COLLABORATIVE STUDY
of
REFERENCE METHOD FOR DETERMINATION
OF SULFUR DIOXIDE IN THE ATMOSPHERE
(PARAROSANILINE METHOD)
(24-Hour Sampling)
Richard A. McCoy
David E. Camann
Herbert C. McKee
Contract CPA 70-40
SnRI Project 01-2811
Prepared for
Me I hods Standardization Branch: O \l Ml
National Environmental Research (.enter
Environmental Protection Agency
Research Triangle Park, N. C. 27711
December 1973
SOUTHWEST RESEARCH INSTITUTE
SAN ANTONIO CORPUS CHRISTI HOUSTON
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"This rnport has been reviewed by the Office of Research and
Development, EPA, and approved for publication. Approval does
not signify that the contents necessaiily reflect the views and
policies of the Environmental 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 78284
COLLABORATIVE STUDY
of
REFERENCE METHOD FOR DETERMINATION
OF SULFUR DIOXIDE IN THE ATMOSPHERE
(PARAROSANILINE METHOD)
(24-Hour Sampling)
Richard A. McCoy Iflo !
David E. Camann I3";
§ o a-
Herbert C. McKee « 5 ?!
Contract CPA 70-40 |n|I||
SwRI Project 01-2811 Ma§^l
o" SJ So 8 e? ff
Prepared for 'i-isHSS.
Methods Stnndardi/.alion Branch: OAEML S!-?3-
O g ? »
National Environmental Research Center l°
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ACKNOWLEDGEMENTS
Our sincere appreciation is extended to the following
organizations for their participation in the collaborative test of the
pararosaniline method of sulfur dioxide determination in the atmosphere
using sampling periods of 24 hours.
Bay Area Air Pollution Control District
939 Ellis Street SgoS™^
San Francisco, California 94109 11. f • a f "
Mr. Milton Feldstein § GOBI'S
Mr. Dario Levaggi 2-'2z~?> *
c o£ fl) o) m a,
.10. "• w] u»
^ CD m ^. ^o
Environmental Protection Agency g 3 !•"",» S
National Environmental Research Center § g> | § °- 3
Research Triangle Park, North Carolina 27711 I- ||l »
Dr . Kenneth T . Knapp I 0 ~ = < I
"* 3 ^ n °* o*
State of California Health and Welfare Agency c | 5--1 ^ f
Department of Public Health ?.^ = ^ I §
2151 Berkeley Way ||||'s
Berkeley, California 94704 g5^?S.
Dr . Peter K. Mueller § | I > a
Mr. EmilR. deVera |-&5'll
c <» S | 3.
w M ~~ 0)
Southwest Research Institute, Houston °- g °-
7 in
2600 South Yoakum Boulevard
Houston, Texas 77006
Mr. R. E. Childers
Mr. C. A. Boldt
Mr. Rudy Marek
The participation of Dr. John B. Clements and Mr. John H.
Margeson of the Methods Standardization Branch, Environmental
Protection Agency, in the planning and reporting of the results was also
of great assistance .
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SUMMARY AND CONCLUSIONS
This report presents the results of a collaborative study of the
pararosaniline reference method which was published by the Environmental
Protection Agency in the Federal Register, April 30, 1971, as the
reference method to be used in connection with Federal ambient air quality
standards for sulfur dioxide . That publication is reproduced as Appendix A
of this report. The present study involved four collaborating laboratories
sampling synthetic SO2 atmospheres over a 24-hour period in their own
laboratories. The atmospheres were generated from calibrated permeation
tubes supplied by the National Bureau of Standards.
The highlights of the statistical analysis which was performed on
the data provided by the four collaborating laboratories are as follows:
The replication error varies linearly with concentration
3 3
from 2.5 |o.g/m at concentration levels of 100|j.g/m to
3 3
7.0 (jig/m at concentration levels of 400 |j.g/m .
The repeatability (day-to-day variations within an
individual laboratory) varies linearly with concentration
o o
from 18.1 fig/m-3 at iOO^g/m0 concentration levels to
3 3
50.9ug/m at400|jLg/m concentration levels .
The reproducibility (day-to-day variability between two or
more laboratories) varies linearly with concentration from
-J -3 -3
a low of 36.9ug/m at 100(jLg/m to a high of 103.5jjLg/m
at 400|ig/m3 .
11
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A laboratory selection bias was inadvertently introduced in the choice
of the four collaborating laboratories for this test, but the effect of
this bias on the reproducibility of the method was eliminated through
a suitable comparison with the 30-minute test results.
The 24-hour sampling method does have a concentration dependent
bias which becomes significant at the 95% confidence level at the high
concentration level. Observed values tend to be lower than the
expected SC>2 concentration level.
Whereas this study used sampling periods of 24 hours, an earlier study
had examined the method for sampling periods of 30 minutes. A comparison
of the results for the two studies at a concentration level of 200(j.g/m is
summarized in the following table:
24-hour 30-minute
Repeatability 29 52
(0.011 ppm) (0. 020 ppm)
Reproducibility 59 102
(0.023 ppm) (0.039 ppm)
This comparison indicates that the 24-hour procedure is capable of better
within- and between-laboratory precision than the 30-minute procedure.
However, it should be pointed out that these differences are based on
collaborative tests that differed in experimental design. Although accepted
statistical techniques were used to process the data, these techniques involve
assumptions which preclude rigorous comparisons between the test results.
Therefore, it is concluded that the exact degree of improved precision
of the 24-hour test method over the 30-minute test method is uncertain.
in
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TABLE OF CONTENTS
Page
SUMMARY AND CONCLUSIONS ii
LIST OF ILLUSTRATIONS v
I. INTRODUCTION 1
II. COLLABORATIVE TESTING OF THE METHOD 3
A. Generation of Test Atmospheres 3
B. Selection of Collaborators 6
C. Preliminary Tests by the Controlling Laboratory 7
D. Additional Collaborative Testing 7
III. STATISTICAL DESIGN AND ANALYSIS 9
A. Outlying Observations 9
B. Analysis of Variance and Variance Components 10
C. Various Sources of Error Within the Analytical
Method 18
1. Calibration Curves 18
2. Control Samples 19
3. Reagent Blanks 19
D. Application of the Results 20
LIST OF REFERENCES 24
Appendix A - Reference Method for the Determination of Sulfur
Dioxide in the Atmosphere (Pararosaniline Method)
Appendix B - Statistical Design and Analysis
Appendix C - Tabulation of Original Data
Appendix D - Instructions to Collaborators for Collaborative Test
of Reference Method for the Determination of Sulfur
Dioxide in the Atmosphere
IV
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LIST OF ILLUSTRATIONS
Figure Page
1 Specifications for Permeation Tube System Used
in Collaborative Tests 5
2 The Reproducibility, Repeatability, and Replication
Error Standard Deviations Obtained by Three
Distinct Analyses 11
3 Replication Error, Repeatability, and Reproducibility
Versus Concentration for 30-Minute Sampling and
24-Hour Sampling 13
4 Between Laboratory Variability Component (Standard
Deviation) Versus Concentration for 30-Minute
Sampling and 24-Hour Sampling 16
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I. INTRODUCTION
In order to determine the relative merits of the pararosaniline
reference method for the determination of sulfur dioxide in the atmosphere
as described in the Federal Register, Vol. 36, No. 84 (see Appendix A),
a collaborative study was conducted and the results analyzed and reported
in September, 1971 , This first study was conducted using a sampling
period of 30 minutes. In the interests of thoroughness, since the
reference method is recommended for the measurement of sulfur dioxide
in ambient air using a sampling period of 24 hours, it was decided that a
subsequent study using sampling periods of 24 hours would be conducted.
This document reports the results of this collaborative study as
conducted by Southwest Research Institute and the Methods Standardization
Branch. The procedures used in conducting the collaborative testing
borrow heavily from the experience gained in conducting the 30-minute
study. In addition, the results gained from the 24-hour sampling were so
similar to those reported for the 30-minute study that the included statistical
analysis is practically a carbon copy of that used in the earlier study.
Therefore, this reports acts as a complement to that original document;
many of the assumptions, analytical arguments, and results from that study
apply in the present case. For this reason, it is recommended that the
report of the 30-minute SO7 sampling study be available and referred to in
C*
conjunction with this document.
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This report of the pararosaniline reference method study was
written in two parts. Part one is a general description of the design,
organization, operation and analysis which form the 24-hour sampling
study. This first section presents the basic assumptions and logic
which served to guide the statistical analysis, together with a brief
summary of the answers which resulted. Part two of the report consists
of a number of appendices in which the many details of the study are
documented. A two-page summary appears immediately
after the title page in which only the highlights of the study are presented.
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H. COLLABORATIVE TESTING OF THE METHOD
Cooperative planning between Southwest Research Institute and
the Methods Standardization Branch began shortly after completion of
the final report of the 30-minute study in September of 1971. A rigid
test method (see Appendix D) was developed and instructions for
conducting tests were supplied to each of the collaborating laboratories.
The clarity and detail of these instructions were an important element
contributing to the efficiency with which the tests were conducted.
A . Generation of Test Atmospheres
Of the available methods for supplying SO? samples to the
collaborating laboratories, the calibrated permeation tube system was
chosen as the most suitable for these tests. Such a system had worked
well for the 30-minute sampling study using calibrated permeation tubes
supplied by the National Bureau of Standards. At the time of that study,
the permeation tube was not a standard reference material; therefore the
accuracy of this generation system was determined by pre and post test
calibration of the permeation tubes by NBS to assure reliable evaluation
of the test method. The SO., permeation tube was issued as a standard
reference material on December 1, 1970, so that recalibration was not
necessary for the present study.
The permeation tubes used consist of a small cylindrical tube of
Teflon containing liquid sulfur dioxide . The rate of diffusion of sulfur
dioxide through the walls of the cylinder depends only on temperature and
is reproducible within a reasonable temperature range. The certification
available from the National Bureau of Standards covered the range of
20°-30°C and provided sufficient accuracy if temperature control to within
0 .1 ° C was maintained.
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If the rate of permeation is controlled accurately through
controlling the temperature, the only other variable controlling the
concentration of the test atmosphere is flow rate. By passing air
through the permeation tube apparatus at a controlled flow rate, and
thus diluting the sulfur dioxide which passed through the walls of the
tube by diffusion, the concentration of sulfur dioxide in the final air
stream could be accurately controlled. A special apparatus was developed
for this purpose which is illustrated in Figure 1. Major portions of this
system were fabricated from Pyrex glass, and temperature control was
achieved by enclosing the permeation tube holder in a water jacket
supplied by circulating water controlled to within 0.1 C. Purified air
used for dilution was measured accurately with calibrated rotameters.
The apparatus consisted primarily of a condenser capable of
accommodating a permeation tube and a 0. 1°C thermometer, a large
Kjeldahl trap to be used as a mixing bulb, and a manifold with Teflon
stopcocks for sampling. The glassware is connected by ground-glass
ball joints. Associated parts for the system include a calibrated flowmeter
covering the range of 0 to lOOml/min with an accuracy of 5 percent, a
flowmeter covering the range of 0 to 1 5 1/min with an accuracy of
1 to 2 percent, a 0. 1°C thermometer, and a constant-temperature bath
equipped with a circulating pump to continuously supply water to the
condenser. The bath must be capable of maintaining the temperature
within + 0. 1°C. Cylinder air or compressed air, purified by carbon
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RubW O' Tygoo Tub-ng
0- to 100-cc/mm 1lo*m;ie
5'*» accuracy
RuQb*r or
n Tubtng
Teflon Stopcock*, 6 mm
Vent to Hood
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filters and drier (e. g. , silica gel, molecular sieve), and cylinder
nitrogen are required to complete the system.
A sulfur dioxide permeation tube obtained from the National
Bureau of Standards was inserted into the condenser, and the system
assembled as shown in Figure 1. Nitrogen was passed continuously
through the condenser, housing the permeation tube and the 0. 1°C
thermometer,at a rate of 50ml/min. It is advisable to maintain this
flow through the system continuously in order to avoid sulfur dioxide
accumulation in the condenser tube. The temperature in the system was
adjusted to the desired temperature (usually 25.0°C). After the permeation
tube had been equilibrated 24 hours, the dilution air was introduced into
the system and the flow adjusted to produce the desired test atmosphere.
Up to one-half of the total flow of the system may be sampled. The
concentration of sulfur dioxide in the standard atmosphere
was calculated according to the formula found in Section 9. 2. 2 of the
method (see Appendix A). In order to conserve dilution air, it was
shut off at the end of a sampling day; however, the constant-temperature
bath and purge nitrogen gas were normally left on.
B. Selection of Collaborators
As is true in all collaborative studies, the selection of collaborators
was a compromise between available resources and the quantity of
information to be gained from the test. A minimum of six laboratories are
desirable for a collaborative test'^). However, because the test requires
2 to 3 man weeks per collaborator, the cooperation of only four laboratories
(see acknowledgements) could be obtained.
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In order to minimize familiarization time to the greatest
possible extent, it was decided to employ laboratories which had
collaborated in the 30-minute sampling study. These conditions were
acceptable in view of the fact that a great deal of knowledge regarding
the test method had already been generated by the earlier study.
C. Preliminary Tests by the Controlling Laboratory
Southwest Research Institute performed the function of organizing
the collaborative test. In order to become familiar with the method as
it applies particularly to a 24-hour sampling period, it was decided that
SwRI should perform the test sequence that would be required of each
collaborating laboratory. Since this test sequence would in every way be
equivalent to that of any other collaborating laboratory, it was also decided
to include the results as a part of the test method study. The test sequence
was performed by SwRI in April, 1972. Difficulty was experienced on the
first two days of the test with poor agreement between the control
concentrations added and those returned. The implications of this problem
are discussed in a subsequent section dealing with outlying observations.
D. Additional Collaborative Testing
Southwest Research Institute and three additional laboratories from
the fourteen which participated in the 30-minute sampling study agreed to
again participate in the 24-hour study. Each laboratory received a
calibrated permeation tube from the National Bureau of Standards as well
as instructions, data forms and a copy of the method from SwRI (see
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Appendix D) for use in the collaborative study. One of the collaborating
laboratories reported equipment malfunctions during particular portions
of the test sequence. The ability of this collaborator to identify
particular problems with a corresponding set of data was of assistance
in dealing with the outlying observations that resulted. Because of their
familiarity with the method and the calculations required, the collaborating
laboratories experienced a minimum of difficulties, and no calculation
errors were discovered.
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III. STATISTICAL DESIGN AND ANALYSIS
Each of the collaborating laboratories was able to maintain the
necessary physical conditions as specified in the reference method
procedure. It was not a requirement to report temperature and pressure
at regular intervals, but the spot checks that were reported indicate that
none of the laboratories had difficulty in this area. The calibration
procedure with sulfite solution was checked for arithmetic errors, and in
no case did the check disagree with the reported figures by more than
round-off differences.
The four collaborating laboratories were each required to analyze
three concentrations of sulfur dioxide . The concentrations were nominally
98, 291 and 475|j.g/m . The observed values are recorded in Table B-l,
the expected values are recorded in Table C-l, the differences between
observed and expected values are shown in Table C-2, the adjusted values
are given in Table C-3 and the transformed values are given in Table B-Z.
The basis for the transformation is discussed in Appendix B.
A. Outlying Observations
The tests that were conducted for outlying observations identified
a total of six samples of three replicates each of a total of eighteen
observations that proved to be outliers. Appropriate substitutions were
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10
made for these outlying observations in order to keep an equal number
of observations for each collaborating laboratory. With only four
laboratories participating in the study, the elimination of any data would
have seriously affected the statistical analysis.
It was possible in the case of each outlying observation to identify
a reasonable cause for the inconsistency. In the case of one laboratory,
attention was drawn to sampling difficulties by unusual flowmeter rates
which were caused by equipment leaks. This occurred on two separate
days and required substitutions for three observations on each of those
days. In the case of a second laboratory, a calibration error was evidenced
by poor agreement between the added and returned control solution. This
necessitated substitutions for all nine observations recorded on that day.
Details of the outlier tests and the substitutions that were made are
contained in Appendix B.
B . Analysis of Variance and Variance Components
Appendix B is a detailed account of the analysis of the results of
the Z4-hour SC>2 sampling collaborative study. As in the 30-minute
sampling study, three individual analyses were conducted, and the results
are compared in Figure 2. The "derived" reproducibility curve is the
result of the reproducibility curve for all concentrations analyzed together
having been corrected for a laboratory bias. The reasons why this was
necessary and the methods by which it was carried out are discussed in
Section II B of Appendix B . The data in Figure 2 are in the original scale.
The first method was an analysis of variance handling the concentrations
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11
FIGURE 2. THE REPRODUCIBILITY, REPEATABILITY,
AND REPLICATION ERROR STANDARD DEVIATIONS
OBTAINED BY THREE DISTINCT ANALYSES
110
100 •
90-
Derived Reproducibility (cons, together)
Concentrations Separately
Concentrations Together
Linear Model
Replication Error
Repeatability
Reproducibility
CD
80
70
o
60
O
A
D
100
SO2 CONCENTRATION -
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12
individually with the data in the original scale. The second method was
again an analysis of variance, but in this case the three concentrations
were handled together, and the data were in a transformed scale. The
final method, the linear model analysis as described by Mandel* ', again
handled the three concentrations together with the data in the transformed
scale. The agreement between the three methods as shown in Figure 2
was quite good.
For the purposes of this study, the definitions of replication error,
repeatability, and reproducibility are the same as those which apply in the
30-minute sampling study. Basically, replication error describes the variability
among observations recorded within an individual laboratory during a single
day of sampling. Repeatability is defined as the sum of the replication error
and the variability among observations recorded by an individual laboratory
on successive days. Reproducibility is then the variability between observations
made by different laboratories plus the repeatability for the method. Each
of these measures is expressed as a standard deviation of a given concentration
in units of micrograms per cubic meter.
The various sources of error within the analytical method will be
expressed with reference to the analysis of variance in which the three
concentrations were treated together in the transformed scale for the following
reasons: (1) the method results in simpler expressions for replication
error, repeatability and reproducibility as a function of concentration which
are more generally understood, and (2) the results of this method were
chosen to express these quantities in the earlier study and, by duplicating
this choice, direct comparisons can be made between the 30-minute and the
24-hour sampling studies. The results of this comparison are illustrated
in Figure 3.
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13
160'
140
120
100
Ofl
*
§ 80
£
P
40t
20
A 14 Laboratories 30-min
D 3 Laboratories 30-min
O 4 Laboratories 24-hour
— Reproducibility
— Repeatability
— Replication Error
o--
200 400 600
SO2 CONCENTRATION -
800
FIGURE 3. REPLICATION ERROR, REPEATABILITY, AND
REPRODUCIBILITY VERSUS CONCENTRATION FOR SO-MINUTE
SAMPLING AND. 24- HOUR SAMPLING
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14
Certain questions arose from a comparison of results from the
30-minute sampling study versus those of the 24-hour sampling study.
The replication errors that resulted were quite similar for the two
studies. However, the repeatability and reproducibility appeared to
be much better (i. e. , smaller standard deviations) for the 24-hour
sampling study. The large differences between studies for both of
these measures could be real; however, one immediately questions
the various randomization processes which are so vital to the statistical
analyses by which the data were treated.
Since three of the four laboratories which collaborated in the
24-hour sampling study had also participated in the 30-minute sampling
study (numbers 927, 345 and 920), the possibility of a laboratory bias
was immediately suspected. At this point, the data for the original
30-minute sampling study were examined. Just a quick look at the
data reported by the three laboratories that are common to both studies
seemed to indicate a unique similarity. The values for these three
laboratories appeared to have less variability with respect to each other
than was the case with the remaining eleven laboratories. Also, the
means of these three laboratories appeared to be closer to the total
concentration means than was true of other laboratories.
On the basis of these examinations, an analysis of variance
was performed on the transformed 30-minute sampling values reported
by laboratories 927, 345 and 920. The results of this analysis are shown
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15
graphically in Figure 3, and in comparison to the curves for all
fourteen laboratories analyzed together, a limited bias is evident.
Agreement between the curves for replication error and those
for repeatability is quite good, and only the curves describing repro-
ducibility indicate a significant difference. Since repeatability and
reproducibility differ by only the lab-to-lab variance component as
defined in the expression (B-9) of Appendix B, this difference in repro-
ducibility must be caused by laboratory bias. A more detailed discussion
of the laboratory variability component may be found on p. 344 of
(2)
Mandel . For example, the laboratory component, in the transformed
scale, for all concentrations analysed together from Table B-6 is simply:
laboratory component =-/ V(L) + V(LC) = Vl07.90 + 12.43 = 10. 97
The variability among the three laboratories analyzed separately is
obviously less than that which exists among all fourteen laboratories
analyzed together. The laboratory variability component which resulted
from each of the three analyses was isolated and is shown in Figure 4 in
order to emphasize this fact. The laboratory component which resulted
from analyzing all fourteen laboratories together is considered to be a
more accurate representation for the entire population of laboratories.
Since these three laboratories--927, 345 and 920--collaborated in
the four-laboratory 24-hour test, the reproducibility results of the 24-hour
study are similarly biased. The difference between the two lower curves
in Figure 4 is thought to be a real between-laboratory component which
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16
j:
sc
W
Q
Q
«
<
Q
z
<
H
50
40
30
20
10
LABORATORY COMPONENT
CSD3
CSD
O Derived Laboratory-
Component
A 1 4 Laboratories- 30 min
Q 3 Laboratories-30min
O 4 Laboratories-24hour
200 400 600
SO2 CONCENTRATION -
800
FIGURE 4. BETWEEN LABORATORY VARIABILITY COMPONENT
(STANDARD DEVIATION) VERSUS CONCENTRATION FOR
30-MINUTE SAMPLING AND 2 4 -HOUR SAMPLING
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17
is a function of sampling time period and as such is included in the quoted
reproducibility of the 24-hour method. This difference could result from
these laboratories becoming increasingly proficient in conducting the test,
operating the generating equipment and/or acquiring improved measuring
equipment. It was not possible, however, to either identify or quantitatively
define the effects of these factors.
But the true between-laboratory component exclusive of laboratory
bias for the 24-hour method must lie close to the upper curve in Figure 4.
A reasonable estimate was made of the laboratory component, and the
result is illustrated by the dashed curve in Figure 4. This adjusted lab-to-
lab component value has been included in the quoted reproducibility for the
24-hour method, and all subsequent calculations involving reproducibility
are based on this assumption. The derived reproducibility curve for the
24-hour sampling method is illustrated by the dashed line in Figure 2, and
details for the calculation of this curve are to be found in Appendix B.
A comparison of the curves for repeatability indicates little
difference between the 30-minute sampling results of the three common
laboratories analyzed separately and the fourteen collaborating laboratories
analyzed together. However, there is considerable difference between the
results of those two analyses and the results of the 24-hour sampling
repeatability curve. This would indicate that a real difference in repeat-
ability is attributable to the length of time over which the sample is taken.
For this study the dilution air flow for the generating system was constant
over the 24-hour period. The improved repeatability of the 24-hour sample
is thought to be due primarily to the normal averaging of day-to-day
variability factors. The better repeatability would tend to recommend the
24-hour sampling method.
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18
C. Various Sources of Error Within the Analytical Method
The various calibration procedures required by the analytical
method were documented by each of the collaborating laboratories.
The following discussion describes the analysis which was conducted
on each of these tasks, and the calibration data provided by the participants
are summarized in Tables C-4 and C-5.
1. Calibration Curves
Each laboratory was required to prepare only one
calibration curve as described in the Instructions to Collaborators
(see Appendix D). The slopes and Y-intercepts of these curves were
investigated to determine interlaboratory variability.
The overall mean slope was 0.030 absorbance unit
per microgram (3 degrees of freedom), while the standard deviation for
between-laboratory variation was 0.004. The 95 percent confidence
interval for between-laboratory variability was therefore 0. 030 + 0. 013.
The overall mean is very close to the figure which is claimed for the
method.
The overall mean Y-intercept was 0.201 absorbance
unit, while the standard deviation was 0.020 absorbance unit (3 degrees
of freedom). This results in a 95 percent confidence interval of 0. 201 +
0. 064. The information in these two measures is limited by the fact that
only one calibration curve was made by only four collaborating laboratories.
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19
2. Control Samples
The control samples of standard sulfite solutions were
recorded by each laboratory on each day on the basis of concentration
added and concentration measured. The differences between these two
figures were subjected to an analysis of variance to determine the
day-to-day within-laboratory variability as well as the between-laboratory
variability. These data consist of twenty-four individual values (four
laboratories x six days) and are included in Table C-5.
The analysis of the control samples revealed that between-
laboratory variability accounted for 72 percent of the total, while
within-laboratory variability was responsible for the remaining 28 percent.
The standard deviation for between-laboratory variability was 0.868(o.g
(3 degrees of freedom) which gives a 95 percent confidence interval of
+ 2.76|j.g. The standard deviation for within-laboratory variability was
found to be 0.543|j.g (20 degrees of freedom), so that the 95 percent
confidence interval of this measure was +_ 1.13(j.g. For a 30-1 air sample,
these standard deviations correspond to concentrations of 38|j.g/m and
92fjtg/m , respectively.
3 . Reagent Blanks
Each of the collaborating laboratories prepared a reagent
blank on each of the six sampling days . The values for the reagent blanks
together with the differences between the reagent blanks
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and the Y-intercepts of the calibration curves in absorption units are
shown in Table C-5. An analysis of variance was conducted on the
intercept/reagent blank differences, and the overall mean was not
significantly different from zero. The standard deviation of the
within-laboratory variability was 0.019 absorbance unit (20 degrees
of freedom), representing 82 percent of the total variability. The
95 percent confidence interval was thus + 0. 040 absorbance unit.
The between-laboratory variability accounted for the remaining
18 percent of the total, and the standard deviation of this component
was 0.009 absorbance unit (3 degrees of freedom). The 95 percent
confidence limit of this component was + 0.028 absorbance unit.
In certain cases, the above measures for the 24-hour sampling
method differ from corresponding results of the 30-minute sampling
method. Part of this disagreement is thought to be due to the limited
number of collaborators (four) participating in the 24-hour study. On
the basis of only four laboratories, the tests for outlying observations
become inconclusive, and there was hesitancy to eliminate observations
which proved to be marginal. Thus, all observed values were retained,
and the results are quoted on the basis of an analysis on the complete
set of data.
D. Application of the Results
It was necessary to employ a number of techniques in analyzing
the data that were submitted by the collaborating laboratories. The details
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21
of these individual analyses are documented in Appendix B, and only
the important results are summarized here. In all instances, the
following results are based on a 0.05 level of significance. This
allows the results of this study of the 24 -hour sampling study to be
compared directly with the results of the 30-minute study for which a
0.05 significance level was chosen.
The following expressions define the replication error (O~^ )»
A A
the repeatability ((T"' ), and the derived reproducibility (O~~ ) of the
24-hour method as a function of SO., concentration. The graphical
L*
representation of these expressions appears in Figure 2, and both the
A
standard deviation ((J~~ ) and concentration level (y ) are in units of
= (.2312 + .0035 y ) (4.31)
(T = 2.77 (.2312 + ,0035y) (11.26)
(T = 2.77 (.2312 + .0035y ) (22.91)
Various measures of precision can be computed on the basis of
these equations. Some of the more fundamental statements of precision
are given below based on results from the analysis of variance treating
the three concentrations together.
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22
With respect to replication, the maximum permissible
difference between duplicates is given by
= (2.82)(.2312 + .0035y )(4.31)
If two replicates differ by more than R , there is less than
one chance in twenty that they belong to the same population. R
max
has been calculated for the three nominal SO2 concentrations which
were sampled in this study, and the results expressed as a percentage
of concentration. These replication percentages are presented in the
first row of Table 1-1.
TABLE 1-1. Rmax AS A PERCENTAGE
OF CONCENTRATION
Concentration, [i
Parameter 100 250 400
Replication Error 7.1 5.4 5.0
Repeatability 25.7 19.5 18.0
Reproducibility 59.9 45.6 42.0
From this, we see that 7.1 is the smallest percentage difference between
two replicates that is significant in the 24-hour test at concentration
3
levels of 100(jig/m .
The following expression is used to compare two single -replicate
observations made by the same analyst on different days.
Rmax= (3.92)(.2312 + . 0035y
-------
23
At a concentration level of 100|j.g/m , it is seen from Table 1-1 that
a difference of less than 25.7 percent cannot be detected between two such
observations.
The expression which allows comparison of two observations
made in separate laboratories on the same sample is:
R = (4.50)(.2312 + .0035y )(22.91)
max
For this measure, the method is unable to distinguish a real difference
of less than 59. 9 percent between observations at concentration levels
of lOOfig/m . For each measure, the percentage difference that can
be detected decreases with concentration; however, the absolute
difference that is detectable increases with concentration.
-------
24
LIST OF REFERENCES
1. McKee, H.C., Childers, R.E., and Saenz, O., Jr.,
Collaborative Study of Reference Method for Determination
of Sulfur Dioxide in the Atmosphere (Pararosaniline Method),
prepared for Office of Measurement Standardization,
Division of Chemistry and Physics, National Environmental
Research Center, Environmental Protection Agency,
Research Triangle Park, N.C. Contract CPA 70-40,
September 1971.
2. Mandel, John, The Statistical Analysis of Experimental Data,
John Wiley and Sons, Inc. New York, Chapter 9, pp 213-18
(1964).
3. Youden, W.J., Statistical Techniques for Collaborative Tests,
A.O.A.C. Publication 1969.
-------
APPENDIX A
Reference Method for the Determination of Sulfur Dioxide
in the Atmosphere (Pararosaniline Method)
-------
RULES AND REGULATIONS
APPENDIX A.—HEITHENCE >frrnoB FOR THE
DLTCRMINATJON OF SULFUR DIOXIDI is' THE
ATMOSPHERE (PAJUROSHNJLINE METHOD?
1. Principle and Applicability. 1.1 Sulfur
dioxide Is absorbed from air In a solution of
potassium tetrachloromercurate (TCM). A
dtchlorosulfltomcrciirate complex, which re-
sists oxidation by the oxygen in the air. is
formed (J. 2). Once formed, this complex Is
stable to strong oxldants (e.g., ozone, oxides
of nitrogen)* The complex Is reacted with
pararosanllltie and formaldehyde to form In-
tensely colored parnrosnnlllue methyl sul-
fonlc add (J). The absorbance of the solu-
tion is measured Bpectrophotometricully.
1.2 The method Is applicable to the meas-
urement of sulfur dioxide lit ambient air
using sampling periods up to 21 hours.
2. Rcnge ant Sensitivity. 2.1 Concentra-
tions of sulfur dioxide In the range of 25 to
1.050 ue/m.' (0.01 to 0.40 p.p.m.) can be meas-
ured under the conditions given. One can
measure concentrations below 25 pg./m.' by
sampling larger volumes of sir. but only If
the absorption efficiency of the particular sys-
tem Is first determined. Higher concentra-
tions can be analyzed by using smaller gas
samples, a larger collection volume, or a suit-
nble aliquot of the collected sample. Beer's
Law Is followed through the working range
from 0.03 to 1.0 absorbance units (0.8 to 27
fjf. of sulflte Ion In 25 ml. Anal solution com-
puted as SO:)-
2.2 The lower limit ol detection ol sulfur
dioxide In 10 ml. TCM Is 0.75 tg., (based on
twice the standard deviation) representing a
concentration of 25 pg/nVSOi (0.01 p.p.m.)
In an air sample of 30 liters.
3. Interferences. 3.1 The effects of the
principal known Interferences have been
minimized or eliminated. Interferences by
oxides of nitrogen are eliminated by sutlamlc
acid (4, S), ozone by time-delay (S). end
heavy metals by EDTA (ethylenedlamlne-
tetroncetlc acid, dlsodlum salt) and phos-
phoric acid («, £,). At least 60 ;>phere at the desired flow rate.
5 1.3 Air non-racier or Critical Orifice.
A calibrated rotumeter or critical orlftce ca-
pable of measuring air flow within ±2 per-
cent. For 30-mlnule sampling, a 22-gnuge
hypodermic needle ] Inch long may be used
as a critical or I flee to give a flow of about 1
liter'minute. For 1-hour sampling, a 23-
gauge hypodermic needle five-eighths of an
Inch long may be.used as a critical orifice to
give a flow of about 0.5 IHer. minute. For
21 hour sampling, a 27-gauge hypodermic
needle three-eighths of an inch long may be
used to give a flow of about 0.2 liter/minute.
Use a membrane niter to protect the needle
(Figure Ala).
6.2 Analysis.
5.2.1 Spertrophototncter. Suitable for
measurement of absorbance at 548 nm. with
an effective spectral band width of less than
15 nm. Reagent blank problems may occur
with spcctropholometrrs having greater
spectral band width. The wavelength cali-
bration of the Instrument should be verified.
If transmlttance Is measured, this can ba
converted to absorbance:
Arrlog,, (1/T)
6. Reagents.
6.1 Sampling.
6.1.1 Distilled water. Must be free from
oxldants.
6.1.2 Absorbing Reagent \0.04 M Potai-
sium TctracMoromercurute (TCM) [.Dissolve
10.96 g. mercuric chloride. O.OS6 g. EDTA
(thylenedlamlnetetraacetlc acid, dlsodoum
salt), and 6.0 g. potassium chtorlde In water
and bring to mark In a 1.000-ml. volumetric
flask. (Caution: highly poisonous. If spilled
on skin, flush off with water Immediately).
The pH of this reagent should be approxi-
mately 4.0, but It tins been shown that there
Is no appreciable difference In collection
efficiency over the range of pH 5 to pH 3.(7)
The absorbing reagent. Is normally stable for
6 months. If a precipitate forms, discard the
reagent.
6.2 Analysis.
6.2.1 Sul/amic Acid (0.6 percent). Dis-
solve 0.6 g. sulfamlc acid in 100 ml. distilled
water. Prepare fresh dally.
6.2.3 Formaldehyde (fl.2 percent). Dilute
5 ml. formaldehyde solution (36-38 percent)
to 1.000 ml. with distilled water. Prepare
dally.
6.2.3 Stock Iodine Solution (0.1 N). Place
12.7 g. Iodine In a 250-ml. beaker; add 40 g.
potassium Iodide and 25 ml. water. Stir until
all is dissolved, then dilute to 1,000 ml. with
distilled water.
6.2.4 Iodine Solution (0.01 rV). Prepare
approximately 0.01 N Iodine solution by di-
luting £0 ml. of stock solution to GOO ml.
with distilled water.
6.2.S Starch Indicator Solution. Triturate
0.4 g. soluble etarch and O.OO2 g. mercuric
Iodide (preservative) with a little water, and
add the paste slowly to 200 ml. boiling water.
Continue boiling until the solution le clear;
cool, and transfer to a glass-stoppered bottle.
6.2.6 Stock Sodivm Thiosulfate Solution
(0.1 N). Prepare a stock solution by dissolving
25 g. sodium thlosulfate In
1,000 ml. freshly boiled,cooled, distilled water
and add 0.1 g. sodium carbonate to the solu-
tion. Allow the solution to stand 1 day before
standardizing. To standardize, accurately
weigh, to the nearest 0.1 mg., 1.5 g. primary
standard potassium lodate dried at ISO* C.
and dilute to volume In a 500-ml. volumetric
flask. To a 500-ml. Iodine flask, plp*t 50 ml.
of lodate solution. Add 2 g. potassium Iodide
and 10 ml. of 1 N hydrochloric acid. Stopper
the flask. After 5 minutes, titrate with stock
thtosuirate solution to a pale yellow. Add 6
ml. starch Indicator solution and continue
the tltratlon until the blue color disappears.
Calculate the normality of the stock
solution:
w
N= —X2.80
M
N=Normality of stock thlosulfate solu-
tion.
M=Volume of thlosulfate required, ml.
W = Weight of potassium lodate. grains.
2.60 =
10»(oonverslon of g. to mg.) XO.l (traction lodate used)
35.67 {equivalent weight of potassium lodate)
6.2.T Sodium Tliiosulfaie Tltrani {0.01 N).
Dilute 100 ml. of the stock thlosulfate solu-
tion to 1.000 ml. with freshly balled distilled
water.
Normality = Normality of stock solution
X 0.100.,
6.2.8 Standardize Svlftte Solution [or
Preparation of Working Sulfitc-TCM Solu-
tion. Dissolve 0.3 g. sodium metablsulfkte
(Na.S,OB) or 0.40 g. sodium sulflte (Na.SCy
In 500 ml. of recently boiled, cooled, distilled
water. (Sulflte solution is unstable: It Is
therefore Important to use water of the high-
est purity to minimize this Instability.) This
solution contains the equivalent of 320 to 400
jig./ml. of SO,. The actual concentration of
the solution is determined by adding excess
Iodine and back-titrating with standard
sodium thlosulfate solution. To back-titrate,
plpet 30 ml. of the 0.01 N Iodine Into each of
two 500-ml. iodine flasks (A and B). To flask
A (blank) add 25 ml. distilled water, and to
flask B (sample) plpet 25 ml. sulflte solution.
Stopper the Masks and allow to react for 5
minutes. Prepare the working sulflte-TCM
Solution .(629) at the same time Iodine
solution Is added to the flasks. By means of
a buret containing standardized 0 01 N thlo-
sulfate. titrate each flask In turn to a pale
yellow. Then add 5 ml. starch solution and
continue the tltratlon until the blue color
disappears.
6.2.9 Working Sulfitc-TCM Solution. Plpet
accurately 2 ml. of the standard solution Into
a 100 ml volumetric flask and bring to mark
with 0.04 M TCM. Calculate the concentra-
tion of sulfur dioxide In the working solu-
tion:
(A - B) (N) (32,000)
"26
xo.oa
A=Volume thlosulfate for blank, ml.
B = Volume thlosulfate for sample, ml.
N = Normality of thlosulfate tltrant.
32,000= MJiHequivalcnt wt. of SO,, pg.
25=Volume standard sulflte solution.
ml.
0.02=Dilution factor.
This solution Is stable for 30 days If kept at
51 C. (re frige rotor). If not kept at 5* C..
prepare dally.
6.2.10 Purified Pararosaniiine Stock Solu-
tion {0.2 percent nominal).
6.2.10.1 Dye Specifications. The pararo-
snnlline dye must meet the following per-
formance specifications: (1) the dye must
have a wavelength of maximum absorbance
ai 540 nm. when assayed In a bulTered solu-
tion of 0.1 M sodium acetate-acetic acid; (2)
the absorbance of the reagent blank, which Is
temperature-sensitive (0.015 absorbancc
unlt/'C). should not exceed 0.170 absorbance
unit at 22* C. with a 1-cm. optical path
length, when the blank Is prepared accord-
ing to the prescribed analytical procedure
and to the specified concentration of the dye:
(3) the calibration curve (Section 8.2.1)
should have a slope of 0.030 ±0.002 absorb-
ance unlts/ig. SO: at this path length when
the dye Is pure and the sulflte solution Is
FCDEPAl REGISTER, VOL. 36, NO. B4—FRIDAY, APRIL 30, 1971
A-]
-------
RULES AND REGULATIONS
properly standardized.
0.2.10.2 Preparation o/ Slock Solution. A
specially purified (99-100 percent pure) so-
lution of parnrosnnlllne. which meets the
above specifications, Is commercially avail-
able In the required 0.20 percent concen-
tration (Harleco'). Alternatively, the dye
may be purified, a stock solution prepared
and then assayed according to the proce-
dure of Scarlngelll. ct al. (4)
6.2.11 Pararosanilinc Reagent. To a 250-
ml. volumetric flftsk, add 20 ml. stock par-
arosanlllnc solution. Add an additional 0.2
ml. stock solution for each percent the stock
assays below 100 percent. Then add 25 ml.
3 M phosphoric acid and dilute to volume
with distilled water. This reagent Is stable
for at least 9 months.
7. Procedure.
7.1 Sampling. Procedures are described
for short-term (30 minutes and 1 hour) and
for long-term (24 hours) sampling. One can
select different combinations of sampling
rate and time to meet special needs. Sample
volumes should be adjusted, GO that linearity
Is maintained between absorbance and con-
centration over the dynamic range.
7.1.1 30-Minufe and 1-Hour Samplings.
Insert a midget Implngcr Into the sampling
system. Figure Al. Add 10 ml. TCM solution
to the Implnger. Collect sample at 1 liter/
minute for 30 minutes, or at 0.5 liter/minute
for 1 hour, using either a rotametcr, as
shown In Figure Al, or a critical orifice, aa
shown In Figure Ala, to control flow. Shield
the absorbing reagent from direct sunlight
during and after sampling by covering the
Implngcr with aluminum foil, to prevent
deterioration. Determine the volume of air
campled by multiplying the flow rate by the
time In minutes and record the atmos-
pheric pressure and temperature. Remove
and stopper the Implnger. If the sample
must be stored for more than a day before
analysis, keep It at 6' C. In a refrigerator
(ECO 4.2).
7.1.9 14-Hour Sampling. Place 60 ml.
TCM solution In a largo absorber and col-
lect tho sample at 0.2 liter/minute for 24
hours from midnight to midnight. Make sure
no entralnment of solution results with the
Implnger. During collection and storage pro-
tect from direct sunlight. Determine the
total air volume by multiplying the air flow
rate by the time In minutes. The correction
of 24-hour measurements for temperature
and pressure Is extremely difficult and Is not
ordinarily done. However, the accuracy of
the measurement will be Improved If mean-
ingful corrections can be applied. If storage
Is necessary, refrigerate at 5* C. (see 4.2).
7.2 Analysis..
7.2.1 Sample Preparation. After collection,
If a precipitate Is observed In the sample,
remove It by centrlfugatlon.
7.2.1.1 30-Minute and 1-Hour Samples.
Transfer the sample quantitatively to a 25-
ml. volumetric flask; use about 5 ml. distilled
water for rinsing. Delay analyses for 20 min-
utes to allow any ozone to decompose.
7.2.1.2 24-Hour Sample. Dilute the entire
sample to 50 ml. with absorbing solution.
PIpct 5 ml. of the sample Into a 25-ml.
volumetric flask for chemical analyses. Bring
volume to 10 ml. with absorbing reagent.
Delay analyses for 20 minutes to allow any
ozone to decompose.
7.2.2 Determination. For each set of de-
terminations prepare n reagent blank by add-
ing 10 ml. uncxposcd TCM solution to a 25-
ml. volumetric flask. Prepare a control solu-
tion by adding 2 ml. of working sulfltc-TCM
solution and 8 ml. TCM solution to a 25-ml.
volumetric flask. To each flask containing el-
•Hartmen-Leddon, 60th and Woodland
Avenue. Philadelphia. PA 19143.
ther sample, control solution, or reagent
blank, add 1 ml. 0.6 percent sulfamlc
acid and allow to react 10 minutes to de-
stroy the nitrite from oxides of nitrogen.
Accurately plpet In 2 ml. 0.2 percent
formaldehyde solution, then 5 ml. par-
arosanlllne solution. Start a laboratory
timer that has been set for 30 minutes. Bring
all flasks to volume with freshly boiled and
cooled distilled water and mix thoroughly.
After 30 minutes end before GO minutes, de-
termine the absorbances of the sample (de-
note as A), reagent blank (denote as A«) and
the control solution at 648 nm. using 1-cm.
optical path length cells. Use distilled water.
not the reagent blank, as the reference.
(NOTEI This is Important because of the color
sensitivity of the reagent blank to tempera-
ture changes which can be Induced In the
cell compartment of a spectrophotometer.)
Do not allow the colored solution to stand
In the absorbance cells, because a dim of dye
may be deposited. Clean cells with alcohol
after use. If the temperature of the determi-
nations does not differ by more than 2* C.
from the calibration temperature (8.2), the
reagent blank should be within 0.03 absorb-
ance unit of the y-lntercept of the calibra-
tion curve (8.2). If the reagent blank differs
by more than 0.03 absorbance unit from that
found In the calibration curve, prepare a new
curve.
7.2.3 Xosorbancc Range. If the absorbance
of the sample solution ranges between 1.0
end 2.0, the sample can be diluted 1:1 with
a portion of the reagent blank and read
within a few minutes. Solutions with higher
absorbance can be diluted up to sixfold with
the reagent blank In order to obtain onscale
readings within 10 percent of the true ab-
sorbance value.
8. Calibration and Efficiencies.
8.1 Flowmetcrs and'Hypodermic Needle.
Calibrate flowmeters and hypodermic nee-
dle (8) against a calibrated wet test meter.
8.2 Calibration Curves.
8.2.1 Procedure with Sulfitc Solution. Ac-
curately plpet graduated amounts of the
working sulflte-TCM solution (6.2.9) (such
as 0, 0.6, 1, 2, 3, and 4 ml.) Into a series of
25-ml. volumetric flasks. Add sufficient TCM
solution to each flask to bring the volume to
approximately 10 ml. Then add the remaining
reagents as described In 7.2.2. For maximum
precision use. a constant-temperature bath.
The temperature of calibration must be
maintained within ±1* C. and In the range
of 20* to 30* C. The temperature of calibra-
tion and the temperature of analysis must be
within 2 degrees. Plot the absorbance against
the total concentration In pg. SOj for the
corresponding solution. The total jig. SOj In
solution equals the concentration of the
standard (Section 6.2.9) In eg- SOVml. times
the ml. sulflte solution added (pg. SO:=
jig./ml. SOrXml. added). A linear relation-
ship should be obtained, and the y-lntcrcept
should be within 0.03 absorbance unit of the
zero standard absorbance. For maximum pre-
cision determine the line of best Dt using
regression analysis by the method of least
squares. Determine the slope of the line of
best fit, calculate Its reciprocal and denote
as Bi. B, Is the calibration factor. (Sec Sec-
tion 6.2.10.1 for specifications on the slope of
the calibration curve). This calibration fac-
tor can be used for calculating results pro-
vided there are no radical changes in
temperature or pH. At least one control
sample containing a known concentration of
SO; for each series of determinations. Is
recommended to Insure the reliability of this
factor.
8.23 Procedure with SOi Permeation
Tubes.
8.2.2.1 Central Considerations. Atmos-
pheres containing accurately known amounts
of sulfur dioxide at levels of Interest can be
prepared using permeation tubes. In the
systems for generating these atmospheres,
the permeation tube emits SO, gas . at a
known, low. constant rate, provided the tem-
perature of the tube Is held constant ( ±0.1 '
C.) end provided the tube has been accu-
rately calibrated at the temperature of use.
Tho SO. gas permeating from the tube Is
carried by a low flow of inert gas to a mix-
Ing chamber where It Is accurately diluted.
with SO,-frce air to the level of Interest and
the sample taken. These systems are shown
schematically In Figures A2 and A3 and have
been described In detail by O'Kecffe and
Ortman (9). Scarlngelll. Prey, and Saltzman
(10). and Scarlngelll, O'Keeffe, Rosenberg,
and Bell (Jl).
8.2.2.2 Preparation of Standard Atmos-
pheres. Permeation tubes may be prepared
or purchased. Scaringclli. O'Kcc.Te. Rosen-
berg, and Bell (11) give detailed, cypher.
directions for permeation tube calibration.
Tubes with a certified permeation rate arc
available from the National Bureau of Stand-
ards. Tube permeation rates from 0.2 to 0.4
ng. /minute Inert gns flows or about 50 ml./
minute and dilution air flow rates from 1.1
to 15 liters/minutes conveniently give stand-
ard atmospheres containing desired levels
of SO, (26 to 390 ug./m.': 0.01 to 0.15 p.p.m.
SO,) . The concentration of SO, In any stand-
ard atmosphere can be calculated as follows:
Where:
O = Concentration of SOj, pg./m."- at ref-
erence conditions.
P =Tube permeation rate. ug. /minute.
Rd=Flow rate of dilution air. Ittcr/mlnutc
at reference conditions.
Rc=Flow rate of inert gas. liter/minute at
reference conditions.
8.2.2.3 Sampling and Preparation of Cali-
bration Curve. Prepare a scries (usually six;
of standard atmospheres containing SOj
levels from 25 to 390 /ig. SO,/m.J. Sample onrh
atmosphere using similar apparatus and tak-
ing exactly the same air volume as will be
done In atmospheric sampling. Determine
absorbances as directed In 7.2. Pint the con-
centration of SOj In pg.,'m.> (x-nxlsV against
A— A0 values (y-axls), draw the straight lino
of best fit and determine the slope. Alter-
natively, regression analysis by the method
of least squares may be used to calculate the
slope.' Calculate the reciprocal of the slope
and denote as Be.
8.3 Sampling Efficiency. Collection effi-
ciency Is above 98 percent; efficiency mny
fall off, however, at concentrations below 25
/ig./m.'. (12, 13)
9. Catenations.
9.1 Conversion of Volume. Convert the
volume of air sampled to the volume at ref-
erence conditions of 25* C. and 760 mm. Kg.
(On 24-hour samples, this mny not be
possible.) p 29fl
v«=vx — x -
760 t + 273
Vn = Volume of air at 25' C. and 760 mm.
Hg, liters.
V = Volume of air sampled, liters.
P =r Barometric pressure, mm. Hg.
t = Temperature of air sample. 'C.
9.2 Sulfur Dioxide Concentration.
9.2.1 When sulfitc solutions arc used to
prepare calibration curves, compute the con-
centration of sulfur dioxide In the sample :
(A-A0) (10*) (B.)
jig. SOj/m.1 = - :•• D
VB
A = Sample absorbance.
A0 = Reagent blank absorbance.
IV>= Conversion of liters to cubic meters.
Va =The sample corrected to 25" C. and
160 mm. Hg, liters.
FEDERAL REGISTER, VOL. 36, NO. 84—FRIDAY, APRIL 30, 1971
A-2
-------
RULES AND REGULATIONS
B. = Callbratlon factor, ^g./absorbance
unit.
D ^Dilution (actor.
For 30-mlnute and 1-hour samples,
D=l.
For 24-hour samples, D=10.
9.33 When SO, gas standard atmospheres
are used to prepare calibration curves, com-
pute the sulfur dioxide In the sample by the
following formula:
SO,,«./m.'=(A-A.)xB.
A = Sample absorbance.
Ao —Reagent blank absorbance.
B,= (S*< 8.2.2.3).
9.2.3 Conversion of ng./m.' to p.p.m.- If
desired, the concentration of sulfur dioxide
may be calculated as p p.m. SO. at reference
conditions as follows:
p.p.m. SO, = Mg SO,/m.' x 3 82 X 10-«
10. Rtterenca.
(1) West. P. W.. and Oaeke. O. C., -Fixa-
tion of Sulfur Dioxide as Sulfltomer-
curate III and Subsequent Colorl-
rnctrlc Determination", Anal. Cliem.
Z», 1816 (1956).
(2) Ephralms, P.. "Inorganic Chemistry,"
p. 562, Edited by P.C I, Thome and
E. R. Roberts, Sth Edition, Inter-
science. (1948).
(3) Lyles. Q. R., Dowllng. F. B., and Blanch-
ard, V. J.. "Quantitative Determina-
tion of Formaldehyde In Parts Per
Hundred Million Concentration Lev-
el", J. Air Poll. Cont. Assoc. IS, 106
(1965). i
(4) Scarlngelll. F. P., Saltzman. B. E.. and
Prey, S. A.. "Spectrophotometrlc De-
termination of Atmospheric Sulfur
Dioxide". Anal. Chcm. 39. 1709 (1967).
(5) Pate, J. B., Ammons, B. E., Swanson,
a. A., Lodge. J. P.. Jr.. "Nitrite In-
terference In Spectrophotometrlc De-
termination of Atmospheric Sulfur
Dioxide", Anal. Chr.m. 37, 942 (1965).
(6) Zurlo. N. and Grimm, A. M.. "Measure-
ment of the SO, Content of Air In the
Presence of Oxides of Nitrogen and
Heavy Metals", Meit. Lavoro, 53, 330
(1963).
(7) Scsrlngelllv F. P.. Elfers, L.. Norrls, D.,
and Hochhelser. S., "Enhanced Sta-
bility of Sulfur Dioxide In Solution",
Anal. Cliem. 42, 1818 (1970).
(8) Lodge, J. P. Jr., Pate, J. B., Ammons,
B. E. and Swanson, Q. A., "Use of
Hypodermic Needles as Critical Ori-
fices In Air Sampling," J. Air Poll.
Cont. Assoc. 16, 197 (1966).
(9) O'Keeffe, A. •£., and Ortman, O. C..
"Primary Standards for Trace Gas
Analysis". Hnal. Ch.cm. 31, 760 (1966).
(/O) Scarlngelll, F P., Frey. S. A., and Saltz-
man, B. E., "Evaluation of Tenon
Permeation Tubes for Use with Sulfur
Dioxide". Amer. Int. Hygiene Assoc.
J. 28, 260 (1967).
(11} Scarlngelll, F. P., O'Keeffe, A. E., Rosen-
berg. E., and Bell. J. P., "Preparation
of Known Concentrations of Oases
and Vapors with Permeation Devices
Calibrated Gravlmetrlcally", Anal.
CArm. 42.871 (1B70).
(12) Urone. P.. Evans, J. B., and Noyes. C. M..
"Tracer Techniques In Sulfur Di-
oxide Colorlmetrlc and Conductlo-
metrlc Methods", Anal Chcm. 37, 1104
(1965).
(13} Bostrom. C. E., "The Absorption of Sul-
fur Dioxide at Low Concentrations
(p.p.m.) Studied by an Isotoplc
Tracer Method". Intern. J. Air Water
Poll. 9,33 (1965),
=0)==^
30ml
20ml
10ml
Figure A1a. Critical orifice flow control.
IMPINGER
Figure A1. Sampllnj train,
FEDERAL REGISTER, VOL. 36, NO. »4—FRIDAY, APRIL 30, 1971
A-3
-------
RULES AND REGULATIONS
TO noon
CYLINDER
[^ . AIR OR
•* HITROQEM
PERMEATION TUBE
UBBLER
FlBure A2. Apparatus br mvlMlrlc ctllbntlea ind (ItU i
-CLEAN MT AM
NEEDLE VALVE
rinrn A}. PignMlton lit* iclKMlte Iw hbtnloy u».
FIOEKAL HIGISTfH, VOL 36, NO. 14—FRIDAY, APRIl 30, 1971
A-4
-------
APPENDIX B
Statistical Design and Analysis
-------
APPENDIX B
Table of Contents
Page
I. Introduction
A. Purpose and Scope of the Experiment B-l
B. Design of the Experiment B-2
II. Preliminary Data Analysis B-7
A. Presentation of Data B-7
B. Tests for Outlying Observations B-9
C. Discussion of Results of Preliminary Data
Analyses B-ll
III. Analysis of Variance B-13
A. Analysis of Variance of Concentrations Separately B-13
B. Analysis of Variance for All Concentrations
Analyzed Together B-18
C. Linear Model Analysis B-21
IV. Application of the Re suits B-30
A. Correction of Laboratory Bias B-30
B. Precision of Method B-34
C. Accuracy and Bias B-38
List of References B-42
B-ii
-------
APPENDIX B - STATISTICAL DESIGN AND ANALYSIS
I. INTRODUCTION
The present study of the pararosaniline method of measuring
sulfur dioxide in the atmosphere is supplemental to and in support of
an earlier similar study' '. Primarily, the two studies differ only by
the fact that the present study used a sampling time period of 24 hours,
while the earlier study investigated the method using 30-minute
sampling periods. For the present study, no familiarization session
was conducted since three of the four collaborating laboratories had
participated in the earlier study and were, therefore, completely
familiar with the method. Southwest Research Institute acted as the
fourth laboratory and was, of course, familiar with the method by
way of having experimented with the method while organizing both
collaborative studies.
A. Purpose and Scope of the Experiment
The purpose of the present study was twofold; (1) to determine
the reliability of the method using sampling periods of 24 hours, and
(2) to compare these measures with corresponding results for the 30-minute
sampling study. In order to facilitate comparisons between the two
studies, it was desirable to duplicate the analysis wherever the
experimental design, the format of the data, and other considerations
permitted.
B-l
-------
The experimental collaborative study should be designed so
that a straightforward analysis of variance can be conducted on the
resulting data. This type of analysis gains the greatest amount of
information that can be obtained from a given amount of data. Resources
are thus optimized by requiring fewer collaborators, samples and
replicate observations. Such an approach requires careful selection of
laboratories, randomization of sample testing, and somewhat confines
the analysis of outlying observations.
Although it was desired that a minimum of six laboratories participate
in the study, the services of only four laboratories could be secured
because of the large manhour requirement to run the tests . Since these
laboratories had provided reliable results in previous studies, there was
no reason to expect an unusually large scatter in the observations they
would-make for the present study.
Each laboratory was required to analyze three separate concentrations
Because individual equipment for generating the sample atmospheres was
supplied to each laboratory, the concentrations could not be identical for
all laboratories. However, calibration points at which the generating
equipment was to be operated were specified so that the expected con-
centrations would be very similar for all laboratories. The expected mean
concentrations were nominally 98, Z91 and 475ug/m .
Bi. Design of the Experiment
The experimental design of this study was structured so that
analysis of variance techniques could be employed. Three such techniques
B-2
-------
were employed in the present study:
(1) A four-factor analysis of variance with data in the original
scale for each concentration separately.
(2) A five-factor analysis of variance with data in a transformed
scale with all concentrations analyzed together.
(3) A linear model analysis with data in the transformed scale.
The experimental design is illustrated in Figure B-l. Each
factor was present in the following quantity; laboratories (four), runs (two),
concentrations (three), samples (three), and analyses (three). This
design results in a total of 216 individual observations. Comparing
the design of the 24-hour study with that of the 30-minute study, the
following analogies between factors should be noted:
Prior 30-minute Study Current 24-hour Study
laboratories (14) laboratories (4)
days (3) runs (2)
concentrations (3) concentrations (3)
replications (3) samples (3)
analyses (3)
The analytical design of this experiment considers the four
laboratories and the three concentrations to be fixed factors, each
randomly selected from a very large population, and crossed with
respect to one another. The run, sample and analysis are random
factors each nested within laboratories.
B-3
-------
R
(same as R.)
V
i J
V
V
\ A
\\ J
^ j
k
\ J
s /
V
S J
\ J
V
\ A ,
S i J
\
FIGURE B-l. DESIGN OF COLLABORATIVE EXPERIMENT. L, LABORATORIES;
R, RUNS; C, CONCENTRATIONS; S, SAMPLES; A, ANALYSES.
B-4
-------
Three general sources of variability were analyzed in the
present study. Because of the 24-hour sampling requirement, only one
concentration could be tested per day. The most fundamental measurement
of the method was therefore due to variations among observations
recorded by a laboratory during a single day. This variation is referred
to as the replication error. The second level of variability is that which
occurs within the observations recorded by a single laboratory on
successive days of testing. This measurement is a combination of
day-to-day variability and the previously defined replication error and,
for this study, shall be termed the repeatability. The third measure is
called reproducibility, and in addition to replication error and repeatability,
it includes the component which describes laboratory-to-laboratory
variability.
All three measures were developed by each of the analysis
techniques. Taken together they describe the source and magnitude of
measurement errors that are inherent within the method. With one
exception, the definitions of these measures are consistent with those
used in the 30-minute study so that comparisons between these studies
are valid. The exception is that repeatability and reproducibility as
defined in the 30-minute study have been multiplied by the factor 2.77 in
(6)
the present study so as to conform with Mandel's definition.
In addition to the analysis of the observations of the sample
concentrations, a large volume of supplemental data was also analyzed.
B-5
-------
These data pertain to calibration procedures required by the method
and include the individual points for each calibration curve, the
concentration and absorbance of all control samples, and the
absorbances of all blanks .
B-6
-------
II. PRELIMINARY DATA ANALYSIS
Each of the collaborating laboratories was able to conduct the
entire series of measurements called for by the experimental design
with only limited equipment difficulties. These equipment malfunctions
will be dealt with in more detail in the section which discusses the handling
of outlying observations.
The data provided by the collaborators were checked for internal
consistency. No obvious deviations from the prescribed method were noted.
The calculations which the collaborators were required to conduct were
checked for arithmetic errors and none were identified beyond the
acceptable disagreements due to rounding.
A . Presentation of Data
The observed values recorded during the tests by each of the
collaborating laboratories are documented in Table B-l. The expected
concentration values based on the calibrated performance of the SO-
generating equipment are given in Table C-l. The observed values,
Table B-l, were adjusted to compensate for the difference in the expected
concentrations for the four laboratories . The adjusted values are found
in Table C-3.
It was not appropriate to conduct an analysis of variance on the
original observations, since the SO^ levels for each of the three concentration
ranges were not identical among laboratories. It was possible, however,
to analyze the differences between the observed and expected values
for each concentration, since the expected values for the four laboratories
for each concentration range were quite similar to one another.
These difference values are recorded in Table C-2 with
B-7
-------
LOV/ CONCENTRATION' SO.
i
Run HI
Run 82
Laboratory
799 Sample =? 1
Sample =2.
Sample =3
£927 Sample = 1
Sample = 2
Sample ==~1
= 345 Sample = 1
Sample £ 2
Sample = 3
= 920 Sample =1
Sample = 2
Sample =3
= 799 Sample =1
Sample £2
Sample «3
:?927 Sample =1
Sample =2
Sample =3
= 345 Sample = 1
Sample r-2
Sample r?3
r'920 Sample = 1
Sample = 2
Sample =3
= 799 Sample =1
Sample = 2
Sample =3
= 927 Sample fr: 1
Sample = 2
Sample = 3
= 345 Sample = 1
Sample = 2
Samplo =3
^920 Sample =1
Sample r 2
lc 4:3
Analysis 1
90
92
83
101. 9
103. 5
104.2
81
84
86
95.2
96.7
91. 9
Analysis 2
85
96
83
101. 9
103. 5
107.3
81
C2
84
97.2
99.4
99.8
Analysis 3
85
96
88
101. 9
103. 5
104. 2
84
84
88
93. 0
95.2
97.2
Analysis 1
85
111
96
96.9
99.2
99.2
85
88
98
90. 2
93.3
92. 4
Analysis 2
87
102
94
96. 9
412
426.4
425.6
425.0
377
393
387
227*
386
383
429
426
403
429. 6
422.4
425. 0
383
391
388
220*
379
375
B-8
-------
observations that ultimately proved to be outliers marked with asterisks.
Table C-3 contains the adjusted values of Table B-l. Finally, Table B-2
gives the values of Table C-3 in a transformed scale with appropriate
substitutions made for the outlying observations as explained in the following
section.
The transformation of the values of Table C-3 was necessary
because of lack of homogeneity of variances between concentrations . It
was not worthwhile to perform the analysis of variance on all concentrations
together until the requirement of homogeneity between concentrations was
established. The details of this transformation are discussed in the section
dealing with the analysis of all concentrations together . The analysis of
variance for all concentrations together was performed on the data in
Table B-2 and appears in Table B-5.
B . Tests for Outlying Observations
Outlier tests were conducted on the data in Table C-2 after a
preliminary review revealed several suspicious observations. Tests for
outliers were conducted among laboratory means, among day means
within laboratories, among sample means, and among analyses . The
tests employed were those developed by Dixon^ ' and David'^'.
Nine observations recorded by laboratory No. 920 and nine additional
observations reported by laboratory No. 799 proved to be outliers
according to these criteria. These outlying observations are noted by
asterisks in Tables B-l and C-2. The values recorded by these laboratories
on these days were significantly different from the values recorded by the
other participating laboratories at these concentration levels.
B-9
-------
It was possible to associate the outlying observations for
laboratory No. 920 with equipment malfunctions. This collaborator
reported that unusual flow rates prompted an investigation which revealed
a leak in the absorber of one of the samples at the cap and tube junction.
This leak was repaired at this time, and subsequent observations did not
prove to be outliers.
In the case of laboratory No. 799, poor agreement was noted
between the added control solution and the measured quantity. This
would indicate a calibration problem, and the mean of this set of
observations made on this day proved to be an outlier above other means
at this concentration level.
The complete elimination of these outlying observations was
rejected, since one of two undesirable circumstances would have resulted;
either an unequal number of values would remain for each laboratory, or
a large amount of otherwise useful data would have to be discarded. The
inclusions of the outliers in the analysis as they were reported would have
the undesirable effect of incorrectly influencing the ultimate measures of
accuracy. It was therefore decided that substitutions for these outlying
values would be the best solution to the problem in this case.
The pattern of the outliers reported by laboratory No. 920 was on
the basis of analyses conducted on a single sample during each of three
days . The remaining six observations on these days provide accurate
measures of the concentration that was tested. The mean and variance
B-10
-------
were calculated for each of the days on the basis of these six valid
observations. Randomized substitutions were then made for the outlying
values which would result in the same mean and variance when all nine
values (i.e., the six valid observations plus the three substitute values)
were analyzed together. In this way, the substitute values neither
contribute nor delete information for the testing during that day.
In the case of laboratory No. 799, all nine values reported for
the first day of measuring the medium concentration were outliers.
Thus, the only remaining valid observations by this collaborator for this
concentration are those made during the second run. The logical
substitution in this case was to duplicate those values observed during
the second day of testing the medium concentration. This substitution
would have a minimal effect on the analyses and sample variance
components for laboratory No. 799.
C. Discussion of Results of Preliminary Data Analyses
As noted previously, a preliminary examination was made of all
data submitted by the collaborating laboratories. Each calculation made
by the participants was checked for consistency with the instructions
given to the collaborators as well as with the requirements of the test
method. No errors were found beyond very insignificant rounding
differences .
In the case of handling outlying observations, the methods
employed were those considered to have the least influence on the final
results of the analysis without undue elaboration or expenditure of effort.
B-H
-------
Such compromises in data analysis are always dependent upon the
judgment of the analyst. In the present study, it was possible to
establish a reasonable physical cause for each outlying observation
so that the outlier test result only confirms and does not dictate the
problem data points.
B-12
-------
III. ANALYSIS OF VARIANCE
Three distinct analyses were conducted on the data submitted by
the collaborators after they had been corrected to eliminate the effects
of outlying observations. An initial analysis of variance was conducted
(Table B-3) on the adjusted data in the original scale (Table C-3) for
each concentration level. A second analysis of variance was performed
which treated all concentrations together (Table B-5) with the data in a
transformed scale (Table B-2). The final linear model analysis (Table B-8)
was conducted primarily to confirm the results of the first two analyses.
A discussion follows which treats each analysis separately with a final
section in which the techniques are compared and the results are
summarized.
A . Analysis of Variance of Concentrations Separately
A separate analysis of variance was performed on the data for
each of the three individual concentrations as though there were three
distinct collaborative studies being analyzed. In this analysis, the
variance components of four factors were compared among the three
concentrations . The mathematical treatment of the data for this analysis
was performed by a flexible computer program * . The inputs to this
program could be formatted according to the design of the desired
mathematical model of the experiment. For this analysis, the mathematical
model was:
y =M + L+R + Sf--,+ ef__l
ikms i k(i) m [k(i}J s im |k(iT] ^ (B-l)
B-13
-------
LOV/ CONCENTRATION' SO.
Run #1
Run H2
Laboratory
799 Sample •? 1
Sample = 2
Sample =3
= 927 Sample =1
Sample i?2
Sample =3
= 345 Sample = 1
Sample = 2
Sample = 3
= 920 Sample =1
Sample =2
Sample =3
= 799 Sample =1
Sample =2
Sample £3
:?927 Sample =1
Sample =2
Sample =3
= 345 Sample s? 1
Sample £2
Sample £3
--920 Sample =1
Sample =2
Sample =3
= 799 Sample =1
Sample = 2
Sample =3
= 927 San-pie -: 1
Sample = 2
Sample =3
= 34 5 Sample = 1
Sample =2
Sample =3
= 920 Sample =1
Sample -2
S a mole ^3
Analysis 1
83.0
86.7
70.3
106.9
110.3
110.3
70.3
75. 5
79.3
103.4
106. 9
97.6
Analysis 2
74.2
94.0
70.3
106. 9
110.3
114.8
70.3
71.6
75. 5
106. 9
110.3
111.4
Analysis 3
74.2
94.0
79.3
106. 9
110.3
110. 3
75. 5
75. 5
83.0
99. 9
103.4
106. 9
Analysis 1
74.2
120.3
94.0
97.6
101. 1
101. 1
78.0
83.0
101. 1
94.0
99. 9
97. 6
Analysis 2
78.0
104.6
90.4
97.6
96.4
106. 9
75. 5
86.7
99. 9
99. 9
110.3
108. p
Analysis 3
67.7
104.6
97.6
97.6
101. 1
106. 9
81.8
85.5
99. 9
92.8
99. 9
101. 1
MEDIUM CONCENTRATION
HIGH CONCENTRATION SO.
295. 1
276.0
294.5
305.6
305. 1
300.4
282.3
284.2
287. 9
315.2
316.9
317. 5
295. 1
266.3
294. 5
305.6
305. 1
300.4
281.7
284.2
287.3
325.0
322.4
326.7
286. 7
276. 0
287.3
305.6
305. 1
300. 4
281. .7
284.2
289. 7
320.2
316. 9
320.8
295. 1
294. 5
276.0
306.8
314. 1
314. 1
270.2
276.0
280. 5
300.4
303.3
301.6
295. 1
287. 3
266.3
306.8
314. 1
314. 1
272.8
276.0
278.6
303. 9
309. 1
305.6
286. 7
294. 5
276. 0
303. 9
314. 1
314. 1
270.2
279.8
284.2
307.3
303.3
301.6
394. 9
404. 0
396.6
400. 3
401. 1
403.6
388. 9
393.6
397.8
412. 5
419- 5
415.6
394. 9
404.0
390.2
402.8
401.1
403.6
388.5
393.6
395.3
419. 1
423. 7
422.6
394. 9
404.0
414.4 '
402.8
401. 1
401. 5
392.3
390.2
389.8
412. 5
419. 5
420. 3
416. n
410. 9
408. .9
412. 5
412. 5
412. 1
388. 5
391. 5
390.2
394.8
399. 1
396. 1
413. 7
417.2
408. 9
412. 5
412. 5
412. 1
385. 0
395. 3
391. 5
401. 1
401. 1
399. 1
41 9. 1
417. 2
403. 6
414.8
410. 1
412. 1
388. 9
394.0
392.3
397. 8
396.6
394.0
Table B-2. Transformed Values, Micrograms Per
Cubic Meter
B-14
-------
m nested in the kth run, and e f r -i) represents the random deviation
s
where
i = 1,2,3... p designates a laboratory
k = 1, 2, 3 ... w designates a run
m = 1, 2, 3 ... n designates a sample
s = 1, 2, 3 ... t designates an individual analysis
The term y., represents the individual observations recorded
by the collaborating laboratories, M represents the overall average,
L. represents the effect of the ith laboratory, R , ...represents the effect
1 K{1)
of the kth run nested in the ith laboratory, S f^/-^3 the effect of sample
m
f r -i)
jm |k(i)| J
associated with an individual measurement.
For this study, there were p = 4 laboratories, w = 2 runs,
n = 3 samples, and t = 3 analyses.
The analysis of variance technique was applied to the data in
Table C-3. The results of this analysis are shown in Table B-3. The
degrees of freedom and mean squares of Table B-3 have been suitably
adjusted in consideration of the substitutions made for outlying observations
While all of the effects shown in B-3 are significant at the 95 percent level
of confidence for at least one concentration, only the sample effect is
significant at all three concentrations .
The variance components for each of the experimental factors
were calculated and appear in Table B-4. The 95 percent confidence
intervals were calculated using a method described by Dixon and Massey .
B-15
-------
TABLE B-3. ANALYSES OF VARIANCE OF INDIVIDUAL
CONCENTRATIONS UNTRANSFORMED DATA
Source
of
Variation
Sum
of
Squares
Degrees of
Freedom
Mean
Square
Expected
Mean Square
L
R(L)
S(LR)
A(LRS)
2231. 93
544. 61
1123.78
260. 67
Low Concentration
3 743.98
4 136.15
16 70.24
48 5.43
7* + 9
-------
TABLE B-4 . COMPONENTS OF VARIANCE FOR
THE INDIVIDUAL CONCENTRATIONS
UNTRANSFORMED DATA
Source
of
Variation
L
R(L)
S (LR)
A (LRS)
Repeat.
Reprod.
L
R (L)
S (LR)
A (LRS)
Repeat.
Reprod.
L
R (L)
S (LR)
A (LRS)
Repeat.
Reprod.
Component
33.77
7.32
21.60
5.43
34.36
68.12
265.66
69.24
51.79
9.32
130.35
396.01
41.45
232.18
17.01
30.93
280.12
321.57
Percent
of
Total
Low
49.57
10.75
31.71
7.97
Degrees of
Freedom
Concentration
3
4
16
48
Standard
Deviation
5.81
2.71
4.65
2.33
5.86
8.25
Medium Concentration
67.08
17.48
13.08
2.35
High
12.89
72/20
'5.29
9.62
3
3
14
38
Concentration
3
4
15
46
16,30
8.32
7.20
3.05
11.42
19.90
6.44
15.24
4.12
5.56
16 . 74
17.93
95% Confidence
Interval
3.29 to 21.66
1.62 to 7.78
3.46. to 7.07
1.95 to 2.90
9.23 to 60.74
4.71 to 31.01
5.26 to 11.35
2.51 to 3.91
3.65 to 23.99
9.12 to 43.80
3.05 to 6.38
4.62 to 7.01
Note: To be consistent with repeatability and reproducibility as defined
by MandeP ', the above standard deviations were multiplied by
the factor 1.96Y 2 resulting in the values which are plotted in
Figure B-2
B-17
-------
The results of this analysis were somewhat inconclusive in their
inconsistency among concentrations. For example, the run (or day)
effect for the low and medium concentrations contributed only minimally
to the total variability. However, for the high concentration, the run
effect proved to be the dominant component. The variance component
due to sample effects is very nearly the same for all concentrations,
whereas the component due to analysis variability is obviously
concentration dependent. Since the replication error does vary with
concentration level, a data transformation is necessary before the data
for all concentrations can be analyzed simultaneously. The transformation
will be discussed in detail in the following section.
In addition to the variance components, Table B-4 contains the standard
deviations for repeatability and reproducibility for the method as it applies to
the individual concentrations. These measures multiplied by the factor 2.77
are displayed graphically in Figure B-2.
B. Analysis of Variance for All Concentrations Analyzed Together
In order to analyze the data for all three concentrations
simultaneously, it is necessary that the variances at the different
concentration levels be equal. The necessary homogeneity of variances
can be accomplished by performing a transformation of the data using a
technique described by Mandel
The purpose of the data transformation is to force the standard
deviation among replicates to be constant with respect to concentration.
B-18
-------
FIGURE B-2. THE REPRODUCIBILITY, REPEATABILITY,
AND REPLICATION ERROR STANDARD DEVIATIONS
OBTAINED BY THREE DISTINCT ANALYSES
110
100
90
e80
00
f?0
§ 60-
W 50
Q
P
K
Q
Z
<;
H
W
40
30
20 -
10
0
O
A
D
Derived Reproducibility (cons, together)
Concentrations Separately
Concentrations Together
Linear Model
Replication Error
Repeatability
Reproducibility
.. o—
100 200 300 400
S02 CONCENTRATION --«(g/m3
B-19
-------
The line which describes the replication standard deviation versus
concentration relationship is defined in terms of its slope and intercept
as
Standard Deviation = 1.0+0.015 x Concentration
The constants for this linear transformation were established by
linear regression applied to the standard deviation of the adjusted original
observations at each concentration level. Each observation is transformed
by the following expression:
z = Kloge (XQ + By) - G (B-2)
where z is the transformed variable, K and G locate the transformed
range of the observations, X = 1.0 and B =0.015, being the intercept
and slope, respectively. K and G were chosen so that the range of the
original observations would be maintained under the transformation.
Their respective values become K = 288.4 and G = 159. 7. This transformation
was applied to the adjusted original data, Table C-3, followed by tests for
homogeneity of variances and tests for outlying observations* '* . In
addition, another analysis of variance was conducted on the transformed
data for each of the three concentrations. This analysis confirmed the
fact that the replication variance for the transformed data was now
independent of concentration.
At this point, an analysis of variance was conducted on the trans-
formed data for all concentrations simultaneously. The mathematical
model for this analysis was:
B-ZO
-------
Y =M + L+C+R + (LC) + S ;+ (CR) +
ijkms i j k(i) ij mc(i) k(i)j
es(m[k(i7]j + (CSW[k(i)| +
-------
TABLE B-5. ANALYSIS OF VARIANCE FOR ALL
CONCENTRATIONS TOGETHER . DATA
IN TRANSFORMED SCALE
Five Factors: L, Laboratories; C, Concentrations; R, Runs;
S, Samples; and A, Analyses.
Source of
Variations
L
C
R (L)
LC
S (LR)
CR (L)
A (LRS)
CS (LR)
CA (LRS)
Sum of Degrees of Mean
Squares Freedom Square
20219.
143637
3651.
3742.
2073.
2800.
832.
3961.
1031.
18
.76
76
84
38
£6
36
96
34
3
2
4
6
16
7
44
32
96
6739.73
81818.88
912.94
623.81
129.59
400.08
18.92
123.81
10.74
Expected Mean Square
«l + 72flrl
B-22
-------
TABLE B-6. COMPONENTS OF VARIANCE FOR ALL
CONCENTRATIONS TOGETHER . DATA
IN TRANSFORMED SCALE.
Source of
Variation
L
C
R (L)
LC
S (LR)
CR (L)
A (LRS)
CS (LR)
CA (LRS)
Repeatability
R epr oducibility
Component
107.90
1130.82
29.01
12.43
12.30
30.70
6.31
37.69
10.74
126.75
247.08
Percent of
Total
7.83
82.07
2.11
0.90
0.89
2.23
0.46
2.74
0.78
Degrees of
Freedom
3
2
4
6
16
7
44
32
96
Standard
Deviation
10.39
33.63
5.39
3.53
3.51
5.54
2.51
6.14
3.28
11.26
15.72
5.88 to 38.71
17.51 to 212.68
3.22 to 15.48
2.27 to 7.77
2.61 to 5.34
3.66 to 11.29
2.09 to 3.17
4.90 to 8.20
2.87 to 3.80
Five Factors:
L - Laboratories
C - Concentrations
R - Runs
S - Samples
A - Analyses
Note: To be consistent with repeatability and reproducibility as defined
by Mandel* , the above standard deviations were multiplied by
the factor 1 . 96V~T
Figure B-2.
resulting in the values which are plotted in
B-23
-------
(1,5,6 and 9)
analyzed by the linear model technique . Basically, the
linear model assumes that systematic differences exist between sets
of measurements made by the same observer at different times or by
different observers in different laboratories, and that these differences
are linear functions of the magnitude of the measurements. The linear
model allows for nonconstant, nonrandom differences between laboratories,
and the method is not as sensitive to outlying observations as is the
conventional analysis of variance.
The design of the experiment with respect to the 24-hour sampling
SO, measuring method is as follows: each of p laboratories has
Lt
measured each of q concentrations a total of n times. For the present
case, the number of laboratories remains at 4. However, because the
linear model as formulated by Mandel is limited to two factors with
replicates, concentrations measured during successive runs are now
considered to be individual materials. This results in q = 6 concentrations
having been analyzed by each laboratory. For this analysis, the total
number of replicate measurements conducted by each laboratory on
each concentration is n = 9; i. e. , 3 analyses recorded for each of 3
samples taken.
The linear model analysis was conducted by use of an efficient
computer program written specifically for collaborative test method
IQ)
studies17'.
B-24
-------
The criterion for homogeneity of data applies in the case of
the linear model as it does for the more conventional analysis of
variance. A preliminary investigation of these data was performed
in order to determine relationships between various parameters among
the collaborating laboratories. These parameters — the mean, slope
and standard error of estimate—appear in Table B-7and are graphically
displayed together with 95 percent control limits in Figure B-3.
The mathematical model for the linear analysis is as follows:
y .. = M + L. + C. + (LC).. (B-4)
ij * J 1J
where
i = 1, Z, 3. . . , p designates a laboratory
j = 1,2,3..., q designates a concentration
The term y .. represents an individual measurement, M represents
the overall average, L. represents the effect of laboratory i, C. represents
the effect of concentration j, and (LC).. represents the interaction effect
between laboratory i and material j and includes the replication error.
The final linear model analysis is shown in Table B-8 with data
in the transformed scale. The concurrence and nonconcurrence terms
are shown even though it was apparent that no appreciable correlation
existed between the means and slopes.
B-25
-------
TABLE B-7. MEANS, SLOPES AND STANDARD ERRORS
OF ESTIMATE FOR LINEAR MODEL ANALYSIS.DATA
IN TRANSFORMED SCALE .
Laboratory Code
Number Mean
799 259.5
927 273.3
345 251.Z
920 274.3
Mean 264.6
Standard Error of
Slope Estimate
1.0275 8.1
0.9792 7.3
1.0000 4.5
0.9933 10.4.
1.0000 9.1*
* pooled estimate
An investigation of the correlation between the means and slopes
revealed practically no correlation.
B-26
-------
FIGURE B-3. CONTROL, CHARTS FOR MEANS, SLOPES, AND
STANDARD ERRORS OR ESTIMATE FOR LINEAR MODEL
ANALYSIS.DATA IN TRANSFORMED SCALE.
280r
270
260
o
250
rt
o
03
4)
s
IH
0
C
tt
e
ff)
<0
5
1. ll
1.0
0. 9
V
a
9
8
7
6
5
4
O
O
0)
.u
ft
in
w ^~
^ "rt
o u
O TJ
^ 4)
tj ^
«s
'D -4
TJ re
*? *<
799
927
345
920
Laboratory Number
B-27
-------
TABLE B-8. ANALYSIS OF VARIANCE FOR LINEAR
MODEL'.DATA IN TRANSFORMED SCALE .
Source of
Variation
Laboratories
Concentrations
Laboratory x Concentration
Linear
Concurrence
Nonconcurrence
Deviation from Linearity
Sum of Degrees of Mean
Squares Freedom Square
2247.67
394769.41
1115.06
121.61
39.30
82.31
993.45
3
5
15
3
1
2
12
749.22
78953.88
74.34
40.54
39.30
41.16
82.79
The data from Table B-8 were used to compute the variance
components which appear in Table B- 9- In addition to the individual
component variations, the repeatability and reproducibility for the
method were calculated from these data and are displayed graphically
in Figure B-2.
B-28
-------
TABLE B-9. COMPONENTS OF VARIANCE FOR THE LINEAR
MODEL ANALYSIS. COMPONENTS ARE EXPRESSED
AS STANDARD DEVIATIONS IN THE ORIGINAL SCALE
Concentration
10
20
50
100
150
200
250
300
350
400
450
500
Std. Dev.
€
1.41
Std. Dev.
2.16
1.60
2.15
3.08
4.01
4.94
5.86
6.79
7.72
8.65
9.58
10.50
2.45
3. 3D
4.73
6.15
7.57
8.99
10.42
11.84
13.26
14.69
16.11
Std. Dev.
8
0
0
0
0
0
0
0
0
0
0
0
0
Std. Dev.
2.89
3.27
4.42
6.32
8.22
10.12
12.03
13.93
15.83
17.74
19.64
21.54
Std. Dev.
Total
3.87
4.39
5.92
8.47
11.02
13.57
16.12
18.67
21.22
23.77
26.33
28.87
For definitions of € , "X , $ and |j., the reader is referred to Mandel
(10)
Note: The total standard deviation is the estimated standard deviation
of reproducibility for the linear model. These estimates are
to be multiplied by the factor 2.77 in order to reconcile them
with the curve for reproducibility in Figure B-2.
B-29
-------
IV. APPLICATION OF THE RESULTS
The results developed in previous sections will be applied in this
section to describe the precision between replicates, the precision
between days and the precision between laboratories for the 24-hour
SO^ sampling method. Only those results from the analysis of variance
technique applied to the transformed data of all three concentrations
simultaneously will be examined. Also, a 95 percent level of confidence
will be adopted for each measure so that a direct comparison of these
results can be made with the results from the 30-minute sampling study.
A. Correction of Laboratory Bias
Before applying the results from the analysis of variance
technique, it will be necessary to correct for a laboratory bias which
was found to exist. The general argument for the detection and isolation
of this bias was presented in Part El of this report. The bias resulted
from the fact that three of the four laboratories which collaborated in the
24-hour study demonstrate less laboratory-to-laboratory variability
than is true for the general population of laboratories of which they are
a subset. This can be demonstrated by isolating and comparing the
laboratory-to-laboratory variability component which was developed by
individual analyses of variance of (1) the 30-minute sampling data for
all 14 collaborating laboratories, (2) the 30-minute sampling data for
the 3 laboratories which were common to both studies, and (3) the 24-hour
B-30
-------
sampling data for the four participating laboratories. The standard
deviations for these individual components are displayed graphically
in Figure B-4.
For discussion purposes, the causes describing these laboratory
components from top to bottom in Figure B-4 have been given the
following labels:
CSDj4 calculated standard deviation, 14 laboratories,
30-minute sampling study
ASD. adjusted standard deviation, 4 laboratories,
24-hour sampling study
CSD^ calculated standard deviation, 3 laboratories,
30-minute sampling study
CSD, calculated standard deviation, 4 laboratories,
24-hour sampling study
The large difference between CSD^ and CSD,,, both resulting
from the same set of data analyzed by identical techniques, must
result from the fact that this subset of three laboratories display a
lab-to-lab variability component that is not typical (i. e. , it is much
lower) of the general population of laboratories. This laboratory bias
obviously occurred also in the 24-hour sampling study as evidenced by
the similarity between CSD, and CSD.. This is a reasonable assumption,
since three of the four laboratories that participated in the 24-hour study
are responsible for the laboratory component CSD^.
B-31
-------
Because of this bias, it was necessary to estimate a "true"
laboratory standard deviation component for the 24-hour sampling
study by adjusting CSD.. This adjusted component was derived from
the ratio of components for the 30-minute study applied to the 24-hour
component as follows:
ASD4 = CSD14 x CSD4 (B-5)
CSD3
The magnitude of the adjusted component was calculated by
equation B-5 at various point estimates over the common concentration
«3 o
range from 150 (j.g/m to 402 |j.g/m . An average adjustment of
ASD. = 1.82 CSD. was obtained. The adjusted laboratory component
for the 24-hour study is shown by the dashed line in Figure B-4.
Since for this study, reproducibility is defined in terms of the
variance components for repeatability and the laboratory-to-laboratory
variability, the adjusted laboratory component will change the previously
calculated value for reproducibility. The derived reproducibility is
illustrated by the dashed curve in Figure B-2. This derived repro-
ducibility curve is the sum of the derived laboratory component from
Figure B-4 and the repeatability curve in Figure B-2. In all cases, the
summation is carried out on variance components, although repeatability
and reproducibility are defined and presented here in terms of standard
deviations.
B-32
-------
FIGURE B - 4. COMPARISON OF CALCULATED AND ADJUSTED
LABARATORY COMPONENT STANDARD DEVIATIONS
00
|T
Z
O
i—i
H
<
>-<
>
W
Q
Q
«
<
Q
Z
<
H
50
40
30
20
10
LABORATORY COMPONENT
CSD3
CSD
O Derived Laboratory
Component
A 1 4 Laboratories-30 min
O 3 Laboratories-30min
O 4 Laboratories-24hour
-t-
200 400 600
CONCENTRATION -
800
B-33
-------
B. Precision of Method
With the laboratory selection bias corrected, it is now possible
to write expressions which will allow the pertinent standard deviations
obtained from the analysis of variance for the three concentrations
together in the transformed scale to be returned to the scale of the
A
original data. These expressions for the replication error ( £J^ ),
A A
repeatability ( J^ ) and reproducibility (O~L ) standard deviation estimates
are:
C£ = (.2312 + .0035y )(4.31) (B-6)
<% = 2.77 (.2312 + .0035y)(ll. 26) (B-7)
Oi = 2.77 (.2312 + .0035y)(22. 91) (B-8)
The replication, repeatability, and reproducibility standard deviation
estimates in the transformed scale (4.31, 11.26, and 22.91, respectively)
are derived from the Table B-6 component variances and standard
deviations:
Replication error =
Vvar(A) + Var(S) = / 6.31 + 12.30 = 4.31
Repeatability standard deviation =
Vvar(CA) + Var(CS) + Var(A) + Var(CR) + Var(S) + Var(R) = 11.26
The reproducibility standard deviation estimate requires correction of
the Table B-6 value to account for the adjustment in the laboratory
B-34
-------
components dictated by the laboratory bias correction equation
ASD4 = 1. 82 CSD4:
Reproducibility std. dev. = War (Repeat.) + 1.822 [Var(LC) + Var(L)] (B-9)
= Vl26.75 + 3.31[12.43 + 107.90J =22.91
Equations (B-6), (B-7), and (B-8) allow one to express the
precision of the 24-hour SO? sampling method for any desired case.
The following examples have been chosen to coincide with those developed
for the 30-minute SO, sampling study. The expression used to determine
the range of two class means of equal sample size which would be
accepted at the 95 percent confidence level as belonging to the same
population is:
max
= t.025(Vl)
where x is the highest mean, x? is the lowest class mean, N represents
the sample size, and (T based on V degrees of freedom is an estimate
of the standard deviation of the class means for which the range is to
be determined, t (V) is the upper 2. 5 percent point of the t
• U Ct J
distribution with \) degrees of freedom.
For the case when the two class means were derived from
different sample sizes, the following expression was applied:
|;, -^ ''.ozs'^VH- + 4- (B-U)
max ' 1 2
Equation (B-ll) reduces to equation (B-lO)when N, = N •
B-35
-------
The expression that was used in the earlier study to establish
the maximum difference that could exist between a fixed value and
an observed mean while still belonging to the same population (at the
95 percent level of confidence) was:
X - JJL
max
-/fir
= 1. 645 07 fN (B-1Z)
where x is the observed mean, fj. is the fixed value, (f is an independent
estimate of the standard deviation, and N is the size of the sample
for which the mean is x.
1. Precision Between Replicates
The precision with which the 24-hour method can distinguish
between individual replicates is given by a combination of equations (B-6)
and (B-10). Since t ,.-,,-(48) = 2.01 and N = 1, expression for this case
becomes:
R max= (2.84)(.2312 + .0035y )(4.31)
If two replicates differ by more than Rm. x they may be assumed with
95 percent confidence to belong to different populations.
At concentration levels below 400 (ig/m , two replications
which differ by more than 5. 0 percent would be suspect, and at concentration
levels below 100 |ag/m agreement of better than 7.1 percent should be
expected between replicates of the same sample.
2. Precision Between Days
When measurements are made using the 24-hour method
on different days by a single collaborator, the precision of the method is
B-36
-------
described by a combination of equations (B-7) and (B-10). The
expression for the precision between days is given by:
Rmax = (3-92)(.2312 + .0035y )(11. 26)
because t n?(-(^) = 2.776 and N = 1. Two observations made on
separate days by the same laboratory may not be considered to belong
to the same population if they differ by Rmax- Accordingly, we see
that at concentration levels of 100 ug/m , R for repeatability of
max
the method is 25. 7 fig/m which represents a percentage of concentration
difference of 25. 7 percent. At the other end of the scale, for a con-
centration level of 400 jig/m , one may accept with 95 percent confidence
that two observations which differ by less than 72.0 |JLg/m or 18.0
percent of concentration belong to the same population.
3. Precision Between Laboratories
The most important measure of the test method is that
which describes the precision with which individual observations by
different laboratories recorded on separate days can be distinguished.
A combination of equations (B-8) and (B-lO)with t 02c(3) = 3- 182 and N = *
results in the following expression by which this measure may be
described.
Rmax = (4< 50)(' 2312 + ' °°35 7 )(22'
R is again the maximum difference between two measures that can
be said with 95 percent confidence to belong to the same population.
B-37
-------
3
At a concentration level of 100 |j.g/m , Rmax for reproducibility is
•2
59.9 ug/m , which represents a concentration difference of 59.9 percent,
while a concentration level of 400 ug/m R is 168.2 |ig/m , which
XTlcLX
represents a concentration difference of 42 percent. Table B-10
summarizes R for the three precision measures at three concentration
max r
levels.
Equations (B-ll) and (B-12) can be used to determine R
between means of different sample size and between a mean and a fixed
value, respectively. Equation (B-12) is also useful when it is desirable
to determine the minimum number of observations required to determine
agreement between an observed and a fixed mean. As an example of this
application, a minimum of 9 observations would be required to determine
with 95 percent confidence that the true mean for the high SO.,
concentration was less than 500 ug/m when the actual value was
•a
475 ug/m . This is determined when the expression is written as follows:
7.645 (.2312 + .0035 u0) (22.
• 9lT1
R
where R is the difference between the fixed and observed mean.
C. Accuracy and Bias
The values for the three SO? concentrations which were sampled
in this study had expected means of 98, 291, and 475 p.g/m , The
values observed by the four participating laboratories had mean values
which deviated from these expected values by -4.0, - 33.1 and
- 72.0 ug/m , respectively. The resulting observed means are shown
B-38
-------
together with their respective 95 percent confidence limits in Figure B-5.
Figure B-5 also contains a plot of the expected mean values with their
respective 5 percent accuracy limits representing the variability of the
SO, generating equipment. This concentration dependent bias becomes
significant at the 95 percent level of confidence for the high SO,
concentration.
B-39
-------
TABLE B-10. Rmax AS A FUNCTION
OF CONCENTRATION LEVEL
Concentration
100 [ig/rrT
Replication Error
7.1
7.1 percent
Repeatability Reproducibility
25.7 jxg/m
25.7 percent
59.9 jig/m3
59.9 percent
250
13.5
5.4 percent
48.8 ng/m 114.0
19.5 percent 45.6 percent
400
20.0 jig/m
5.0 percent
72.0 (j.g/m 168.1
18.0 percent 42.0 percent
B-40
-------
FIGURE B-5. THE ACCURACY OF THE 24-HOUR
PARAROSANILINE METHOD
j[
00
2
H
w
u
s
o
o
P
W
W
o
o
o
o
o
o
ro
O
O
IM
O
o
5% Accuracy Limits
Expected Mean Values
Observed Mean Values
95% Confidence Limits
100
200
300
400
500
EXPECTED SO2 CONCENTRATION -
B-41
-------
Appendix B
References
1. McKee, H. C. , Childers, R. E. , and Saenz, O. , Jr.,
"Collaborative Study of Reference Method for Determination
of Sulfur Dioxide in the Atmosphere (Pararosaniline Method), "
prepared for Office of Measurement Standardization, Division
of Chemistry and Physics, National Environmental Research
Center, Environmental Protection Agency, Research Triangle
Park, N. C. , Contract CPA 70-40, September 1971.
2. Dixon, Wilfred J. , and Massey, Frank J. , Jr. , Introduction
to Statistical Analysis, McGraw-Hill Book Company, Inc. ,
New York, Chapter 9, p. 104 (1957).
3. 1968 Book of ASTM Standards, Part 30, Recommended Practice
for Dealing with Outlying Observations, ASTM Designation:
E 178-68, pp. 444-447.
4. Dixon, W. J. , (ED.), BMD Blomedical Computer Programs,
Second Edition, University of California Press, Berkeley
and Los Angeles, pp. 586-600 (1968).
5. Mandel, J. , "The Measuring Process," Technometrics, J_,
pp. 251-267 (1959).
6. Mandel, J. , and Lashof, P. W. , "The Interlaboratory Evaluation
of Testing Methods," ASTM Bulletin 239, pp. 53-61 (1959).
7. Dixon, Wilfred J. , and Massey, Frank J. , Jr. , Introduction to
Statistical Analysis, McGraw-Hill Book Company, Inc. , New York,
Chapter 10, pp. 179-180 (1957).
8. ASTM Manual for Conducting an Interlaboratory Study of a Test
Method, ASTM SPP No. 335, American Society for Testing
and Materials (1963).
9. Southwest Research Institute, Houston, Texas, Computer Program
LINMOD, for Linear Model Analysis, Unpublished (1973).
10. Mandel, J. , The Statistical Analysis of Experimental Data,
John Wiley & Sons, New York, Chapter 13, p. 312 (1964).
B-42
-------
APPENDIX C
Tabulation of Original Data
-------
LOV/ CONCENTRATION SO.
Run
Run 02
Laboratory
799 Sample •?'!
Sample = 2
Sample =3
= 927 Sample = 1
Sample r- 2
Sample = 3
= 345 Sample = 1
Sample = 2
Sample =3
= 920 Sample =1
Sample =2
Sample =3
= 799 Sample =1
Sample =;2
Sample =3
:^927 Sample =1
Sample =2
Sample =3
if 3-4 5 Sample £ 1
Sample =2
Sample ^3
-'920 Sample = 1
Sample = 2
Sample ff3
= 799 Sample =1
Sample = 2
Sample ;?3
= 927 Sar.--.plc r- 1
Sample = 2
Sample = 3
= 345 Sample = 1
Sample = 2
Sample =3
i=920 Sample =1
Analysis 1
100 1
^
9
i
f
9
Y
98
1
1
^4
I
1
Analysis 2
Analysis 3 Analysis 1
( 1
Analysis 2
Analysis 3
V
I >
>
MEDIUM CONCENTRATION SO.
San-solo = 3
300
\
1
^
293
1
1
290
)
1
k
2bO
\
47
' J
4F
>
4"?
J
4ft
>
^
i
^
HIGH CONCENTRATION SO2
5 f
[
3 —
f
H
f
2
1
^
_^
X^
Table C-l. Expected Concentrations, Micrograms per Cubic Meter
-------
LOV/ CONCENTRATION SO.
i
Run 3 1
Run HZ
Laboratory
799 Sample =1
Sample -2
Sample =3
£927 Sample = 1
Sample - 2
Sample
= 345 Sample - 1
Sample =2
Sample =3
17920 Sample =1
Sample :
Sample =3
= 799 Sample -1
Sample -2
Sample -3
:?927 Sample =1
Sample 2
Sample -3
£345 Sample 1
Sample ~2
Sample ~3
^920 Sample ~1
Sample =2
Sample =3
= 799 Sample =1
Sample = 2
Sample =3
= 927 Sample =1
Sample =2
Sample = 3
= 345 Sample = 1
Sample =2
Sample =3
= 920 Sample =1
Sample = 2
Sample =3
Analysis 1
- 10
- 8
- 17
3
5
5
- 17
- 14
- 12
1
3
- 2
ME
4 *
8 *
- 6 *
- 23
- 24
- 29
- 49
- 47
- 43
- 75 *
- 10
- 9
Analysis 2
- 15
4
- 17
3
5
8
- 17
- 16
- 14
3
5
6
DIUM CONCJ
4 *
21 *
8 *
- 23
- 24
- 29
- 50
- 47
- 44
- 72 *
3
2
Analysis 3
- 15
- 4
- 12
3
5
5
- 14
- 14
- 10
- 1
1
. 3
ENTRATION
13 *
21 *
4 *
- 23
- 24
- 29
- 50.
- 47
- 41
- 73 *
- 10
- 5
Analysis 1
- 15
11
- 4
- 2
0
0
- 13
- 10
0
- 4
- l
- 7.
so2
- 35
- 36
- 56
- 22
- 13
- 13
- 62
- 56
- 51
-131 *
- 26
- 28
Analysis 2
- 13
2
- 6
- 2
- 3
3
- 14
- 8
- 1
- 1
s
4
- 35
- 44
- 66
- 22
- 13
- 13
- 59
- 56
- 53
-126 *
- 19
- 23
Analysis 3
- 18
2
- 2
- 2
n
3
- 11
- 9
- 1
- 5
i
n
- 44
- 36
- 56
- 25
- 13
• 13
- 62
- 52
- 47
-131 *
- 26
- 28
HIGH CONCENTRATION SO.
- 86
- 71
_ 83
_ 77
. 76
_ 72
- 95
-88
-81
- 57
-45
- 52
- 86
- 71
- 93
_ 73
_ 76
_ 72
- 96
- 88
- 85
- 46
- 38
- 40
- 86
- 71
- 54
- 73
- 76
- 75
- 90
-93
-94
- 57
-45
-44
- 51
- 5R
-63
- 57
- 57
- 58
-96
-91
-93
-240 *
-79
-84
- 55
- 40
-63
- 57
- 57
- 58
-101
-85
-91
-235 *
-76
-79
-46
- 4Q
- 72
- 53
-61
- 58
- 95
-87
- 90
-242 *
-83
-87
#Outlying Observations
Table C-2. Deviations from Expected Values, Micrograms per Cubic Meter
-------
LOW CONCENTRATION SO.
Run HI
Run #2
Laboratory
799 Sample rl
Sample =2
Sample F3
= 927 Sample =1
Sample = 2
Sample £3
= 345 Sample = 1
Sample =f 2
Sample =3
= 920 Sample =1
Sample = 2
Sample = 3
= 799 Sample = 1
Sample =.1
Sample «3
:?927 Sample =1
Sample =2
Sample f=3
= 345 Sample =1
Sample -r-2
Sample £3
7f920 Sample =1
Sample =2
Sample ?3
= 799 Sample =1
Sample ^2
Sample =3
= 927 Sample == 1
Sample = 2
Sample =3
= 345 SaiTiple = 1
Sample =2
Sample =3
= 920 Sample =1
Sample =2
Samole =3
Analysis 1
88
90
81
101
103
103
81
84
86
99
101
96
Analysis 2
83
94
81
101
103
106
81
82
84
101
103
104
Analysis 3
83
94
86
101
103
103
84
84
88
97
99
101
Analysis 1
83
109
94
96
98
98
85
88
98
94
• 97
96
Analysis 2
85
100
97.
96
95
101
84
90
97
97
103
102
Analysis 3
80
100
96
96
98
101
87
89
97
91
97
98
MEDIUM CONCENTRATION SO,
HIGH COI\7CENTRATION SO.
Table C-3. Observed Values (adjusted)
256
235
255
268
267
262
242
244
248
280
281
282.
256
225
255
268
267
262
241
244
247 _,
290
288
293
247
235
247
268
267
262
241
244
250
285
281
286
256
255
235
269
278
278
229
235
240
262
265
263
256
247
225
269
278
278
232
235
238
266
272
268
247
255
235
266
278
278
229
239
244
270
265
263
389
404
392
398'
399
403
380
387
394
418
430
423
389
404
382
402
399
403
379
387
390
429
437
435
389
404
421
402
399
400
385
382
381
418
430
431
424
417
412
418
418
417
379
334
382
395
396
391
420
426
417.
418
418.
417
374
390
384
404
399
396
429
426
4M
422
414
417
380
388
385
398
392
3?§
Note: The original observed values were adjusted by either adding or subtracting the
amount necessary to put all observations on an equivalent basis regarding the
means of the expected concentrations for low, medium and high levels.
-------
Laboratory
799
927
345
920
Slope
0.0354
0.0302
0.0256
0.0277
Intercept
A
0.1945
0.2229
0.2109
0.1770
Bs
MS/A
28.2
33.1
39.1
35.7
Mean
Variance
Standard
Deviation
Degrees of
Freedom
tO.95
Slope V
L
Intercept V..
Bs V.
0.02973
0.00002
0.00422
3.182
0.02973 +
0.20133+
34.025 +
0.01343
0.06351
14.622
0.20133
0.00040
0.01996
3
3.182
34.025
21.116
4.5952
3
3.182
Table C-4. Calibration Curve Parameters for
Sulfur Dioxide 24-hour Sampling Study
-------
Laboratory
799
927
345
920
Parameter
BB
Ao
Yo-Ao
A Cont. Samp.
Bs
Ao
Yo-Ao
ACont. Samp.
Bs
Ao
Yo-Ao
ACont. Samp.
Bs
Ao
Yo-Ao
ACont. Samp.
Units
Hg/A
A
A
H-g
jig /A
A
A
Hg
Hg/A
A
A
Hg
Hg/A
A
A
Hg
Day 1
28.2
.170
.015
1.79
33.1
.195
.020
-0.06
39.1
.198
.007
-0.80
35.7
.171
-.001
-0.36
Day !
28.2
.210
-.025
2.74
33.1
.190
.025
-0.29
39.1
.195
.010
-0.49
35.7
.168
.002
-0.32
Day 3
28.2
.210
-.025
0.69
33.1
.220
-.005
-0.03
39.1
.200
.005
-0.70
35.7
.165
.005
-0.14
Day 6 Mean
33.1
.202
.013
0.18
39.1
.213
-.008
-0.45
35.7
.165
.005
-0.54
33.1
.200
.015
-0.13
39.1
.206
-.001
-0.80
35.7
.222
•0.52
0.36
28.2
.185
.000
0.02
33.1
.208
.007
0.10
39.1
.195
.010
•0.40
35.7
.220
-.050
0.58
28.2
.191
-.006
1.46
33.1
.203
.013
-.098
39.1
.201
.004
-.607
35.7
.185
-.015
-.070
Std. Dev.
032
001
967
Oil
Oil
134
007
007
181
.028
.028
.443
Table C-5. Calibration Data for Sulfur Dioxide 24-Hour Sampling Study
-------
APPENDIX D
Instructions to Collaborators for Collaborative Test
of Reference Method for the Determination of
Sulfur Dioxide in the Atmosphere
(Pararosaniline Method) (24-hour sampling)
-------
I. INTRODUCTION
A. Background
The Reference Method for the Determination of Sulfur Dioxide in
the Atmosphere (Pararosaniline Method) was published *~2 by the
Environmental Protection Agency as the method to be used in connection
with federal ambient air quality standards for sulfur dioxide. The 30-
minute sampling procedure of this method has been collaboratively tested
and the resulting precision and accuracy information has been reported.
B . Purpose and Scope
The purpose of this collaborative test is to broaden the previous
information by testing the 24-hour sampling procedure. More specifically,
the purpose is to evaluate the precision and accuracy characteristics of
the method as it is published in the Federal Register. For this test,
there is no interest in studying any modifications. Many similarities exist
between the 24-hour procedure and the 30-minute procedure. Some of the
precision parameters can be expected to be identical with those for the
30-minute procedure and need not be redetermined. The effects of four
different factors will be evaluated using sulfur dioxide permeation tubes
as standard reference materials. The collaborative test procedure is to
be similar to that used for testing the 30-minute sampling procedure.
The estimated effort for a collaborator is 2-3 man-weeks.
Environmental Protection Agency, "National Primary and Secondary
Ambient Air Quality Standards," Federal Register, Vol.36, No.84,
Part H, Appendix A, pp8187-8191, Friday, April 30, 1971.
Op cit, Federal Register, Vol. 36, No. 228, Appendix A, pp 22385-
22388, Thursday, November 25, 1971.
McKee et al, "Collaborative Study of Reference Method for
Determination of Sulfur Dioxide in the Atmosphere (Pararosaniline
Method)," for Environmental Protection Agency, Contract CPA70-40,
Southwest Research Institute, September, 1971.
D-l
-------
C. Experimental Design
The effects of laboratories, concentrations, samples, and
analyses upon the precision and accuracy of the method will be
determined using the experimental design shown in Figure 1.
An individual observation is denoted y.,. which is to be inter-
preted as the nth analysis of the mth sample from the j th concentration
during the kth run by the ith laboratory. From Figure 1, it can be seen
that there are 2 runs, 3 concentrations, 3 samples, and 3 analyses.
Consequently, each laboratory will generate 2x3x3x3 = 54 individual
observations. The order in which the concentrations within a run are to
be handled should be randomized and specific instructions will be issued
in this regard.
To clarify certain features of the experiment design in Figure 1,
the following definitions should be observed.
1. The two runs are identical (except for the randomized
order of handling concentrations) and the first run should
be completed before beginning the second.
2. The three concentrations (unknown to the collaborator)
are the same for each run and represent the range of
interest for this collaborative test. The order should
be random.
3. The three samples for each concentration are to be
taken simultaneously from a common manifold using
similar sampling apparatus. The analysis of the three
samples should be conducted simultaneously.
4. The three analyses for each sample are to be processed
simultaneously. (Each analysis represents an identical
aliquot from the same sample.)
Other specific instructions will be presented in the next section.
D-2
-------
<
k
V
4
\ i
S '
(
£
-
2
L .
V
S
\ J
3
\J
S '
£
^ .
>4
^2^
S ^
I
(
S
^
T,
1 =
1,2,
...,P
J
(same as R.)
:2
2
i'
1
S
3
2
V
c
51
(
£
;*
2 S3
^ A3 4 \ *
FIGURE 1. DESIGN OF COLLABORATIVE EXPERIMENT. L, LABORATORIES;
R, RUNS; C, CONCENTRATIONS; S, SAMPLES; A, ANALYSES.
D-3
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II. COLLABORATIVE TEST PROCEDURE
A. General Rules
1. Read the method carefully; if you have any questions, check
them with Southwest Research Institute before you begin
the collaborative determinations.
2. Make at least one practice run to familiarize yourself with
the method so that you can avoid errors in manipulation.
3. Make the determinations as soon as possible after receiving
the permeation tubes. Handle the permeation tubes
according to instructions.
4. When you make the collaborative determination, follow the
method exactly in every detail. Do not insert minor
modifications, even though they may be in common use in
your laboratory. You will destroy the value of the collaborative
study if you depart from these instructions or those given in
the method. If for any reason you are unable to follow all
instructions to the letter, report the deviations to Southwest
Research Institute.
5. Report all your results, unless you have been specifically
instructed otherwise. Do not take the "best two out of three"
values; do not report averages unless you were asked to do so.
6. Make only the number of determinations requested, (more
or less data complicate the statistical analysis.)
7. Prepare a full report of your work on the forms provided,
including all the data you obtained, and send it to Southwest
Research Institute.
8. Return original data forms. Copies, no matter how legible,
are not acceptable. You may make copies for your own re
records.
9. You are invited to submit any comments, suggestions,
criticisms, or description of difficulties that you feel are
important. If you tried out a modification of the method,
report your findings but keep these data separate from your
collaborative report.
D-4
-------
10. For this collaborative test, take the attitude that you, the
analyst, will be asked to testify, under oath, that the results
you submit are those obtained on the samples provided while
following the method exactly in every detail.
B. Generation of Test Atmospheres
A special apparatus was developed for generating test
atmospheres using certified permeation tubes. The apparatus is described
in the reference and a unit will be made available to each collaborator. The
manifold of the apparatus has been modified to permit the simultaneous
collection of three to six samples. A constant temperature bath with
circulation pump (capable of + 0.1 °C temperature control) and a source of
pure dry air are essential to complete the system. This system will be
referred to as the standard system.
A certified sulfur dioxide permeation tube (permeation rate unknown
to the collaborator) will be supplied to each collaborator. The system is
to be operated at 25 + 0.1°C. (Temperature variations greater than this
will invalidate the results of a collaborator and jeopardize the success of
the entire collaborative test.)
Keep the permeation tube in the system at 25+ 0.1°C with both the
air over the permeation tube and the dilution air flowing continuously.
There will be no need to remove the tube once it has been installed in the
system and equilibrium will be established at all times . Install the tube in
the system as soon as possible and maintain constant temperature and air
flow over the tube until the collaborative determination is complete. The
air flow over the permeation tube should be maintained constant at a rate
between 50 and 100 ml/minute. (A reading of 8 for the stainless steel ball
in the rotameter in the standard system is recommended.) Constant
dilution air flow is not required but a moderate flow is necessary at all
times. (A dilution air flowmeter reading of 5 (stainless steel ball) for the
standard system is suggested.) Do not make any modifications in the
standard system without prior approval.
(1)
McKee et al, "Collaborative Study of Reference Method for
Determination of Sulfur Dioxide in the Atmosphere (Pararosaniline
Method), " for Environmental Protection Agency, Contract CPA 70-40,
Southwest Research Institute, p 3-4,' September, 1971.
D-5
-------
Allow at least 48 hours after initial installation of the tube to
reach equilibrium - more if the tube has been at a temperature very
different from 25 °C. Do not begin a collaborative determination within
24 hours following a temperature upset exceeding + 0.5°C.
The dilution air flow rates to achieve the concentrations to be
used in the test will be specifically prescribed in the following instructions.
C. Preparation of Calibration Curve
Prior to the sampling of test atmospheres, prepare a calibration
curve using sulfite solution in accordance with Section 8.2.1 of the
Reference Method. (A supply of pararosaniline in accordance with
Section 6.2.10.2 will be provided.) Run triplicates at each of the six
calibration points (0, 0.5, 1, 2, 3, and 4ml) and record each of the 18
individual observations on the data forms provided (see Form B). It is
important that you prepare the calibration curve in this manner even
though this may not be your usual practice. Do not run more or less
calibration points or replicates. Please note that the calibration curves are
to be in terms of gross rather than net absorbance.
Compute the slope and intercept of the curve (method on Form B
suggested) and compare with the specifications in Sections 6.2.10.1 and
8.2.1 and recalibrate if there are gross departures from these specifications,
Compute the calibration factor and retain for use in future analyses.
All collaborative determinations will be based on this calibration
factor unless subsequent control samples indicate it to be unreliable. If
this should occur, prepare a new calibration curve in accordance with the
instructions above and notify Southwest Research Institute. Do not discard
any calibration data. Report complete data on each calibration curve
prepared.
D. Sampling and Analysis of Test Atmospheres
Refer to Figure 1 and the itemized instructions below for the
sequence of steps in the sampling and analysis of the test atmospheres.
When you receive your data forms, they will be preassembled into
what shall be referred to as packets. You will receive six packets (one
for each concentration for each run) which will contain Preparation of
Standard Atmospheres (Form D) and Sampling and Analysis Data (Form A).
A separate form for calibration (Form B) is included but is not part of a
D-6
-------
packet. Each packet will contain a green circled number on the upper
right hand corner of Form D which indicates the chronological order
in which the experiment is to be done. The order of the concentrations
within a run has been randomized. Please follow this order, and do not
separate the forms of a packet.
Each packet indicates the prescribed flow rate through the per-
meation system (on Form D in red) to achieve the desired concentration.
See the next subsection of these instructions for a brief description of
each data form .
Read the following instructions over carefully, and if there are
any questions contact Southwest Research Institute before proceeding.
1. Be sure that the permeation system is in equilibrium
and properly operating.
2. Be sure that the calibration curve is complete and that
its slope and intercept meets specifications .
3. Begin a run. Make sure that all incompleted data form
packets are in ascending numerical order. The lowest
numbered incompleted data form packet is referred to
as the next data form packet.
4. Begin processing a concentration. Consult the next data
form packet and set permeation system dilution air flow
to the setting shown in red on Form D of the respective
data form packet. Commence monitoring the system and
allow one hour for the system to stabilize.
5. Begin sampling. Prepare three absorbers according to
Section 7.1.Z and connect them to the sampling manifold
and sample flow rate control device (Section 5.1.3).
Start sample flow and record time . Sampling from midnight
to midnight as specified in Section 7.1.2 is not mandatory
for this test.
6. Continue sampling. Complete 24-hour monitoring data is
not required; however, the following data should be
recorded as normal working hours permit. Monitor
permeation system and record hourly on Form D.
Monitor sample temperature (at manifold discharge) and
pressure (barometric) and record hourly on the back of
Form A.
D-7
-------
7. Stop sampling. After 24 hours, stop sample flow and
record time and flow rate for each sample on Form A.
Disconnect absorbers and set aside for analysis.
8. If a subsequent run or concentration is to be initiated
immediately, proceed simultaneously with Steps 9 and
12. Otherwise, proceed with Step 9.
9. Prepare samples for analysis. Follow instructions in
Sections 7.2.1 and 7.2.1.2. Samples may be stored in
accordance with Section 7.1.2; however, do not store
all samples for analysis at one time. Samples are to be
analyzed in batches corresponding to each concentration
for each run (a data form packet). There will thus be
six batches - three for each run. If samples are stored,
record length of storage and temperature of storage in
the bottom margin on the back of the respective Form A.
10. Begin determination. Follow the instructions of Section
7.2.2 exactly. Record data on Form A.
11. Calculate results according to Section 9 and record on
Form A. It may not be possible to convert sample
volume according to Section 9.1. Do so only if meaningful
corrections can be applied.
12. Repeat from Step 4 if other concentrations within a run
remain to be processed.
13. Repeat from Step 3 if a run remains to be made.
14. Prepare report. Your report will consist of all data
forms plus any comments or criticisms you may care
to make. Return original data forms in the addressed
and stamped envelope provided. Because of color coding
and double-sided data forms, it is imperative that
original forms be returned. You may make whatever
copies you wish for your own records.
15. Await acknowledgement of receipt of your results and
further instructions if any are required.
You may be assured that your careful and complete execution of
this test represents a significant contribution to the improvement of air
quality measurement methods and to the resultant improvement in air
quality. Your efforts are most appreciated. Thank you.
D-8
-------
Following data analysis, you will receive a copy of the formal
report on the collaborative testing of this method.
E. Description of Data Retrieval Forms
A series of data retrieval forms have been designed for use with
the Pararosaniline Method for sulfur dioxide in the atmosphere, some of
which are used in this collaborative test.
The actual information each form retrieves can be seen by
inspection of the following samples; however, some additional comments
on each form used are given below. In all cases, the notation and
procedure is identical to and is keyed with the method published in the
Federal Register.
Form A. Sampling and Analysis Data Form: This form
accommodates the sampling and analysis of ambient or synthetic atmos-
pheres with any sampling time and either sulfite or gaseous calibration.
Up to twelve individual determinations can be recorded along with up to
three control samples and the necessary calibration and reagent blank
information. Where meaningful temperature and pressure corrections can
be made, the back of the form provides for the required monitoring. Up
to 24 observations on up to four samples can be recorded.
Form B. Calibration Procedure with Sulfite Solution; Space is
provided for up to 18 individual sulfite standards in addition to the
directions for calculating the slope by the method of least squares. A
graph for plotting the curve is provided on the back of the form.
Form D. Preparation of Standard Atmospheres; The operating
conditions of a permeation tube system can be recorded on this form.
Up to 24 observations can be recorded.
D-9
-------
REFERENCE METHOD FOR THE DETERMINATION
OF SULFUR DIOXIDE IN THE ATMOSPHERE
(PARAROSANILINE METHOD)
SAMPLING AND ANALYSIS DATA FORM
Laboratory Identification Number
Name and Title of Analyst
Name and Address of Laboratory
Date
SAMPLE TEMPERATURE AND PRESSURE
Note: Use reverse side for monitoring if appropriate.
Temperature of air sample, t = ° C. (Sec. 7. 1. 1)
Barometric pressure, P = mm Hg (Sec. 7. 1. 1)
CALIBRATION
Note: Use Form B or Form C whichever is appropriate.
Calibration factor, Bs = /;g/absorbance unit (Sec. 8. 2. 1)
or Be = (/;g/m3 )/absorbance unit (Sec. 8. 2. 2. 3)
REAGENT BLANK
Reagent blank absorbance, Ao =
absorbance units (Sec. 7. 2. 2)
Sample
Number
1
2
3
Control
SAMPLING (Sees. 7. 1. 1 & 9. 1)
-f/min
min
V
Vg added = (Sec.
VR
7. 2. 2)
DETERMINATION (Sees. 1.2.2 k 9- 2)
A
A - A0
D
US
fjg/m3
Reference: Environmental Protection Agency, "National Primary and Secondary
Ambient Air Quality Standards, " Federal Register, Vol 36, No. 84, Part II,
Appendix A, pp 8187-8191, Friday, April 30, 1971.
FORM A
-------
SAMPLE TEMPERATURE AND BAROMETRIC PRESSURE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Time
Average
Sample
Number
t
P
Sample
Number
t
P
Sample
Number
t
P
Sample
Number
t
P
FORM A (Back)
-------
REFERENCE METHOD FOR THE DETERMINATION
OF SULFUR DIOXIDE IN THE ATMOSPHERE
(PARAROSANILINE METHOD)
CALIBRATION PROCEDURE WITH SULFITE SOLUTION
(Section 8. 2. 1)
Laboratory Identification Number
Name and Title of Analyst
Name and Address of Laboratory
Date
Working Sulfite-TCM Solution Concentration =
/ig/ml (Sec. 6.2.9)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
ml
0
0
0
0.5
0.5
0.5
1
1
1
2
2
2
3
3
3
4
4
4
Summation
X, //g
IX =
Y=A, abs.
IY =
X2
IX' =
XY
IXY =
Number of points, N =
IX IY
IXY -
Slope =
N
IXJ
ix rx
N
absorbance units//jg
Calibration Factor, Bs =
Slope
/jg/absorbance unit
Reference: Environmental Protection Agency, "National Primary and Secondary
Ambient Air Quality Standards, " Federal Register, Vo.l 36, No. 84, Part II,
Appendix A, pp 8187-8191,. Friday, April 30, 1971.
FORM B
-------
CALIBRATION CURVE WITH SULFITE SOLUTION
1.4
1.3
1.2
1.1
1.0
0.9
,4.,..
0.8
.tJ 0.7
§
u
y
s
0.6
J3
flj
T~
0. 5 '-
0.4
0.3
0.2
0.
•-t-
•• i
m
.T'
a
44-
:.:.-±
.«.. i
F;J
I'M'
m
'•• p
81
--4-
-H-'t-
-rrrl
±lt!
-H-
^
rrt
Irjr:z.
i
. . . i .
i ...
i
. i .*
... ;... _.
----t
i. . . ._,
.[" ;
"~ t —
, ..._„..
1 •-—;.-
.. _!...-_ .
' ••* • •
.- :.
' i ' -
. . "i .'."".
~— . . ,.
^; ^ i
— i
t; - ; ; i
. J - . —
^- -3
i-rt— -i -'- i r + ]
iili
:.q-
15 20 25
Sulfur Dioxide, //g
30
35
40
FORM B (Back)
-------
REFERENCE METHOD FOR THE DETERMINATION
OF SULFUR DIOXIDE IN THE ATMOSPHERE
(PARAROSANILINE METHOD)
PREPARATION OF STANDARD ATMOSPHERES
(Sections 8. Z. 2. 1 & 8. 2. 2. 2)
Laboratory Identification Number
Name and Title of Analyst
Name and Address of Laboratory
Date
Permeation Tube Number
Permeation Rate, P =
^g/min
1
2
3
4
5
6
7
8
9
10
11
1Z
13
14
15
16
17
18
19
20
21
22
23
24
Time
t
*d
Ri
C
Reference: Environmental Protection Agency, "National Primary and Secondary
Ambient Air Quality Standards, " Federal Register, Vo.l 36, No. 84, Part II,
Appendix A, pp 8187-8191, Friday, April 30, 1971.
FORM D
------- |