaborator-block combinations.
30
-------
Using these values in the equation for the laboratory bias coefficient of variation, we estimate
fa = ( V(0.387)2 - (0.253)2]
= \/67086
= 0.293,
and thus, the estimated laboratory bias standard deviation is
= (0.293)6.
31
-------
LIST OF REFERENCES
1. Environmental Protection Agency, "Standards of Performance for New Stationary Sources," Federal Register,
Vol. 36, No. 247, December 23, 1971, pp 24876-24893.
2. Dixon, W. J. and Massey, F. J., Jr., Introduction to Statistical Analysis, 3rd Edition. McGraw-Hill, New York,
1969.
3. Hamil, Henry F. and Camann, David E., "Collaborative Study of Method for the Determination of Particulate
Emissions from Stationary Sources (Portland Cement Plants)," Southwest Research Institute report for
Environmental Protection Agency, in preparation.
4. Hamil, Henry F. and Camann, David E., "Collaborative Study of Method for the Determination of Nitrogen
Oxide Emissions from Stationary Sources," Southwest Research Institute report for Environmental Protection
Agency, October 5, 1973.
5. Hamil, Henry F. and Thomas, Richard E., "Collaborative Study of Method for the Determination of Particulate
Matter Emissions from Stationary Sources (Fossil-Fuel Fired Steam Generators)," Southwest Research
Institute report for Environmental Protection Agency, in preparation.
6. Searle, S. R., Linear Models. Wiley, New York, 1971.
7. Ziegler, R. K., "Estimators of Coefficients of Variations Using k Samples," Technometrics, Vol. 15, No. 2,
May, 1973, pp 409414.
8. Cramer, H., Mathematical Methods of Statistics, Princeton University Press, New Jersey, 1946.
33
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