EPA-650/4-75-003
COLLABORATIVE STUDY OF METHOD
FOR THE DETERMINATION
OF SULFURIC ACID MIST
AND SULFUR DIOXIDE EMISSIONS
FROM STATIONARY SOURCES
by
H. F. Hamil, D. E. Camann, and R. E. Thomas
Southwest Research Institute
8500 Culebra Road
San Antonio, Texas 78284
Contract No. 68-02-0626
ROAP No. 26AAG
Program Element No. 1HA327
EPA Project Officer: M. R. Midgett
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
November 1974
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EPA REVIEW NOTICE
This report has been reviewed by the National Environmental Research
Center - Research Triangle Park, Office of Research and Development,
EPA, and approved for publication. Approval does not signify that the
contents necessarily 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.
This document is available to the public for sale through the National
Technical Information Service, Springfield, Virginia 22161.
11
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SUMMARY AND CONCLUSIONS
This report presents the analyses of data which were obtained from collaborative testing of EPA Method 8
(Determination of Sulfuric Acid Mist and Sulfur Dioxide Emissions from Stationary Sources). Method 8
specifies that a gas sample be extracted from a sampling point in the stack and the acid mist including sulfur
trioxide be separated from sulfur dioxide. Both fractions are then measured separately by the barium-thorin
titration method.
The collaborative test was conducted at a sulfuric acid plant. The samples were collected by traversing
the stack according to EPA Method 1, as specified in the test methods and procedures section of the Federal
Register. Fourteen sampling runs were made, but one lab did not participate in the first two, and twice col-
laborators had to abort runs due to equipment difficulties. This resulted in a total of 52 separate determinations
for each of sulfur dioxide and sulfuric acid mist.
Separate precision estimates are obtained for the determination of each pollutant. In addition, standard
sulfate solutions were prepared for analysis by the collaborators in conjunction with the source samples. The
actual concentration of these was unknown to the collaborators, so these allow an assessment to be made of
the accuracy and precision of the analytical phase by itself.
There were several high values in the acid mist determinations which were of a magnitude to suggest that
they were not representative of the true concentration in the stack. These values were associated with low sulfur
dioxide concentrations at a higher frequency than could be expected from chance alone. The conclusion was
that some condition existed which caused these values to occur together. Since it was impossible to determine
that these were invalid determinations, the evaluation of Method 8 was performed with these in the data set.
However, to allow for the possibility that this phenomenon is not method-related, the six acid mist values above
60 Ib/scf X 10"7 were excluded, along with their corresponding sulfur dioxide values, and a separate evaluation
performed. The results are summarized below.
Method 8—The precision estimates are given below in terms of between-laboratory, within-laboratory, and
laboratory bias components.
(1) S02 —The precision components for the sulfur dioxide data are shown to be independent of the mean
level. The estimated between-laboratory standard deviation is 98.60 Ib/scf X 10"7 with 3 degrees
of freedom. The within-laboratory standard deviation is estimated as 76.94 Ib/scf X 10""7 with
40 degrees of freedom. From these, a laboratory bias standard deviation of 61.66 Ib/scf X 10~7 is
estimated.
(2) H2SO4/SO3—The precision components for the sulfuric acid mist data are shown to be proportional
to the mean level, 5. The between-laboratory standard deviation is estimated as 95.8 percent of
6 with 3 degrees of freedom. No within-laboratory or laboratory bias terms could be estimated
due to the high values.
Method 8, High Values Excluded—The precision estimates follow the same models as in the full data
sets.
(1) SO2-The estimated between-laboratory standard deviation is 71.50 Ib/scf X 10~7 with 3 degrees
of freedom. The within-laboratory standard deviation is estimated as 76.94 Ib/scf X 10~7 with
40 degrees of freedom. From these, a laboratory bias standard deviation of 61.66 Ib/scf X 10~7 is
estimated.
(2) H2 864/503—The estimated between-laboratory standard deviation is 66.1 percent of 6 with 3 degrees
of freedom. The estimated within-laboratory standard deviation is 58.5 percent of 6 with 42 degrees
of freedom. This gives an estimated laboratory bias standard deviation of 30.8 percent of 5.
in
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Analytical Phase-The results from the analyses of the unknown sulfate solutions are used to evaluate the
accuracy and precision of the analytical phase of the method separate from the field phase.
(1) Precision. The precision of the analytical phase of the method is expressed in terms of within-laboratory,
between-laboratory and laboratory bias terms. The within-laboratory standard deviation is inde-
pendent of the mean level and is estimated as 2.19 X 10~7 Ib/scf. The between-laboratory standard
deviation is proportional to the mean level and is estimated as 3.68 percent of 8. The laboratory bias
standard deviation is estimated to be 3.53 percent of 6.
(2) Accuracy. The analytical phase is shown to be accurate, within the precision of the method, at all
three levels of concentration studied. These levels cover the range from 158.6 X 10~7 to 669.8 X
10-7 Ib/scf.
A comparison is made between the analytical phase results from this test and the results of a similar test
performed in conjunction with collaborative testing of Method 6 (Sulfur Dioxide) which utilizes the same barium-
thorin titration procedure for sample analysis.
IV
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TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS vii
LIST OF TABLES vm
I. INTRODUCTION 1
II. COLLABORATIVE TESTING OF METHOD 8 2
A. Collaborative Test Site 2
B. Collaborators 3
C. Philosophy of Collaborative Testing 4
III. STATISTICAL DESIGN AND ANALYSIS 5
A. Statistical Terminology 5
B. The Design and Conduct of the Collaborative Test 6
C. Test Data 7
IV. PRECISION ESTIMATES FOR METHOD 8 11
A. S02 11
B. H2S04/S03 12
V. PRECISION OF METHOD 8 WITH HIGH VALUES EXCLUDED 14
A. S02 14
B. H2S04/S03 15
VI. PRECISION AND ACCURACY OF ANALTYICAL PHASE 17
A. The Unknown Sulfate Solution Test 17
B. Analytical Phase Precision 17
C. Analytical Phase Accuracy 17
D. Comparison With Method 6 18
APPENDIX A—Method 8—Determination of Sulfuric Acid Mist and Sulfur Dioxide Emissions
From Stationary Sources 20
APPENDIX B-Statistical Methods 24
B.1 Preliminary Data Analysis 26
B.2 Negative Correlation in the Concurrent Concentration Determinations of Sulfur
Dioxide and Sulfuric Acid Mist 27
B.3 Blocking the Determinations 28
B.4 Distributional Nature of S02 Determinations 29
B.5 Precision Estimates for SO2 Determinations 33
B.6 Distributional Nature of H2S04/S03 Determinations 35
B.7 Unbiased Estimation of Standard Deviation Components 37
B.8 Weighted Coefficient of Variation Estimates 39
B.9 Precision of H2SO4/SC>3 Determination 42
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TABLE OF CONTENTS (Cont'd)
Page
B.10 Analysis of Data Excluding High Mist Values 43
B.11 The Unknown Sulfate Solution Test Data 47
B.12 Analysis of Variance in the Unknown Sulfate Solution Test 47
LIST OF REFERENCES 50
VI
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LIST OF ILLUSTRATIONS
Figure Page
1 Overall View of Sampling Site 2
2 Sample Platform 2
3 Typical Velocity Profile 3
4 Analysis of Unknown Sulfate Solutions 6
5 Special Instructions 7
B.I Negative Correlation of Concurrent Method 8 Determinations 28
B.2 Between-Laboratory Run Plot, Sulfuric Acid Mist Data 36
B.3 Within-Laboratory Collaborator-Block Plot, Sulfuric Acid Mist 37
vn
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LIST OF TABLES
Table Page
1 Design of the Method 8 Collaborative Test 7
2 Corrected Sulfur Dioxide Concentration Determinations Arranged by Block .... 9
3 Corrected Acid Mist Concentration Determinations 9
4 Plant Operating Parameters During Sampling 10
5 Method 8 Analytical Phase Precision Estimates 17
6 Accuracy of the Analytical Phase of Method 8 18
7 Comparison of Method 6 and Method 8 Analytical Phase Precision Data 18
8 Analytical Phase Standard Deviation Estimate Comparison 19
9 Accuracy of the Barium-Thorin Titration Procedure 19
B.I Originally Reported Collaborative Test Data 26
B.2 Correlation of Concurrent Method 8 Determinations of H2S04 and SO2 28
B.3 Friedman Rank Test, All S02 Runs 30
B.4 Friedman Rank Test, SO2 Blocks 30
B.5 Friedman Rank Test, Acid Mist 30
B.6 S02 Data Transformation Summary 31
B.7 Sulfur Dioxide Run Summary 31
B.8 Sulfur Dioxide Collaborator-Block Summary 31
B.9 Acid Mist Data Transformation Summary 36
B.10 Acid Mist Run Summary 36
B.ll Acid Mist Collaborator-Block Summary 37
B.I 2 Acid Mist Run Beta Estimates and Weights 43
B.I3 Acid Mist Collaborator-Block Beta Estimates and Weights 43
B.I4 S02 Data Transformation Summary, High Mist Values Excluded 44
B.I 5 Sulfur Dioxide Run Summary, High Mist Values Excluded 44
B.16 Sulfur Dioxide Collaborator-Block Summary, High Mist Values Excluded 45
B.I7 Acid Mist Collaborator-Block Summary, High Values Excluded 46
viii
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LIST OF TABLES (Cont'd)
Table Page
B.I8 Acid Mist Run Summary, High Values Excluded 46
B.I9 Acid Mist Collaborator-Block Summary, High Values Excluded 47
B.20 Corrected Sulfate Solution Concentrations, 10~7 lbSO2/scf 48
B.21 Average Laboratory Sulfate Solution Concentrations, ICf7 Ib SO2/scf 48
B.22 Analysis of Variance of Sulfate Solution Data by Concentration 49
B.23 Analytical Phase Precision Estimation 49
B.24 Intraclass Correlation Coefficients 50
B.25 Analytical Phase Replication Error, Lab 101 50
IX
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I. INTRODUCTION
This report describes the work performed and the results obtained on Contract 68-02-0626, Southwest
Research Institute Project 01-3462-005, which includes collaborative testing of Method 8 for sulfur dioxide and
sulfuric acid mist emissions as given in "Standards of Performance for New Stationary Sources.''^)
This report describes the collaborative testing of Method 8 at a sulfuric acid plant, the statistical analyses
of the data and the conclusions based on the analyses of the data.
*Supersciipt numbers refer to List of References at the end of this report.
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II. COLLABORATIVE TESTING OF METHOD 8
A. Collaborative Test Site
Arrangements were made for a collaborative test of Method 8 at NL Industries Titanium Pigment Division
sulfuric acid plant in St. Louis, Missouri.
The plant site was visited in August, 1973, to evaluate suitability for collaborative testing. The sulfuric
acid plant is a sulfur burning unit, and utilizes a dual absorption process. Rated capacity of the unit is 900 tons/day
of concentrated H2 S04. The exhaust gas from the absorbers is fed to a 200-ft-high stack. A 360-deg platform
located on the stack 129 ft above grade was selected as the sample point. Diameter of the stack at the sample
point is 6 ft. Sample ports were not available at this platform, and arrangements were made for the installation
of four sample ports spaced 90-deg apart, located 5 feet above the platform floor. This placed the sample
ports 41 ft above a constriction in the stack and 66 ft below the stack outlet. As a result, 20 traverse points
were selected, 10 on each diameter. Due to the relatively small work space on the sampling platform, the
control consoles were located on a platform 62 ft above grade, and 67 ft below the sampling platform. Arrange-
ments were made to obtain plant analytical data on the stack gas, and to obtain daily sulfuric acid production
data.
An overall view of the sampling site is shown in Figures 1 and 2. In Figure 1, both the sample platform
and the platform on which the consoles were placed can be seen, while Figure 2 shows the sample platform.
Typical velocity profiles in the stack are shown in Figure 3.
Figure 1. Overall View of Sampling Site
B. Collaborators
Figure 2. Sample Platform
The collaborators for the NL Industries sulfuric acid plant test were Mr. Charles Rodriguez and Mr. Ron
Hawkins of Southwest Research Institute, San Antonio Laboratory, San Antonio, Texas; Mr. Mike Taylor and
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40
Stack Diameter, Ft
o
D
A-C Diameter
B-D Diameter
Figure 3. Typical Velocity Profile
Mr. Rick Hohman, Southwest Research Institute, Houston Laboratory, Houston, Texas; Mr. Roger Johnson
and Mr. Bruce Callahan, Environmental Research Corporation, St. Paul, Minnesota; and Mr. Daniel Vornberg,
Mr. Andrew Polcyn, Mr. David Givens, Mr. Richard Hagaman and Mr. J. W. MacClarence of Environmental
Triple S, St. Louis, Missouri.
The collaborative test was conducted under the supervision of Mr. Nollie Swynnerton of Southwest
Research Institute. Mr. Swynnerton had the overall responsibility for assuring that the test was conducted in
accordance with the collaborative test plan and that the collaborators adhered to Method 8 as written in the
Federal Register.^ Collaborators for the test were selected by Dr. Henry Hamil of Southwest Research Institute.
C. Philosophy of Collaborative Testing
The concept of collaborative testing followed in the tests discussed in this report involves conducting the
test in such a manner as to simulate "real world" testing as closely as possible. "Real world" testing implies
that the results obtained during the test by each collaborator would be the same results obtainable if he were
sampling alone, without outside supervision, and without any additional information from outside sources, i.e.,
test supervisor or other collaborators.
The function of the test supervisor in such a testing scheme is primarily to see that the method is
adhered to as written and that no individual innovations are incorporated into the method by any collaborator.
During the test program, the test supervisor observed the collaborators during sampling and sample recovery. If
random experimental errors were observed, such as mismeasurement of volume of impinger solution, improper
rinsing of probe, etc., no interference was made by the test supervisor. Since such random errors will occur in
the everyday use of this method in the field, unduly restrictive supervision of the collaborative test would bias
the method with respect to the performance test results which will be obtained when the method is put into
general usage. However, if gross deviations were observed of such magnitude as to make it clear that the col-
laborator was not following the method as written, these would be pointed out to the collaborator and corrected
by the test supervisor.
While most of the instructions in the Federal Register are quite explicit, some areas are subject to inter-
pretation. Where this was the case, the individual collaborators were allowed to exercise their professional judge-
ment as to the interpretation of the instructions.
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III. STATISTICAL DESIGN AND ANALYSIS
A. Statistical Terminology
To facilitate the understanding of this report and the utilization of its findings, this section explains
the statistical terms used in this report. The procedures for obtaining estimates of the pertinent values are
developed and justified in the subsequent sections.
We say that an estimator, 9, is unbiased for a parameter 6 if the expected value of 0 is 6 , or expressed in
notational form, E(S) = 6 . From a population of method determinations made at the same true concentration,
ju, let Xi , . . ., xn be a sample of n replicates. Then we define:
1 "
(1) x = ~~/_..Xj as the sample mean, an unbiased estimate of the true determination mean, 5 , the center
"« = 1
of the distribution of the determinations. For an accurate method, 6 is equal to ju, the true con-
centration.
(2) x2 = - ^ (xi — x)2 as the sample variance, an unbiased estimate of the true variance, a1 . This
n ~ l,tl
term gives a measure of the dispersion in the distribution of the determinations around 6.
(3) x = ys2 as the sample standard deviation, an alternative measure of dispersion, which estimates a,
the true standard deviation.
The sample standard deviation, s, however, is not unbiased for a/2) so a correction factor needs to be
applied. The correction factor for a sample of size n is an , and product of an and x is unbiased for a. That is,
E(ans) = o. As n increases, the value of
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For example, a run mean is the average of all the determinations made in a run as obtained by Method 8.
A collaborator-block coefficient of variation is the ratio of the unbiased standard deviation to the sample
mean for all the collaborator's runs grouped in the block.
The variability associated with a Method 8 determination is estimated in terms of the within-laboratory
and the between-laboratory precision components. In addition, a laboratory bias component can be estimated.
The following definitions of these terms are given with respect to a true concentration, n.
• Within-laboratory— The within-laboratory standard deviation, a, measures the dispersion in replicate
single determinations made using Method 8 by one laboratory team (same field operators, lab-
oratory analysts, and equipment) sampling the same true level, (i. The value of a is estimated from
within each collaborator-block combination.
• Between-laboratory— The between-laboratory standard deviation, a^, measures the total variability
in a determination due to simultaneous Method 8 determinations by different laboratories sampling
the same true stack concentration, p.. The between laboratory variance, a\, may be expressed as
and consists of a within-laboratory variance plus a laboratory bias variance, a2L . The between-
laboratory standard deviation is estimated using the run results.
• Laboratory bias— The laboratory bias standard deviation, a^ = \JaJ, — a2 , is that portion of the
total variability that can be ascribed to differences in the field operators, analysts and instru-
mentation, and due to different manners of performance of procedural details left unspecified
in the method. This term measures that part of the total variability in a determination which
results from the use of the method by different laboratories, as well as from modifications in
usage by a single laboratory over a period of time. The laboratory bias standard deviation is esti-
mated from the within- and between-laboratory estimates previously obtained.
B. The Design and Conduct of the Collaborative Test
The collaborative test plan called for 16 sampling runs over a two-week period from October 22 to
November 2, 1973. Only 14 runs were actually made because the unit was down for repairs during two days
of the sampling period. Each sampling run was 2 hours in duration, with each team sampling 30 minutes at
each of the four ports on the stack. The sampling sequence used by each collaborator to obtain the sample
is shown in Table 1 .
The starting port for each collaborator at the beginning of each day was chosen through a randomization
technique, as was the direction of rotation to the next port. When a second run was made on a given day, the
starting port was the finishing port of the first run, and the rotation was in the opposite direction. This was
done to avoid entanglement of the umbilicals and to make the operation of the crews on the sampling platform
easier.
In addition to the Method 8 samples, the collaborators were given three sulfate solutions to analyze in
conjunction with the test samples. The concentrations of these solutions were unknown to the collaborators,
and the analytical results allow estimation of the accuracy and precision of the analytical phase of the method.
The collaborators were instructed to analyze each solution in triplicate on three separate days. These analyses
were to be performed during the time period in which the stack samples were being analyzed. A copy of the
instruction and data sheet given to the collaborators is shown in Figure 4.
During the course of the test, two operating parameters were observed for later use in estimating the
true concentration level of the pollutants. The first was the Reich test for S02 in the gas stream, and the second
was the daily amount of acid produced. The Reich test analyzes the exit gas for S02 and is made at 2-hr intervals
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A series of sulfate solutions are provided to each collaborator.
These solutions are labeled A, B, and C, and the concentrations are
unknown to the collaborators.
Each unknown solution is to be analyzed in triplicate on each of
three separate days during the period when analyses of the collaborators
stack gas samples are being performed. Use a 10 ml aliquot, add 40ml
isopropanol and 2 to 4 drops Thorin indicator. Titrate the solution with
0.01N barium perchlorate to a pink endpoint.
Calculate the concentration in lbs/ft3 using the following equation:
v -'V
'7.05x10-5 lb-M ^t'V)
SO-
Use V
soln
"Va~~
3,-ml
m
std
m
= 40ft"
std
V , = 1000ml,
soln
= 10ml
Submit the results on this sheet along with your other collaborative test
data.
Analyst:
Day
Day 1
Date
Day 2
Date
Day 3
Date
Replicate
1
2
3
1
2
3
1
2
3
SO? Concentration, Ib/ft
Solution A
Solution B
Solution C
Figure 4. Analysis of Unknown Sulfate Solutions
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Table 1. Design of the Method 8 Collaborative Test
Day
10/22/73
10/23/73
10/24/73
10/29/73
10/30/73
10/31/73
11/1/73
11/2/73
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Port Sampling Sequence*
Lab 1 01
BCDA
ABCD
DCBA
DABC
CBAD
DABC
CBAD
BCDA
ADCB
DCBA
DABC
CBAD
CDAB
BADC
Lab 102
-
CBAD
CDAB
BADC
ABCD
DCBA
CDAB
BADC
CBAD
CDAB
BADC
BCDA
ADCB
Lab 103
CDAB
BCDA
ADCB
BCDA
ADCB
CDAB
BADC
ABCD
DCBA
BADC
BCDA
ADCB
ABCD
DCBA
Lab 104
ABCD
CBAD
BADC
ABCD
DCBA
BCDA
ADCB
DABC
CBAD
ADCB
ABCD
DCBA
DABC
CBAD
*Sequence BCDA means that consecutive radius traverse
samples were obtained through port B, port C, port D, and
port A.
during the day by plant personnel. The daily
amount of acid produced is given as daily produc-
tion rate in tons of 100 percent H2SO4/24 hr,
proportional to the 10 hr of actual production.
One modification to the S02 sample recovery
and analysis was found to be necessary. If the pro-
cedure specified in the method was used, excessively
large volumes of titrant (greater than 50 m£) were
required. To avoid the errors inherent in repeated
filling of the burette during titration of a sample,
the dilution factor during sample recovery was
increased, and the aliquot size was decreased. The
special instructions given the collaborators are
shown in Figure 5.
C. Test Data
The determinations of sulfur dioxide and acid
mist concentrations as reported by the collaborators
are shown in Table B.I. The raw data sheets were
provided to SwRI, and these were used to check the
calculations of the collaborators. In this manner,
the results reported here are not influenced by cal-
culation errors. The recalculated values for the sul-
fur dioxide concentrations appear in Table 2 and
the recalculated acid mist concentrations are in
Table 3. A detailed discussion of the preliminary data
analysis is in Appendix B.I.
SPECIAL NOTE TO COLLABORATORS
To avoid excessively large titrant volumes in the determination of SC>2 concentration
(paragraph 4.3.1 and equation 8-3, Method 8, Federal Register, Vol. 36, Dec. 23, 1971) the following
modification of Method 8 has been made for this test, with the approval of the EPA Project Officer.
Take the container holding the contents of the second and third impingers and add the contents
to a one liter volumetric flask. Rinse the container with deionized distilled water and add the rinsings
to the volumetric flask. Dilute to the mark with deionized distilled water. Mix thoroughly. Pipette a
10 mC aliquot of sample into a 250 m£ Erlenmeyer flask. Add 40 m£ of isopropanol and 2 to 4 drops
of thorin indicator. Titrate with barium perchlorate to a pink endpoint. Record the volume of titrant.
Repeat the titration with a second aliquot of sample. Titrate the blanks in the same manner as the
samples.
It should be noted that this modification applies only to that portion of paragraph 4.3.1
concerning determination of SO2 concentration. The initial portion of paragraph 4.3.1 concerning
the determination of sulfuric acid mist remains unchanged, and should be followed as written in the
Federal Register.
Figure 5. Special Instructions
There are four missing values in the data set. On the first day of testing, Lab 102 was not prepared to
sample and missed both runs 1 and 2. On run 3, Lab 102 was forced to abort due to a broken carriage. On
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run 6, Lab 104 could not complete the run due to broken glassware. There was no substitution made for
these values, but rather the analysis was performed using only the 52 valid determinations.
There are some values in the data sets which appear unusual. In the acid mist concentration determination,
there are values which range from 2 to 10 times the other values for that run. In the sulfur dioxide data, there are
values which are on the order of one-half of the remaining values for that lab. While these would appear to be outliers
in a statistical sense, they are not excluded from the analysis. Since there is no evidence to suggest that these deter-
minations were made improperly, nor to indicate that this type of result is unexpected with the field use of
Method 8, they are retained.
The interesting phenomenon is that the high mist and low sulfur dioxide determinations appear to occur
in conjunction with one another. That is, a high acid mist concentration is usually accompanied by a low sulfur
dioxide concentration. To investigate this idea, a correlation coefficient is determined between the SC>2 and
H2S04/S03 determinations. The details appear in Appendix B.2.
The correlation coefficient obtained from the 52 pairs of determinations is r = -0.51 which indicates a
significant negative correlation. By investigating the correlation between determinations for each collaborator
separately, it is apparent that this negative correlation is related to the occurrence of high acid mist deter-
minations. The more high values in a lab's data, the greater the degree of correlation present. If the 6 values
which exceed 601b/scf X 10~7* are deleted, the correlation among the remaining 46 pairs is estimated by
r = —0.14, which is not significantly different from zero.
The conclusion drawn from this is that there is a reason for these values occurring together. What cannot
be determined is whether the reason is related to Method 8 itself, or whether there was some disturbance or
condition at the test site which led to this phenomenon. Without a strong basis, the values may not be removed
Table 2. Corrected Sulfur Dioxide
Concentration Determinations
Arranged by Block
(Ib/scfX 10-->)
Table 3. Corrected Acid Mist Con-
centration Determinations
(Ib/scfx. lO-'1)
Block
1
2
3
Run
4
5
10
1
2
3
6
7
8
9
11
12
13
14
Labs
101
313
375
461
453
314
401
404
412
428
476
301
460
483
471
102
403
271
436
*
*
t
494
564
562
599
587
597
579
568
103
298
341
327
226
455
367
377
166
402
444
432
441
459
438
104
284
400
242
506
578
233
t
491
438
564
514
552
379
582
*Run not made.
fRun not completed due to glassware
breakage.
Dim
Kun
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Labs
101
37.0
109.5
49.9
44.6
8.5
7.8
3.2
9.7
11.4
13.3
97.1
74.7
7.7
6.2
102
*
*
t
5.0
5.3
5.5
6.7
8.6
8 3
8.6
6.3
5.7
10.2
6.6
103
64.3
31.9
11.7
24.2
10.1
14.1
112.9
11.1
13.9
8.6
8.6
9.3
12.7
7.0
104
6.0
10.5
7.1
4.2
12.4
t
7 0
22.2
7.5
112.9
18.9
25.8
22.8
22.9
*Run not made.
I Run not completed due to glassware
breakage.
*EPA policy is to express all measurements in Agency documents in metric units. When implementing this practice will result
in undue cost or difficulty in clarity, NERC/RTP is providing conversion factors for the particular nonmetnc units used in the
document. For this report, the factor is:
10^' Ib/scf = 1.6018 X 103 Mg/m3.
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from the data set prior to analysis. Thus, the results presented here for the method will be those obtained
using all 52 concentration determinations for each pollutant. To account for the possibility that these values
are not representative of a Method 8 test result, a second analysis is done on the data sets with high mist
determinations and their corresponding sulfur dioxide values eliminated.
Since no techniques were available for producing a stable S02/S03/H2S04/air mixture, there could
be no assessment of the accuracy of the method. The statistical results contained in this report for the method
concern only the precision that can be expected with its use as a field testing method.
The first step in the analysis is to group the runs into blocks. In Appendix B.3, the Friedman test is
used to establish that the true mean concentration of sulfur dioxide varied over the test period. To account
for this variation, three blocks are established based upon the operating parameters observed. The average
values of the Reich test over each sampling run and the daily production rates are shown in Table 4. The
first block consists of those runs where the Reich test was low (2.5), the second where the Reich was high
and production rate was low, and the third where both were high. The run where the Reich test was not
made was included in the third block on the basis of the high production rate. In Appendix B.3, the adequacy
of this blocking scheme is demonstrated.
Table 4. Plant Operating Parameters
During Sampling
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Reich Test,
%SO2
3.0
3.0
3.0
2.5
2.5
3.0
3.0
*
3.0
2.5
3.0
3.0
3.0
3.0
DaUy Pro-
duction Rate,
tons H2SO4
915
913
913
915
915
919
919
940
940
923
949
949
947
947
SO 2 Blocking Scheme
Block Runs
1 4,5,10
2 1,2,3,6,7
3 8,9,11,12,13,14
*Not taken.
For the acid mist determination, the Friedman test indicates
no significant variation in the true value from run to run. Thus,
these runs are treated as a single block of size 14. The details of
the Friedman test are shown in Appendix B.3.
The within-laboratory precision estimates are obtained from
the collaborator-blocks under the assumption that each run in the
block had the same true mean concentration. Since there is
undoubtedly some variation in the concentration levels, it is likely
that these estimates are conservative. That is, one would expect
the within-laboratory variance, a1, to be no larger than the esti-
mated value, and probably to be smaller.
The between-laboratory precision estimates are taken from
the differences among laboratories in a sample run. As such, they
represent differences between samples taken from the same traverse
points during the same 2-hr period. The only possible fluctuation
in the true concentration would be due to a changing pattern of gas
flow during the course of the run.
-------
IV. PRECISION ESTIMATES FOR METHOD 8
A. SO2
Prior to analyzing the data, transformations are used to determine the distributional nature of the deter-
minations. Three forms of the data are tested: linear, logarithmic and square root. The transformed data are
tested using Bartlett's test for homogeneity of variance. The results of the transformations and tests are shown
in Appendix B.4.
The original or linear form of the data obtains the highest degree of equality for the SO2 data. The
acceptance of the linear transform as the best model implies that there is a constant variance for both the run
data and the collaborator-block data, regardless of the level of the mean concentration. These variances are
estimated by combining the estimates obtained for them from each run and from each collaborator-block.
The technique is referred to as pooling, and is discussed in Appendix B.4.
The precision estimates are of the form
/= l
y k
E («<• -1)
;= i
where
s,2 - sample variance of the r sample
«, — size of the / sample
k — number of samples
In Appendix B.5, the individual standard deviations and sample sizes are presented and used to obtain the
precision estimates. The within-laboratory variance, a2 , is estimated from the collaborator-block terms, and
has an estimated variance, a2 , of
o2 = 5920.12
with 40 degrees of freedom. The estimated within-laboratory standard deviation, then, is
= 76.941b/scfX 10"7
Letting 5 represent the sample mean of all 52 determinations, it is possible to estimate a within-laboratory
coefficient of variation as
76.94
429.77
= 0.18.
10
-------
The between-laboratory variance, o\, is estimated using the 14 run standard deviations obtained. Sub-
stituting into the pooled variance formula gives
a£ = 972 1.76
with 3 degrees of freedom. This gives an estimated between-laboratory standard deviation of
= 98.60 Ib/scfX 10"7
The between-laboratory coefficient of variation is
98.60
~ 429.77
= 0.23.
The laboratory bias variance, a\ , is estimated from the above as
6i=6ft2-*2
= (9721. 76) -(5920.12)
= 3801.64,
with a laboratory bias standard deviation of
aL =-s/3801.64
= 61.661b/scfX ID'7
The laboratory bias coefficient of variation, then, is estimated by
»-r
61.66
429.77
= 0.14.
B. H2SO4/SO3
The acid mist determinations were passed through the same transformations as were the SO2 . In Appendix B.6,
it is demonstrated that for these data, the logarithmic transformations gives the highest degree of equality of
variance. This implies that there is a proportional relationship between the true mean and true standard deviation.
That is, the variability in an acid mist determination increases as the mean concentration increases, but the ratio
of the standard deviation to the mean, the coefficient of variation, remains constant. Thus,
11
-------
and
provide the best information concerning the variability in the determination of acid mist concentration in a
gas stream. To estimate the precision, then, the coefficients of variation are estimated and the standard deviations
presented as a coefficient of variation times an unknown mean, 6.
In Appendices B.7 and B.8, the technique for obtaining a point estimate of a coefficient of variation
from several individual estimates is presented. The run and block sizes vary since there are missing values in
the data set, so the individual estimates are weighted according to their sample size.
For the run data, there are 14 individual estimates of /3/>. In Appendix B.9, the estimates and their
respective weights are shown. Combining these gives an estimated coefficient of variation, fa , of
fe= 0.958.
The standard deviation estimate, then, is
ab = (0.958)5
or 95.8 percent of the mean value, with 3 degrees of freedom.
The collaborator-blocks give 4 estimates of |3, the within-laboratory coefficient of variation. These esti-
mates appear in Appendix B.9 along with their respective weights, and give an estimated coefficient of variation,
Mf
(3=1.015
and a standard deviation estimate, &, of
= (1.015)6.
Since the between-laboratory component contains the within-laboratory component, it is theoretically
impossible to obtain a larger within- than between-laboratory component. When the within is larger than the
between, as it is here, the usual conclusion that is drawn is that there is no laboratory effect. That is, the
laboratory bias component, a£ , is assumed to be equal to zero.
In this case, however, that is not a reasonable conclusion. By inspection of the data, it is easy to see that
there are tendencies among the collaborators to be consistently higher or lower than the rest, most notably with
Lab 102. The conclusion drawn in this case is that the high values are of such magnitude that they prevent the
separation of within-laboratory and laboratory bias terms from the total variability.
Since the between-laboratory component is free from run-to-run source variation, it is considered a
good estimate of the precision of the acid mist determination with the occurrence of occasional high values.
No attempt is made to partition this component into its within-laboratory and laboratory bias components.
12
-------
V. PRECISION OF METHOD 8 WITH HIGH VALUES EXCLUDED
As discussed previously, there is no information available to show whether the high H2S04/SO3 values
(in excess of 60 Ib/scf X 1CT7) are typical of Method 8 results or whether there were factors peculiar to the
test site or test period which caused their occurrence. If these values are atypical, then they should not be
used in the data analysis, since they would unfairly bias the results. To account for this possibility, a second
analysis is performed on each data set with these runs excluded. Due to the significant negative correlation
between the S02 and H2S04/S03 determinations, the SO2 determinations corresponding to the high acid
mist values are also eliminated from the data set for the second analysis. This results in 46 determinations
used in the analyses blocked in the same manner as the complete data set.
A. SO2
The distributional characteristics of the determinations remain unchanged. The linear transformation pro-
vides the highest degree of equality of variance. This implies that the within- and between-laboratory variances,
a2 and a2,, are independent of the mean level. The estimates are obtained using the pooled variance technique
as before.
The run data provide 14 estimates of a2,, and these are shown in Table B.I 5. Substituting into the
formula gives
6^ = 51 11.79
and
1.79
= 71.501b/scfX lO"7
with 3 degrees of freedom. For the 46 determinations, the sample mean is 8 = 448.67 Ib/scf X 1(T7 . Using this,
the coefficient of variation for the between-laboratory component is
71.50
448.67
= 0.16.
There are 12 estimates of a2 obtained from the collaborator-block data, and these are summarized in
Table B.16. Pooling these estimates gives
62 =4351.42
with 34 degrees of freedom. From this, the estimated standard deviation is
6=^4351.42
= 65.97 Ib/scf X 10^7.
13
-------
The estimated coefficient of variation, then, is
- a
fmT
65.97
448.67
= 0.15.
The laboratory bias variance, a£, is estimated as
«l=8& ~o2
= 5111.79-4351.42
= 760.37
and the laboratory bias standard deviation estimate is
= V760.37
= 27.57 Ib/scfX 10"7
This gives an estimated laboratory bias coefficient of variation of
27.37
448.67
= 0.06.
B. H2S04/S03
The 46 acid mist determinations are shown in Appendix B.10 to have the same distributional nature as
the full data set. That is, the logarithmic transformation is the best suited to the data which implies a proportional
relationship between the true mean and the true standard deviation. The estimation procedures of Appendices B.7
and B.8 are used to obtain estimates of the coefficients of variation for the within- and between-laboratory com-
ponents.
The between-laboratory coefficient of variation, j3j , is estimated by using a weighted combination of the
run beta estimates. This gives
ft, =0.661
and an estimated between-laboratory standard deviation of
= (0.661)6.
There are 3 degrees of freedom associated with this estimate.
14
-------
The collaborator-block data provide 12 estimates of the within-laboratory coefficient of variation, (3.
Combining these gives an estimated value of
|3 = (0.585).
The within-laboratory standard deviation, then, is
5=06
= (0.585)6
with 42 degrees of freedom.
The laboratory bias standard deviation, a/,, is estimated by
= V[(0.661)2-(0.585)2]62
= \/(0.095)62
= (0.308)6.
15
-------
VI. PRECISION AND ACCURACY OF ANALYTICAL PHASE
A. The Unknown Sulfate Solution Test
An unknown sulfate solution test was conducted as part of the Method 8 collaborative study to assess
the precision and accuracy of the analytical phase of Method 8 separately. Three different sulfate solutions,
with the actual concentrations concealed, were provided to each of the four collaborative laboratory teams
for sample analysis by the Method 8 barium-thorin titration procedure along with the collaborative test sam-
ples. Sample aliquots of 10 m£ each from each solution were analyzed by each collaborative team in triplicate
on each of three of the sample analysis days. The instruction and reporting form for the unknown sulfate
solution test is illustrated in Figure 5. The reported data are presented and summarized in Tables B.20 and
B.21 ofAppendixB.il.
It should be noted that the sulfuric acid mist/sulfur trioxide and the sulfur dioxide sample fractions are
analyzed separately by the same barium-thorin titration procedure in Method 8. Hence, the precision esti-
mates and accuracy statements derived in this section from the unknown sulfate solution test data pertain
to the Method 8 analytical phase concentration determinations of both sulfuric acid mist and sulfur dioxide.
B. Analytical Phase Precision
A separate analysis of variance has been performed on the data for each of the three unknown sulfate
solution concentrations. These analyses of variance, described in Appendix B.I 1, utilized a random effects
model to analyze the importance of the laboratory bias (collaborator) and within-laboratory (day and repli-
cation) components of the analytical phase variance. Because Lab 104 consistently obtained determinations
that were from 6 to 9 percent too low, a significant large laboratory bias component occurred with every
solution. The day factor was only significant for the solution with the highest S02 concentration.
Table 5. Method 8 Analytical Phase Precision Estimates
Precision Measure
Within-Laboratory
Laboratory Bias
Between-Laboratory
Component Estimates
Coefficient
of Variation
3i = 0.0353
&b = 0.0368
Standard
Deviation
& = 2.19X 10~7 Ib/scf
01 = (0.0353)5
ob = (0.0368)6
The analytical phase precision estimates
developed from the analysis of variance are pre-
sented in Table 5. A constant within-laboratory
standard deviation estimate a = 2.19 X 10"7 Ib/scf
was obtained from the pooled within-laboratory
variance, because the within-laboratory variance
remained quite stable with increasing solution
concentration. Hence, there is no constant within-
laboratory coefficient of variation for the analytical
phase. The laboratory bias standard deviation, aL = 0.03536, and the between-laboratory standard deviation,
&[, = 0.03685, were derived by the coefficient of variation technique of Appendices B.7 and B.8. Note that
since the within-laboratory component is constant, laboratory bias is the major component of the between-
laboratory variability of the Method 8 analytical phase in the normal range of concentrations.
C. Analytical Phase Accuracy
In this report, the accuracy of a procedure refers to its ability to obtain, on the average, the true value
of the quantity being measured, taking into account the precision uncertainty that has been determined for
the procedure. To phrase the definition in statistical terminology, an accurate procedure is one that is unbiased
within the procedure's precision. Hence, a statement regarding a procedure's accuracy connotes nothing
about the procedure's precision (i.e., its ability to repeatedly obtain the same value in measuring a fixed
quantity).
The accuracy of the analytical phase of Method 8 is examined by comparing the average of all the
collaborators' determinations of the S02 concentration for a given unknown solution against the "true"
effective SO2 concentration represented by that sulfuric acid solution. This comparison is shown in Table 6.
16
-------
Table 6. Accuracy of the Analytical Phase of Method 8
Sulfur Dioxide Concentration, 10 7 Ib/scf
Solution
C
A
B
Prepared
"True"
Value
158.6
423.0
669.8
Mean
Over All
Collaborators
156.9
410.1
653.5
Difference
- 1.7
-12.9
-16.3
95-Percent Confidence Level
Range
± 6.0
±14.4
±22.7
Interval About Mean
(150.9,162.9)
(395.7,424.5)
(630.8, 676.2)
Percentage
Difference
-1.1
-3.0
-2.4
The 95-percent confidence range and interval for the mean over all collaborators is based on a standard deviation
of V<% /4 + If/3 = V(0.08536)2/4 + (2.19 X 1(T7 lb/scf)2/3.
All the Method 8 solution means were lower (from 1.1 to 3.0 percent) than their respective "true" values.
But inspection of Table 6 shows that for all three solutions the prepared "true" SOa concentration level lies
within the 95-percent confidence interval about the collaborators' mean Method 8 determination. Therefore,
the analytical phase of Method 8 is unbiased within the precision of the method.
D. Comparison With Method 6
The same barium-thorin titration procedure is utilized for sample analysis both in Method 8 and in Method 6.
Furthermore, the unknown sulfate solution tests performed with the Method 8 and the Method 6 collaborative
tests both specified use of a 10 m£ sample aliquot and addition of 40 m£ of isopropanol. Since they are both
derived from the unknown sulfate solution test data, the analytical phase precision and accuracy findings for
Method 8 should be comparable to the Method 6 analytical phase precision and accuracy presented m our
Method 6 collaborative test report.(4)
The analytical phase precision point estimates obtained for each unknown solution in both the Method 6
and the Method 8 collaborative studies are tabulated as Table 7. The actual analytical phase precision estimates
Table 7. Comparison of Method 6 and Method 8 Analytical Phase Precision Data
Method
6
8
6
6
8
6
8
Unknown
Solution
B
C
D
A
A
C
B
Mean, 10~7 Ib/scf
True
0.0
158.6
176.3
352.5
423.0
528.8
669.8
Method 6
0.1
174.4
349.0
522.0
Method 8
156.9
410.1
653.5
Within Laboratory
Std. Dev.
0.41
2.82
2.68
4.16
1.24
3.23
2.20
Laboratory Bias
Std. Dev.
0.49
5.47
4.41
6.68
16.09
11.09
22.33
Coef. of Var.
0.0345
0.0250
0.0189
0.0380
0.0210
0.0333
Between-Laboratory
Std. Dev.
0.64
6.16
5.16
7.87
16.14
11.55
22.44
Coef. of Var.
0.0388
0.0293
0.0223
0.0382
0.0218
0.0335
obtained using all the unknown solution estimates except those for the blank solution B of Method 6 are sum-
marized in Table 8 both for Method 6 and Method 8. There is reasonably good agreement between the Method 6
and Method 8 precision estimates. Method 6 had the higher within-laboratory precision variation, while Method 8
exhibited more laboratory bias and between-laboratory variation. Given the relatively small magnitude of these
discrepancies, they are probably attributable to the normal random variation to be expected between different
sets of four laboratories and four analysts performing the same procedures. Combined estimates of the analytical
phase precision standard deviations of the barium-thorin titration procedure are also presented in Table 8. The
within-laboratory estimate was derived by pooling the Method 6 and Method 8 variances estimates, with each
method's estimate given equal weight. The laboratory bias and between-laboratory estimates were obtained
by averaging the two methods' coefficients of variation for each precision component.
A summary of the Method 6 and Method 8 evidence regarding the accuracy of their analytical phase
barium-thorin titration procedure is presented in Table 9. Both in Method 6 and Method 8, the barium-thorin
17
-------
Table 8. Analytical Phase Standard Deviation Estimate Comparison
Precision
Component
Within-Laboratory
Laboratory Bias
Between-Laboratory
Method 6
Estimates
o=3.4 IX 10~7lb/scf
OL = (0.0219) «
ab = (0.0245) S
Method 8
Estimates
a=2.19X 10-7lb/scf
aL = (0.0353) 6
CT6 = (0.0368) 6
Combined Barium-
Thorin Titration Estimates
CT = 2.86 X 10-7lb/scf
OL = (0.0286) 6
ab = (0.0306) 6
Table 9. Accuracy of the Barium-Thorin Titration Procedure
Method
6
8
6
6
8
6
8
Unknown
Solution
B
C
D
A
A
C
B
Sulfur Dioxide Concentration, 10"' Ib/scf
Prepared
"True Value"
0.0
158.6
176.3
352.5
423.0
528.8
669.8
Method 6
Mean
0.1
174.4
349.0
522.0
Method 8
Mean
156.9
410.1
653.5
Difference
+0.1
-1.7
-1.9
-3.5
-12.9
-6.8
-16.3
95-Percent Confidence
Interval About Mean
( -0.4, 0.6)
(150.9,162.9)
(170.6,178.2)
(341.4, 356.6)
(395.7,424.5)
(510.6,533.4)
(630.8, 676.2)
Percentage
Difference
-1.1
-1.1
-1.0
-3.0
-1.3
-2.4
titration procedure consistently yields 862 concentration determinations that are slightly (i.e., from 1.0 percent
to 3.0 percent) below the true value. However, for each unknown solution, the prepared "true" value lies
within the 95 percent confidence interval about the mean value. Therefore, the barium-thorin titration procedure
utilized in the analytical phases of Method 6 and Method 8 is accurate within its limits of precision. The con-
sistently slightly low average readings obtained with the procedure apparently result from a low-value bias by
some of the collaborative laboratories.
18
-------
APPENDIX A
METHOD 8-DETERMINATION OF SULFURIC ACID MIST AND SULFUR
DIOXIDE EMISSIONS FROM STATIONARY SOURCES
Federal Register, Vol. 36, No. 247
December 23, 1971
19
-------
METHOD 8 DETERMINATION OF STUJHTBIC ACID
MIST AND SULFUB DIOXIDE EMISSIONS FROM
STATIONARY SOURCES
1. Principle and applicability.
1.1 Principle. A gas sample Is extracted
from a sampling point in the stack and the
acid mist Including sulfur trloxide is sepa-
rated from sulfur dioxide. Both fractions are
measured separately by the barium-thorln
tltratlon method.
1.2 Applicability. This method is applica-
ble to determination of sulfurlc acid mist
(Including sulfur ttioxlde) and sulfur diox-
ide from stationary sources only when spe-
cified by the test procedures for determining
compliance with the New Source Perform-
ance Standards.
2. Apparatus.
2.1 Sampling. See Figure 8-1. Many of
the design specifications of this sampling
train are described In APTD-0581.
2.1.1 Nozzle—Stainless steel (316) with
sharp, tapered leading edge.
2.1.2 Probe—Fyrex1 glass with a heating
system to prevent visible condensation dur-
ing sampling.
2.1.3 Pitot tube—Type S, or equivalent,
attached to probe to monitor stack gas
velocity.
2.1.4 Filter holder—Pyrex»glass.
2.1.6 Implngers—Four as shown in Figure
8-1. The first and third are of the Greenburg-
Smith design with standard tip. The second
and fourth are of the Greenburg-Smith de-
sign, modified by replacing the standard tip
with a 1/2-inch ID glass tube extending to
one-half Inch from the bottom of the 1m-
plnger flask. Similar collection systems,
which have been approved by the Adminis-
trator, may be used.
2.1.6 Metering system—Vacuum gauge,
leak-free pump, thermometers capable of
measuring temperature to within 5' F, dry
gas meter with 2% accuracy, and related
equipment, or equivalent, as required to
maintain an Isoklnetlc sampling rate and
to determine sample volume.
2.1.7 Barometer—To measure atmospheric
pressure to ±0.1 inch Hg.
2.2 Sample recovery.
2.2.1 Wash bottles—Two.
2.2.2 Graduated cylinders—250 ml, 600
ml.
2.2.3 Glass sample storage containers.
2.2.4 Graduated cylinder—260 ml.
2.3 Analysis.
2.3.1 Pipette—26 ml., 100 ml.
2.3.2 Burette—50 ml.
2.3.3 Erlenmeyer flask—250 ml.
2.3.4 Graduated cylinder—100 ml.
2.3.5 Trip balance—300 g. capacity, to
measure to ±0.05 g.
2.3.6 Dropping bottle—to add indicator
solution.
3. Reagents.
3.1 Sampling.
3.1.1 Filters—Glass fiber, MSA type 1106
BH, or equivalent, of a suitable size to fit
in the filter holder.
3.1.2 Silica gel—Indicating type, 6-16
mesh, dried at 175* C. (350' F.) for 2 hours.
3.1.3 Water—Deionized, distilled.
3.1.4 Isopropanol, 80%—Mix 800 ml. of
isopropanol with 200 ml. of delonlzed, dis-
tilled water.
3.1.5 Hydrogen peroxide, 3%—Dilute 100
ml. of 30% hydrogen peroxide to 1 liter with
deionized, distilled water.
3.1.6 Crushed ice.
3.2 Sample recovery.
3.2.1 Water—Deionized, distilled.
3.2.2 Isopropanol, 80%.
3.3 Analysis.
3.3.1 Water—Deionized, distilled.
3.3.2 Isopropanol.
3.3.3 Thorin Indicator—l-(o-arsonophen-
ylazo)-2-naphthol-3, 6-disulfonlc acid, di-
sodium salt (or equivalent). Dissolve 0.20 g.
in 100 ml. distilled water.
3.3.4 Barium perchlorate (0.01N)—Dis-
solve 1.95 g. of barium perchlorate [Ba
(CO4)a 3 H2OJ In 200 ml. distilled water and
dilute to 1 liter with Isopropanol. Standardize
with sulfurlc acid.
3.3.5 Sulfuric acid standard (0.01AO —
Purchase or standardize to ± 0.0002 N against
0.01 N NaOH which has previously been
standardized against primary standard po-
tassium acid phthalate.
1 Trade name.
PROBE
-/• STACK
•rL—WALL
v U
FILTER HOLDER
THERMOMETER
.CHECK
VALVE
REVERSE-TYPE
PITOT TUBE
.VACUUM
LINE
VACUUM
GAUGE
MAIN VALVE
VUR-TIGHT
PUMP
Figure 8-1. Sulfurlc acid mtst sampling train.
4. Procedure.
4.1 Sampling.
4.1.1 After selecting the sampling site and
the minimum number of sampling points,
determine the stack pressure, temperature,
moisture, and range of velocity head.
4.1.2 Preparation of collection train.
Place 100 ml. of 80% Isopropanol in the first
impinger, 100 ml. of 3% hydrogen peroxide in
both the second and third Implngers, and
about 200 g. of silica gel in the fourth im-
pinger. Retain a portion of the reagents for
use aa blank solutions. Assemble the train
without the probe as shown in Figure 8-1
with the filter between the first and second
impingers. Leak check the sampling train
at the sampling site by plugging the inlet to
the first Impinger and pulling a 15-Inch Hg
vacuum. A leakage rate not In excess of 0.02
c-f-m. at a vacuum of 15 Inches Hg is ac-
ceptable. Attach the probe and turn on the
probe heating system. Adjust the probe
heater setting during sampling to prevent
any visible condensation. Place crushed ice
around the impingers. Add more ice during
the run to keep the temperature of the gases
leaving the last impinger at 70' F. or less.
4.1.3 Train operation. For each run, re-
cord the data required on the example shee',
shown in Figure 8—2. Take readings at each
sampling point at least every 5 minutes and
when significant changes in stack conditions
necessitate additional adjustments in flow
rate. To begin sampling, position the nozzle
at the first traverse point with the tip point-
ing directly into the gas stream. Start the
pump and immediately adjust the flow to
Isokinetic conditions. Maintain isokinetic
sampling throughout the sampling period.
Nomographs are available which aid in the
rapid adjustment of the sampling rate with-
out other computations. APTD-0576 details
the procedure for using these nomographs.
At the conclusion of each run, turn off the
pump and record the final readings. Remove
the probe from the stack and disconnect it
from the train. Drain the ice bath and purge
the remaining part of the train by drawing
clean ambient air through the system for 15
minutes.
4.2 Sample recovery.
4.2.1 Transfer the isopropanol from the
first impinger to a 250 ml. graduated cylinder.
Rinse the probe, first impinger, and all con-
necting glassware before the filter with 80%
Isopropanol. Add the rinse solution to the
cylinder. Dilute to 250 ml. with 80% Isopro-
panol. Add the filter to the solution, mix,
and transfer to a suitable storage container.
Transfer the solution from the second and
third Impingers to a 500 ml. graduated cyl-
inder. Rinse all glassware between the filter
and silica gel impinger with deionized, dis-
tilled water and add this rinse water to the
cylinder. Dilute to a volume of 500 ml. with
deionized, distilled water. Transfer the solu-
tion to a suitable storage container.
4 3 Analysis.
4.3.1 Shake the container holding Iso-
propanol and the filter. If the filter breaks
up, allow the fragments to settle for a few
minutes before removing a sample. Pipette
a 100 ml. aliquot of sample into a 250 ml.
Erlenmeyer flask and add 2 to 4 drops of
thorlu indicator. Titrate the sample with
barium perchlorate to a pink end point. Make
sure to record volumes. Repeat the titra-
tion with a second aliquot of sample. Shake
the container holding the contents of the
second and third impingers. Pipette a 25 ml.
aliquot of sample into a 250 ml. Erlenmeyer
flask. Add 100 ml. of isopropanol and 2 to 4
drops of thorin indicator. Titrate the sample
with barium perchlorate to a pink end point.
Repeat the tltration with a second aliquot of
sample. Titrate the blanks in the same
manner as the samples.
21
-------
5. Calibration.
5.1 Use standard methods and equipment
which have been approved by the Adminis-
trator to calibrate the orifice meter, pilot
tube, dry gas meter, and probe heater.
5.2 Standardize the barium perchlorate
with 25 ml. of standard sulfuric acid con-
taining 100 ml. of isopropanol.
6. Calculations.
6.1 Dry gas volume. Correct the sample
volume measured by the dry gas meter to
standard conditions (70° P., 29.92 inches Hg)
by using Equation 8-1.
PLANT
LOCATION
OPERATOR
DATE
BUN NO.
SAMPLE BOX NO^
METER BOX NO.
AMBIENT TEMPEMTURE_
BAROMETRIC PRESSURE _
ASSUMED MOISTURE. %_
HEATER BOX SETTING
PROBE LENGTH, m.
NOZZLE DIAMETER. hl<
PROBE HEATER SETTING..
SCHEMATIC OF STACK CROSS SECTION
TAAVERSE POINT
NUMBER
TOtAL
SAMPLING
TIME
l«l.m,n.
AVERAGE
STATIC
PRESSURE:
IPSI. In. Ha.
STACK
TEMPERATURE
(Tsi.'f
VELOCITY
HEAD
<«PS>-
PRESSURE
DIFFERENTIAL
ACROSS
ORIFICE
METER
( *HJ,
ta-MjO
GAS SAMPLE
VOLUME
IVml. I\S
GAS SAMPLE tWEUTURt
AT ORV GAS METER
INLET
""In.'-*'
Avg.
OUTLET
('•%„,>.•'
Avg.
Avg.
SAMPLE BOX
TEMPLRATURE.
«F
IMPINGER
TEMPERATURE.
•F
Figure >4. flat tut.
vm..J=vm{ •=?-
where:
Vm.,.,
"1
m.Hg
Volume of gas sample through the
dry gas meter (standard condi-
tions) , cu. ft.
Volume of gas sample through the
dry gas meter (meter condi-
tions) , cu. ft.
CHaso,= Concentration of sulfuric acid
at standard conditions, dry
basis, Ib./cu. ft.
1.08 X10-«= Conversion factor including the
number of grams per grain
equivalent of sulfuric acid
(49 g./g.-eq.), 453.8 g./lb., and
1,000 ml./l., Ib.-l./g.-ml.
Vt = Volume of barium perchlorate
T,ld= Absolute temperature at standard
conditions, 530° B.
Tm = Average dry gas meter temperature,
°E.
Pb.r= Barometric pressure at the orifice
meter, inches Hg.
= ( 1.08X10-'
g.-n
.t(1
titrant used for the sample,
ml.
Vtb= Volume of barium perchlorate
titrant used for the blank, ml.
N = Normality of barium perchlorate
tltrant, g.-eq./l.
V,ola = Total solution volume of sul-
furic acid (first implnger and
Cso =(7.05X10-5
where:
Csos= Concentration of sulfur dioxide
at standard conditions, dry
basis, Ib./cu. ft.
7.05X 10-""Conversion factor including the
number of grams per gram
equivalent of sulfur dioxide
(32 g./g.-eq.) 453.6 g./lb., and
1,000 ml./l., Ib.-l./g.-ml.
V," Volume of barium perchlorate
tltrant used for the sample,
ml.
Vtb-= Volume, of barium perchlorate
tltrant used for the Wank, ml.
N-= Normality of barium perchlorate
tltrant, g.-eq./l.
'otal solution volv
dioxide (second and third 1m-
Ib.-l.
g.-ml.
pingers), ml.
V,*" Volume of sample aliquot ti-
trated, ml.
Vm,ta=Volume of gas sample through
the dry gas meter (standard
conditions), cu. ft,, see Equa-
tion 8-1.
7. References.
Atmospheric Emissions from Sulfurlo Add
Manufacturing Processes, U.S. DHHW, PHB,
Division of Air Pollution, Public Health Serv-
ice Publication No. 898-AP-13, Cincinnati,
Ohio, 1965.
Corbett, D. P., The Determination of SO,
and SO3 in Flue Oases, Journal of the Insti-
tute of Fuel, 24:237-243, 1961.
equation 8-1
AH = Pressure drop across the orifice
meter, inches H,O.
13.6= Specific gravity of mercury.
P,tt*~ Absolute pressure at standard con-
ditions, 29.93 inches Hg.
6.3 ,Sulfurie acid concentration.
equation 8-2
filter), ml.
V. = Volume of sample aliquot ti-
trated, ml.
Vm,ta=Volume of gas sample through
the dry gas meter (standard
conditions), cu, ft., see Equa-
tion 8-1.
6.3 Sulfur dioxide concentration.
equation 8-3
Martin, Robert M., Construction Details of
Tsoklnetlc Source Sampling Equipment, En-
vironmental Protection Agency, Air Pollution
Control Office Publication No. APTD-O581.
Patton, W. P., and J. A. Brink, Jr., New
Equipment and Techniques for Sampling
Chemical Process Oases, J. Air Pollution Con-
trol Assoc. 13, 163 (1983).
Bom, Jerome J., Maintenance, Calibration,
and Operation of Isokinetic Source Sam-
pling Equipment, Environmental Protection
Agency, Air Pollution Control Office Publi-
cation No. APTD-O576.
Shell Development Co. Analytical Depart-
ment, Determination of Sulfur Dioxide and
Sulfur Trioxlde In Stack Oases, Emeryville
Method Series, 4616/59*.
22
-------
APPENDIX B
STATISTICAL METHODS
23
-------
APPENDIX B. STATISTICAL METHODS
This appendix is composed of various independent sections each of which contains a statistical analysis
pertinent to a particular question or problem encountered in the analysis of the Method 8 collaborative test
data. References to these sections have been made at various junctures in the body of the report.
B.1 Preliminary Data Analysis
The original Method 8 test data appears in Table B.I. This table lists the sulfur dioxide concentration
determinations, CgCh. afid the acid mist concentration determinations,CHSS0t> f°r tne 14 runs as reported
by the four collaborating laboratories. These quantities were recomputed from the raw data for several runs
from each laboratory to detect systematic and random calculation errors. All discovered calculation errors
that exceed acceptable round-off error were corrected. When a systematic calculation error was found, the
calculations were rechecked for all the laboratory's runs.
An outlier analysis was performed on the corrected data. Any determination which differed by more
than 40 percent from the closest corresponding value obtained by any of the other three collaborators for
that run was subjected to further scrutiny. Such potential outliers were to be rejected only if physical evidence
showed them to be invalid determinations.
Table B. 1. Originally Reported Collaborative Test Data
(Ib/scfX lO-'1)
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Lab 101
CSO2
469
319
393
319
382
412
423
436
484
466
306
468
492
480
CH2SO4
38.3
111.6
49.0
45.4
8.7
7.9
3.3
9.9
11.6
13.5
98.8
76.1
7.8
6.3
Lab 102
CS02
*
*
204f
161
108
198
226
225
240
174
235
239
232
227
CH2SO4
*
*
27 9f
5.0
5.3
5.5
6.7
8.6
8.3
8.6
6.3
5.7
10.2
6.6
Lab 103
CS02
226
455
367
298
341
377
166
402
444
327
432
441
459
438
CH2SO4
64.3
31.9
11.7
24.2
10.1
14.1
112.9
11.1
13.9
8.6
8.6
9.3
12.7
7.0
Lab 104
CSO2
506
578
233
284
400
t
491
438
564
242
514
552
379
582
CH2SO4
6.0
10.5
7.1
4.2
12.4
t
7.0
22.2
7.5
112.9
18.9
25.8
22.8
22.9
*Run not made.
|Run not completed due to equipment problems.
Through this process, several systematic calculation problems were discovered. Throughout the col-
laborative test Lab 101 experienced erratic and unreliable operation of its digital temperature indicator for
measuring the dry gas meter temperature. For this reason, Lab 101 usually estimated Tm , the average dry
gas meter temperature, as 10 deg above the ambient temperature, Ta(Tm = Ta + 10°). However, the Lab 101
meter temperature estimation was inconsistent, taking on values of Tm = Ta + 20° on run 1, Tm = Ta - 10°
on run 3 and Tm=Ta + 14° on run 7. Lab 103, which used identical equipment, also experienced difficulty
with its digital temperature indicator, but used an auxiliary thermocouple harness and portable thermocouple
to obtain Tm. These values usually differed by less than 3 degrees from Ta. Hence, to obtain consistency,
Tm = Ta was used to re-estimate the Lab 101 dry gas meter temperatures for each run. This slight change
in Tm produced correspondingly small changes in the determined concentrations.
25
-------
The outlier analysis revealed that the sulfur dioxide concentrations reported by Lab 102 were con-
sistently low by about a factor of 2, but no error could be found in the calculations. Through discussion
with Lab 102 personnel, it was learned that a factor of 2.5 was required to obtain the actual concentrations.
A special note to the collaborators specified the use of a 10-m£ aliquot in determining the S02 concentration
rather than the 25-mfi aliquot as in the Federal Register.(3) The analysts used the 10-m8 aliquot, but upon
performing the calculations, inserted 25 m£ into the equation. Hence, each reported concentration had to
be multiplied by 2.5 to obtain the actual concentration of S02 determined by Lab 102.
There are four missing values in each data set. Lab 102 was not present at the beginning of the test
period and missed the first run. During the second run, Lab 102's equipment was not fully assembled and
they were unable to participate in that run. On run 3, Lab 102 was forced to abort the run due to a
broken carriage after completing only one traverse, and thus their determination was not usable. On run 6,
broken glassware caused Lab 104 to abort the sampling run. The statistical analyses were based upon the
remaining 52 determinations, with no substitutions made for these missing values.
B.2 Negative Correlation in the Concurrent Concentration Determinations of Sulfur Dioxide
and Sulfuric Acid Mist
When a test method specifies making multiple chemical determinations using connected apparatus from
a single sampling run, an important consideration is whether the determinations are independent of each
other. For Method 8, the question is whether the sulfur dioxide concentration determination for a run is
correlated with the sulfuric acid mist concentration determination.
Intuitively, one would expect some positive correlation to exist between the true sulfuric acid mist
concentration and the true sulfur dioxide concentration in the stack. This intuitive expectation follows
from the consideration that plant process changes that would cause an increase (decrease) in stack sulfuric
acid mist concentration would be likely to produce an increase (decrease) in stack sulfur dioxide concentration.
In Figure B.I, the sulfur dioxide concentration determination for a run is plotted against the sulfuric
acid mist concentration determination for that same run for the 52 pairs of values. Figure B.I indicates
that, contrary to expectation, a significant negative correlation may exist, i.e., a high acid mist value is
accompanied by a low S02 value. The correlation coefficient for the 52 pairs is calculated, as are the cor-
relation coefficients for each laboratory's results separately, and these are shown in Table B.2.
Using the test statistic(2)
the significance level (d) of each correlation coefficient can be determined. The null hypothesis is that the
true correlation coefficient, p, is equal to zero. The test statistic follows Student's / distribution with n - 2
degrees of freedom. Using a significance level of 5 percent, the combined correlation coefficient and those
from Labs 101 and 103 are shown to be significant, while the Lab 102 and 104 data are not.
If all acid mist determinations above 60 Ib/scf X 10 7 are eliminated, a correlation coefficient can be
computed for the remaining 46 pairs. The value of r = —0.1355 is not significantly different from zero, and
60 Ib/scf X 10"7 is chosen as the cutoff point for a high value.
There are 6 high values for the complete data set, with 3 from Lab 101,2 from Lab 103, 1 from Lab 104
and none from Lab 102. This also suggests that the negative correlation is related to the high value phenomenon,
since the more high values present, the higher the degree of negative correlation for that lab.
26
-------
Table B.2. Correlation of Concurrent Method 8 Determinations ofHiSO* and SO2
Laboratory
All
101
102
103
104
All-With H2SO4
Determinations Above
60 X 10~7lb/scf Excluded
Runs,
n
52
14
11
14
13
46
Number of H2SO4
Determ. Above
60 X 10-7 Ib/scf
6
3
0
2
1
0
Correlation
Coefficient,
r
-0.5105
-0.6276
+0.4186
-0.7947
-0.3862
-0.1355
Test
Statistic,
-4.198
-2.793
1.383
-4.535
-1.388
-0.907
Significance
of Correlation,
a
< 0.0001
0.009
0.10
0.0005
0.10
0.19
• - Lab 101
O - Lab 102
A - Lab 103
X - Lab 104
30 40 50 60 70 80 90 100 110 120
Method 8 Sulfunc Acid Mist Concentration Determination, 10~7 Ib/scf
Figure B.I. Negative Correlation of Concurrent Method 8 Determinations
B.3. Blocking the Determinations
In order to obtain good estimates of the within-laboratory precision associated with Method 8 deter-
minations it is necessary to group the runs into blocks where the true mean concentration on each run is
essentially the same. Friedman's rank test(7) is used to test the hypothesis that all the run means are equal.
27
-------
The Friedman test is a two-way analysis of variance based upon the ranks of the observations. The factors
for this test are runs and laboratories, with laboratories serving as a blocking factor. The determinations for each
laboratory are ranked from lowest to highest, then a rank sum, Rf, for each run is computed. The test statistic
is
12 * 2
X? = - V RJ - 3nO + 1)
r n(k)(k + 1) L ' v '
i= 1
where
n — the number of labs
k — the number of runs.
The test statistic follows an approximate chi-square distribution with k — 1 degrees of freedom.
For this test, the high values (>60 Ib/scf X \(f} for acid mist and their associated S02 values are not
used. While it cannot be determined that these are invalid results, they clearly do not represent the true
stack concentration, which is under consideration here. These values are assigned the median rank of 7.5,
as are the missing values in the data set. This will affect the determined significance level, but in this case
it is felt that the result will be to make the test more conservative.
The ranks for the corrected S02 data from Table 1 are shown in Table B.3. The test statistic for the
S02 data is
/=!
= — [(34)2 +...+(46)2] -180
840
= 36.91
Comparing this to a chi-square distribution with 13 degrees of freedom, the significance level is less than 0.001.
Thus, there is significant variation in the run mean levels, and blocking of the runs must be done .
The blocks are established using the concurrent data that was taken during the test, and is discussed in
Section III. To demonstrate that this is an effective scheme, the Friedman test is applied to the blocks separately.
The summaries of these tests are shown in Table B.4. The significance levels associated with the three blocks
are 0.273, 0.1 16 and 0.068, respectively. None of these show significant differences in mean levels at the 5 per-
cent level.
Similarly, the acid mist determinations are tested for equality of run means. With the high values eliminated,
the rank sums are computed, as shown in Table B.5. The test statistic is X? = 6.78 with 13 degrees of freedom.
The significance level associated with this value is 0.913, and the hypothesis cannot be rejected. Thus, there is
no blocking required, and the determinations may be treated as 14 repetitions at the same true mean con-
centration.
B.4 Distributional Nature of SO2 Determinations
In order to obtain information about the distributional nature of the determinations, the corrected values
are tested for equality of variance using Bartlett's test. (2) in addition, the determinations are transformed using
28
-------
Table B.3. Friedman Rank Test,
All SOj Runs
Table B. 4. Friedman Rank Test, 5O2
Blocks
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Labs
101
10
7.5f
3
1
2
4
5
7.5
13
11
7.5f
7.5t
14
12
102
7.5*
7.5*
7.5*
2
1
4
7.5
5
14
3
12
13
11
10
103
7.5f
13
4
1
3
5
7.5f
6
12
2
9
11
14
10
104
9
13
1
2
4
7.5*
6
5
12
7.5f
10
11
3
14
n
Ri
34
41
15.5
6
10
20.5
26
23.5
51
23.5
38.5
42.5
42
46
H0: All run means are equal.
Test Statistic: x-f = 36.91.
Significance Level: a < 0.001.
Conclusion: Reject H0.
*Missing value.
fHigh value (above 60 Ib/scf X lO"7).
Table B.5. Friedman Rank Test, Acid Mist
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Labs
101
12
7.5f
14
13
5
4
1
7.5
10
11
7.5f
7.5f
3
2
102
7.5*
7.5*
7.5*
1
2
3
10
12.5
11
12.5
5
4
14
7.5
103
7.5f
14
9
13
5
12
7.5f
6
11
5
2.5
4
10
1
104
2
6
4
1
9
7.5*
3
11
5
7.5t
10
14
12
13
Ri
29
35
34.5
28
21
26.5
21.5
37
37
33.5
25
29.5
39
23.5
H0: All run means equal.
Test Statistic: Xy? = 6.78.
Significance Level: a = 0.913.
Conclusion: Accept H0.
*Missing value.
fHigh value not used.
Block
1
Run
4
5
10
Labs
101
1
2
3
102
2
1
3
103
1
3
2
104
1
3
2*
Ri
5
9
10
X? = 3.50 df=2 a = 0.273
2
1
2
3
6
7
5
3*
1
2
4
3t
3t
3t
1
5
3*
5
1
3
3*
4
5
1
3t
2
15
16
6
9
4
X? = 7.40 d/=4 d = 0.1 16
3
8
9
11
12
13
14
1
5
3.5*
3.5*
6
2
1
6
4
5
3
2
1
5
2
4
6
3
2
5
3
4
1
6
5
21
12.5
16.5
16
13
X?= 10.25 d/=5 a= 0.068
*High value, assigned median rank.
t Missing value assigned median rank.
two common variance-stabilizing transformations, the log-
arithmic and the square root, and retested. The test statistic
is compared to a chi-square distribution with the appropriate
degrees of freedom to determine significance levels. The
results are summarized in Table B.6 for both the run and the
collaborator-block data.
For both the run and the collaborator-block data the
best equality is achieved by the linear or original form of the
data. For the run data, the significance level indicates almost
perfect agreement among the variances, even though the means
varied considerably. For the collaborator-block data, the
significance level would not usually indicate acceptance, but
the linear is the best of the three forms. The means and
standard deviations for the run data are shown in Table B.7,
and for the collaborator-block data in Table B.8.
For a set of data divided into groups with possibly dif-
ferent means but common variance, a2, the method used to
estimate the common variance is referred to as pooling. Define
)>ij — they observation in group /
y~i — the mean of group i
sf - the i variance estimate
«,- — the size of the i group
29
-------
Table B.6. SO2 Data Transformation Summary
Data
Run
Collaborator-Block
Transformation
Linear
Logarithmic
Square Root
Linear
Logarithmic
Square Root
Test
Statistic
8.988
15.505
11.466
28.140
37.670
32.188
df
13
13
13
11
11
11
Significance
Level
0.774
0.277
0.572
0.003
<0.001
0.001
Table B. 7. Sulfur Dioxide Run Summary
Block
1
2
3
Run
4
5
10
1
2
3
6
7
8
9
11
12
13
14
Mean Concentration,
Ib/scf X 10~7
324.50
346.75
366.50
395.00
449.00
333.67
425.00
408.25
457.50
520.75
458.50
512.50
475.00
514.75
Standard Deviation,
Ib/scf X 10~7
53.66
55.99
101.36
148.74
132.10
88.82
61.26
173.02
71.30
72.77
122.61
74.32
82.37
71.09
Sample
Size
4
4
4
3
3
3
3
4
4
4
4
4
4
4
Table B.8. Sulfur Dioxide Collaborator-Block Summary
Block
1
2
3
Collaborator
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Mean Concentration,
Ib/scf X 10~7
383.00
370.00
322.00
308.67
396.80
529.00
318.20
452.00
436.50
582.00
436.00
504.83
Standard Deviation
Ib/scf X 10~7
74.32
87.31
21.93
81.84
50.78
49.50
118.55
150.86
69.13
15.13
18.94
80.08
Sample
Size
3
3
3
3
5
2
5
4
6
6
6
6
30
-------
and assume
a\ = a\ = . . . = a\ = a2
where
a2 - the true variance of the r group
k — the number of groups.
There are k separate estimates of a2 , and the problem is to combine these into a single estimate. By
definition, a single estimate of a2 is (y,y - jT;)2 , for any i and/. From group i, then, there are n\ of these
estimates and
E (yit-yif
/=!
would be the total sum of squares from group i for estimating a2, with (n, - 1) degrees of freedom. Com-
bining the sums of squares for all groups gives
/=!/=!
the "pooled" sums of squares. Since there are («/ — 1) degrees of freedom for each group, the "pooled"
degrees of freedom are
k
^/Pooled = ]C ("i"1)
/= 1
k
= Z>-*.
;=i
The pooled variance estimate, s2, is obtained by dividing the sums of squares by the degrees of freedom, or
k n,-
\
£
o2 J ~~
i= 1
But since
"•-I
31
-------
then
"i
(nf- !>?= £(
/=!
and
i= 1
Given the sample variances or standard deviations and the size of the sample, the best estimate of the common
variance, a1, is obtained by this formula.
B.5 Precision Estimates for SO2 Determinations
In Appendix B.4, it is shown that the S02 determinations can be assumed to have common variance
terms for both the run data and the collaborator-block data, regardless of the mean level. To estimate these,
then, the individual run and collaborator-block standard deviations are combined to give a single estimate.
The method of pooling variances is also discussed in Appendix B.4. The estimate is of the form
4--
u 11 c i e
s, the standard deviation of the / sample
u, si/e of the / sample
A the number of samples.
Tins method will be used to estimate both the within- and between-laboratory components.
There are 12 estimates of the within-laboratory standard deviation, a, from the collaborator-blocks.
These and the block sizes are shown in Table B.8. Substituting into the above formula gives
12
Z(n - nx2
i«I 1JX,
.2 _'= 1
12
32
-------
^ _ (3 - 1)(74.32)2 + .. . + (6 - 1)(80.08)2
52-12
_ 236,804.75
40
= 5920.12
This estimate has («,- — 1) degrees of freedom associated with it from each collaborator-block for a total of
40. This gives an estimated standard deviation for the within-laboratory component of
The overall mean of the 52 determinations is 6 = 429.77. Using this, a within-laboratory coefficient
of variation is estimated by
76.94
429.77
= 0.18.
The between-laboratory variance is estimated from the 14 run standard deviations in Table B.7. Sub-
stituting these and the run sizes into the pooled variance formula gives
14
£ -i4
1 = 1
_ 369,427.00
38
= 9721.76
with 3 degrees of freedom from the four laboratories. This gives an estimated between-laboratory standard
deviation of
33
-------
Using the overall mean of 429.77, this gives a coefficient of variation for between-laboratories of
6
98.60
429.77
= 0.23.
The laboratory bias variance, a£, is defined as
4 = a2-a'.
Substituting the estimates for between- and within-laboratory gives
ei = ^-&2
= 9721.76-5920.12
= 3801.64
and an estimated laboratory bias standard deviation of
OL =v/3801.64
= 61.66
The laboratory bias coefficient of variation is estimated as
= 0.14.
B.6 Distributional Nature of H2SO4/SO3 Determinations
As an indication of the distributional nature of the determinations, the corrected values from Table 3
are tested for their equality of variance in their original form and under two transformations, the logarithmic
and the square root. Bartlett's test for homogeneity of variance(2) is used to determine the degree of equality
obtained. The test statistic follows a chi-square distribution and the results, along with degrees of freedom
and significance levels are shown in Table B.9.
For the run data, the logarithmic transformation provides the only acceptable form of the data. For the
collaborator-block data none of the three transformations is acceptable, but the smallest value of the test
statistic is obtained by the logarithmic transformation. If a logarithmic transformation is accepted, the indi-
cation is that there is a proportional relationship between the true mean and true standard deviation.
To test this further, the sample means and sample standard deviations are compared. These
statistics are shown for the run data in Table B.10, and the tendency for the standard deviations and
means to increase together is apparent. The paired means and standard deviations are plotted in Figure B.2.
34
-------
Table B. 9. Acid Mist Data Transformation Summary
Table B.IO. Acid Mist Run Summary
(Ib/scfX. lO^)
Data
Run
Collaborator-Block
Transformation
Linear
Logarithmic
Square Root
Linear
Logarithmic
Square Root
Test
Statistic
48.378
16.246
28.702
46.643
18.783
30.845
df
13
13
13
3
3
3
Significance
Level
0.000
0.236
0.007
0.000
0.000
0.000
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mean
Concentration
35.8
50.6
22.9
19.5
9.1
32.4
35.8
12.9
10.3
35.8
32.7
28.9
13.3
10.7
Standard
Deviation
29.2
52.1
23.5
19.1
4.5
53.7
51.4
6.3
2.9
51.4
43.3
31.8
6.6
8.2
Run —50-
Standard '
deviation,
Ib/scf X 10~7 " -
^P
fiun I
:ar<, (Wsff fy tOfj
rfi
Figure B.2. Between-Laboratory Run Plot, Sulfuric Acid Mist Data
Similarly, the collaborator-block means and standard deviations are compared. These values are shown in
Table B.I 1, and plotted in Figure B.3. Once again there is a clear tendency of the standard deviations to rise
as the mean concentration rises.
From the above, models are proposed for the between- and within-laboratory standard deviations of
ah = ft,5
35
-------
Table B.I I. Acid Mist Collaborator-Block Summary
and
Block
1
Collaborator
Lab 101
Lab 102
Lab 103
Lab 104
Mean
Concentration
34.33
6.98
24.31
21.55
Standard
Deviation
36.15
1.69
29.62
28.49
a = 05
where j3j and /3 are the true coefficients of variation for
between- and within -laboratory, taken to be constant. Then
to estimate a^ and a, the coefficients of variation are
estimated and 5j, and & are defined as
d = |35
where (3^, and |3 are the estimated coefficients of variation. The standard deviations, then, are expressed as
percentages of an unknown mean, 5 .
B.7 Unbiased Estimation of Standard Deviation Components
In Appendix B.6, the theoretical and empirical arguments from the collaborator-block data indicate
that a suitable model for the within-lab standard deviations of the acid mist data is
&=/36
To estimate this standard deviation, we use the relationship
Figure B.3. Within-Laboratory Collaborator-Block Plot, Sulfuric Acid Mist
36
-------
where
sy — the collaborator-block standard deviation
Xj — the collaborator block mean
C — a constant
As previously discussed, s.- is a biased estimator for the true standard deviation, a. The correction factor for
removing the bias is dependent on the sample size n, and is given by Ziegler
2
where P represents the standard gamma function. Thus, we can say that
E(ans/) = a
or
a = anE(sj)
so that in obtaining an unbiased estimate of /3, we can obtain an unbiased estimate of a as well. Thus, we
define an estimator for a, a, where
From Appendices B.I and B.2, we determined that a suitable model for the acid mist run data is
ob=Pb&
where a^ = \/a/, + o2 is the between-lab standard deviation. Empirically, we have
Sj = CbXi
where
Sj - the run standard deviation
Xi — the run mean
Q, - a constant
and Sj is a biased estimator for aj . Thus, for p collaborators,
E(apSi) = a
37
-------
and we have
a = E(apSi)
= apCbE(Xj)
Obtaining an estimate of fo , we have a new estimator, 6j, , of ab given by
and substituting our estimates of aj and a, we have
so that the laboratory bias standard deviation may be estimated as a percentage of the mean as well.
B.8 Weighted Coefficient of Variation Estimates
The technique used for obtaining estimates of the coefficients of variation of interest is to use a linear combi-
nation of the individual beta values obtained. The linear combination used will be of the form
r "A
Ki= 1
where jfy is the/th coefficient of variation estimate, k is the total number of estimates, and vvy is a weight applied to
the /th estimate.
As previsouly discussed, the individual estimate of j3 is obtained as
for a sample of size n. This estimator is shown in B.7 to be unbiased for the true coefficient of variation. However,
since we are dealing with small samples to obtain our individual estimates, weighting is more desirable in that it pro-
vides for more contribution from those values derived from larger samples. There is more variability in the beta
values obtained from the smaller samples, as can be seen by inspecting the variance of the estimator. We have that
38
-------
Varfl!) = Var (~
x
£
2«
for normally distributed samples, (1) and true coefficient of variation, j3. Rewriting this expression, we have
Vaitf) = -5
-U + 202)
and all terms are constant except for c?n and n. Thus, the magnitude of the variance changes with respect to the
factor e$/n. Now, since an decreases as n increases, the factor o£/« must decrease as n increases, and the variance
is reduced.
The weights, wy, are determined according to the technique used in weighted least squares analysis' ', which
gives a minimum variance estimate of the parameter. The individual weight, w,-, is computed as the inverse of the
variance of the estimate, $/, and then standardized. Weights are said to be standardized when
To standardize, the weights are divided by the average of the inverse variances for all the estimates. Thus, we can
write
where
Uj =
1 Var(ft)
and
w=-y
Now, from the above expressions we can determine M,-, u and w/ for the beta estimates. For any estimate, ft,
1
«; =
Var(ft-)
M; =
39
-------
for sample size «/, and
Thus, the /th weight, w,-, is
1 * 1
1 k
The estimated coefficient of variation is
W; = —
4
k n-
^
ATI,-
fr n/_
40
-------
/ = 1 "j
a2
i = 1 a«i
/=i"«yj '=1
B.9 Precision of H2S04/SO3 Determination
In Appendix B.6 the models for the standard deviations for between- and within-laboratory are deter-
mined as
and
a = 06
where fa and |3 are the between-laboratory and within-laboratory coefficients of variation, respectively.
The coefficients of variation are taken to be constant, and the standard deviations estimated by obtaining
estimates of the coefficients of variation. The manner of estimating coefficients of variation is given in
Appendix B.7 and B.8.
The estimates are obtained by taking a linear combination of the individual beta estimates,
"--V "
0-^I>.-&
where
ft, — the z estimate of the coefficient of variation
w, — the weight assigned to the z estimate
k — the number of estimates.
There are 14 estimates of the between-laboratory coefficient of variation obtained from the run data.
These are shown in Table B.12, along with their weights. The estimated between-laboratory coefficient of
variation, then, is
14
= — (13.411)
14
= 0.958
41
-------
Table B.I2. Acid Mist Run Beta
Estimates and Weights
Table B.13. Acid Mist Collaborator-Block
Beta Estimates and Weights
Run
1
2
3
4
5
6
1
8
9
10
11
12
13
14
Beta Hat
0.9203
1.1609
1.1577
1.0641
0.3567
0.5501
1.7949
0.5287
0.3110
1.5566
1.4350
1.1945
0.5384
0.8293
Weight
0.760
0.760
0.760
1.096
1.096
0.760
1.096
.096
.096
.096
.096
.096
.096
.096
Block
1
Collaborator
Lab 101
Lab 102
Lab 103
Lab 104
Beta Hat
1.0735
0.2484
1.2419
1.3496
Weight
1.080
0.839
1.080
1.000
This gives an estimated standard deviation for the between-lab-
oratory component of
= (0.958)6.
There are 4 - 1 = 3 degrees of freedom for this estimate.
The collaborator-block data provide 4 estimates of (3, the true within-laboratory coefficient of variation.
This gives
.
!= 1
The beta estimates and weights are shown in Table B. 13. Substituting into the above formula gives
. 1
(3 = - (4.060)
4
= 1.015.
There are (ny — 1) degrees of freedom from each collaborator-block associated with this estimate. Summing
over the four blocks gives a total of 40 degrees of freedom.
The laboratory bias coefficient of variation cannot be estimated from these data since the between-
laboratory coefficient of variation is less than the within-laboratory, and hence (3$ — /32 is less than zero.
B.10 Analysis of Data Excluding High Mist Values
To determine the best means of analyzing the data with the high mist and corresponding sulfur dioxide
values excluded, the data transformations are once again applied. The results of Bartlett's test on the three
forms of the data are shown below for each variable.
(1) S02
The test statistics and significance levels for the three forms of the data are shown in Table B.14.
For both the run and collaborator-block data the linear transformation once again provides the best agreement.
The estimates are obtained by pooling the sums of squares and degrees of freedom as shown in Appendix B.4.
The run standard deviations and sample sizes are shown in Table B.I 5. Substituting these into the pooled variance
formula gives :
42
-------
Table B.14. SO-t Data Transformation Summary, High Mist Values Excluded
14
Data
Run
Collaborator-Block
Transformation
Linear
Logarithmic
Square Root
Linear
Logarithmic
Square Root
Test
Statistic
1.624
2.763
1.655
31.146
37.744
34.028
df
13
13
13
11
11
11
Significance
Level
1.000
0.999
1.000
0.001
<0.001
<0.001
Table B.I5. Sulfur Dioxide Run Summary, High Mist Values Excluded
E «<--14
; = 1
_ 163,577.25
32
= 5111.79.
The estimated standard deviation, then,
is
Block
1
2
3
Run
4
5
10
1
2
3
6
7
8
9
11
12
13
14
Mean Concentration
Ib/scf X 10~7
324.50
346.75
408.00
479.50
516.50
333.67
425.00
489.00
457.50
520.75
511.00
530.00
475.00
514.75
Standard Deviation
Ib/scfX 10~7
53.66
55.99
71.25
37.48
86.97
88.82
61.26
76.02
71.30
72.77
77.54
80.29
82.37
71.09
Sample
Size
4
4
3
2
2
3
3
3
4
4
3
3
4
4
ab =v/5111.79
= 71.50
with 3 degrees of freedom from the four
labs. Using 5 = 448.67, the sample mean
of the 46 determinations, a coefficient
of variation for between-lab oratories is
estimated as
_ 71.50
448.67
= 0.16
The within-laboratory pooled variance estimate is taken from the 12 collaborator-blocks estimates
shown in Table B.16. This gives
12
E (««• - os/2
i= 1
12
147,948.37
34
= 4351.42
The within-laboratory standard deviation, then, is estimated by
a=v/4351.42
= 65.97.
43
-------
Table B.16. Sulfur Dioxide Collaborator-Block Summary, High Mist Values Excluded
Block
1
2
3
Collaborator
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Mean Concentration,
Ib/scfX 10~7
383.00
370.00
322.00
342.00
417.50
529.00
399.67
452.00
464.50
582.00
436.00
504.83
Standard Deviation
Ib/scf X 10~7
74.32
87.31
21.93
82.02
24.12
49.50
48.18
150.86
24.83
15.13
18.94
80.08
Sample
Size
3
3
3
2
4
2
3
4
4
6
6
6
There are 34 degrees of freedom associated with this estimate. The estimated coefficient of variation is
. a
'•I
_ 65.97
448.67
= 0.15
The laboratory bias variance is estimated from the between- and within-laboratory components as
% = <%-?
= 5111.79-4351.42
= 760.37.
This gives an estimated laboratory bias standard deviation of
aL =^760.37
and a coefficient of variation estimate of
= 27.57,
27.57
448.67
= 0.06.
(2) H2SO4/S03
The data transformation results for the acid mist data excluding the 6 values above 60 Ib/scf X Iff1
are given in Table B.I7. The results correspond to those of the complete data set, with the logarithmic transformation
44
-------
Table B.I 7. Acid Mist Collaborator-Block Summary, High Values Excluded
Data
Run
Collaborator-Block
Transformation
Linear
Logarithmic
Square Root
Linear
Logarithmic
Square Root
Test
Statistic
27.850
12.139
18.192
35.417
15.338
23.219
df
13
13
13
3
3
3
Significance
Level
0.009
0.516
0.150
0.000
0.002
0.000
of the run and collaborator-block beta hats, weighted according
obtain the estimates.
the only acceptable one for the run
data and the best for the collaborator-
block data. Thus, a coefficient of
variation approach is again used to
obtain precision estimates for the acid
mist data.
The estimated values for
j3j and (3 are obtained by the technique
of Appendices B.7 and B.8. The esti-
mates obtained are linear combinations
to the number of observations used to
From the run data, the estimated between-laboratory coefficient of variation is
• --T w"
*~i4,rT"'
The beta estimates and their respective weights are given in Table B.I8. Substituting into the above formula
gives
06=0.661,
Table B.18. Acid Mist Run Summary, High
Values Excluded
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mean
Concentration
21.5
21.2
22.9
19.5
9.1
9.1
5.6
12.9
10.3
10.2
11.3
13.6
13.3
10.7
Standard
Deviation
21.9
15.1
23.5
19.1
3.0
4.5
2.1
6.3
2.9
2.7
6.7
10.7
6.6
8.2
Beta
Hat
1.2778
0.8946
1.1577
1.0641
0.3567
0.5501
0.4232
0.5287
0.3110
0.3012
0.6720
0.8893
0.5384
0.8293
Weight
0.481
0.481
0.890
1.283
1.283
0.890
0.890
1.283
1.283
0.890
0.890
0.890
1.283
1.283
and an estimated standard deviation of
°b
= (0.661)6.
There are 3 degrees of freedom associated with this
estimate.
The four collaborator-block beta estimates
and their weights shown in Table B.I 9 give an estimated
within-laboratory coefficient of variation of
1 = 1
= 0.585.
The within-laboratory standard deviation is estimated by
a-(36
= (0.585)5
with 42 degrees of freedom.
45
-------
Table B.I9. Acid Mist Collaborator-Block Summary, High Values Excluded
(Ib/scfX 10-"1)
Block
1
Collaborator
Lab 101
Lab 102
Lab 103
Lab 104
Mean
Concentration
18.12
6.98
13.60
13.94
Standard
Deviation
16.97
1.69
7.28
7.98
Beta
Hat
0.9602
0.2484
0.5474
0.5857
Weight
0.954
0.954
1.046
1.046
The laboratory bias com-
ponent is estimated from the above. The
estimated laboratory bias coefficient of
variation is
= V(0.661)2 -(0.585)2
= 0.308.
The laboratory bias standard deviation, then, is estimated as
= (0.308)6.
B.11 The Unknown Sulfate Solution Test Data
An unknown sulfate solution test was conducted as part of the Method 8 collaborative study to isolate
the precision and the accuracy of the analytical phase of Method 8. 10-m)2 samples of three sulfate solutions,
labeled Solution A, Solution B, and Solution C, in which the prepared sulfate concentrations were unknown
to the collaborative laboratory teams, were analyzed in triplicate on each of three days by each team in con-
junction with its collaborative test samples. Figure 4 in the main report shows the instruction and reporting
form.
The corrected sulfate solution concentration data are presented in Table B.20. Lab 101 introduced a
0.7 1 percent error into its sulfur dioxide concentration calculation on four of its aliquots by incorrectly
copying its barium perchlorate titrant normality determination. The error has been corrected in the Table B.20
data. Table B.21 is a summary of the Table B.20 data averaged over replicates and days to show the col-
laborator (laboratory bias) effect. Whereas Labs 101, 102, and 103 obtained reasonably accurate sulfur
dioxide determinations using Method 8, Table B.21 shows that Lab 104's determinations fell 6 to 9 percent
below the true values. Table B.20 affirms the consistency of this Lab 104 negative bias.
B. 12 Analysis of Variance in the Unknown Sulfate Solution Test
A separate analysis of variance was performed on the Table B.20 data reported for each unknown
solution. The factors in each analysis of variance consist of a collaborator factor, C, a day factor,
D(C), nested within C, and a replicate factor, R(CD), nested within days within collaborators. Based
on a random effects model, the analysis of variance, the variance components, and their significance
levels are tabulated as Table B.22 for each of the three unknown solutions. The collaborator factor C
is a very significant effect (d < 0.001) at every solution concentration. The size of the collaborator
effect results, as Appendix B.ll discussed, from the consistently 6 to 9 percent low Lab 104 deter-
minations. The day factor D(C) is only significant at the high Solution B concentration.
The precision of the Method 8 analytical phase can be estimated from the Table B.22 analysis of
variance. The collaborator factor C corresponds to the laboratory bias precision component of the main
report. Since the Method 8 runs comprising a collaborator block were generally analyzed on different
days in the laboratory, the day factor D is a within-laboratory effect. So the day and replication
factors together correspond to the within-laboratory precision component of the main report. Thus,
the Method 8 analytical phase variance components at each unknown solution concentration are esti-
mated as s\ = de for laboratory bias, s2 = d + OR for within-laboratory, and s£ = o£ + tip + (fa
46
-------
Table B.20. Corrected Sulfate Solution Concentrations,
IQ-"1 Ib SOjscf
Unknown
Solution
A
B
C
Day
1
2
3
1
2
3
1
2
3
Replicate
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
Collaborator
Lab 101
423
423
419
422
422
425
424
424
424
672
672
670
673
673
673
669*
665
673*
158
163
166
156
159
158
173*
158
158
Lab 102
415
412
414
415
414
415
414
412
415
656
658
656
658
656
658
658
658
656
159
160
160
160
160
159
160
160
159
Lab 103
419
417
417
417
416
416
416
417
416
664
662
663
668
669
668
663
663
663
159
159
159
159
158
158
158
158
157
Lab 104
385
387
387
387
387
386
387
386
387
621
620
622
622
622
621
620
621
621
149
149
149
149
149
149
148
148
149
*Reported concentration adjusted upward by 0.71 percent to correct for
normality calculation error.
Table B.21. Average Laboratory Sulfate Solution Concentrations,
10* IbSOjscf
Unknown
Solution
A
B
C
Prepared SO2
Concentration
423.0
669.8
158.6
Collaborator
Lab 101
422.9
671.1
161.0
Lab 102
414.0
657.1
159.7
Lab 103
416.8
664.8
158.3
Lab 104
386.6
621.1
148.8
47
-------
Table B.22. Analysis of Variance ofSulfate Solution Data by Concentration
Factor
Sum of
Squares
D.F.
Mean
Square
Expected Mean Square
Variance
Component
F-Ratio
Significance,
d
Solution C, Mean = 156.9 X 10~7 Ib/scf
C
D(C)
R(CD)
832.33
54.22
191.33
3
8
24
277.44
6.78
7.97
94 + 34 + 4
ij f)
1°D + "R
°&
a£ = 29.94
°D= °
4= 7.97
34.81
0.85
<0.001
>0.50
Solution A, Mean = 410.1 X 10~7 Ib/scf
C
D(C)
R(CD)
6999.22
14.00
34.67
3
8
24
2333.07
1.75
1.44
o 2 3(J2 2
2 2
"R
aD= 0.10
4= 1.44
1333.18
1.22
«0.001
Solution B, Mean = 653.5 X lO"7 Ib/scf
C
D(C)
R(CD)
13494.75
83.56
48.67
3
8
24
4498.25
10.44
2.03
*) o o
9ac + 3oD + OR
3<7Z) + "R
°R
4 = 498.65
o% = 2.80
a^ = 2.03
430.87
5.14
«0.001
0.001
Table B.23. Analytical Phase Precision Estimation
Unknown
Solution
C
A
B
Mean, 10~7 Ib/scf
True,
M
1586
423.0
669.8
Method 8,
3?
156.9
410.1
653.5
Within-Laboratory
Variance,
7.97
1.54
4.83
a2 = 4.78
Std. Dev.,
2.82
1.24
2.20
Laboratory Bias
Std. Dev.,
5.47
16.09
22.33
a = 2.19 X 10~7 Ib/scf
Coef. ofVar.,
PL
0.0345
0.0380
0.0333
(JL = 0.0353
Between-Laboratory
Std. Dev.,
sb = "J't + °D + °R
6.16
16.14
22.44
Coef. of Var.,
0.0388
0.0382
00335
pb = 0.0368
for between-laboratory. The analytical phase precision estimates for each solution are developed and presented
in Table B.23. Note that the within-laboratory standard deviation estimates are relatively constant, whereas
the between-laboratory standard deviation estimates are proportional to the mean. On this basis, the Method 8
analytical phase within-laboratory precision was estimated in terms of the constant standard deviation a = 2.19
obtained by pooling the solution within-laboratory variance estimates. In contrast, the average between-lab-
oratory coefficient of variation for the three solutions, oj = 0.0368, was utilized as the Method 8 analytical
phase between-laboratory estimate, using the technique of Appendices B.7 and B.8.
There were no instructions given to the collaborators regarding how to integrate the standard solution
analyses with the stack sample analyses. In the case of Lab 101, one analyst prepared the samples for titration,
and a second analyst performed the titration. The samples were assigned designations which did not indicate
whether they were standard solutions or stack samples. As a result, the analyst performing the titration was
unaware of which samples were the standard solutions and the estimated replication error from these data is
truly an error term.
For the remaining labs, the analyst both prepared the samples and performed the titrations. Because
of this, there was no way to prevent the analyst from knowing which were stack samples and which were
standards. Also, the three replicates of the standard were probably run consecutively. Due to the difficulty
inherent in determining the end point of the barium-thorin titration, the possibility exists that the volume of
titrant required on the first sample influenced the volume used on the two subsequent repetitions.
48
-------
To test this, an intraclass correlation coefficient (5) is calculated to determine if the errors, determined
concentration minus true concentration, are related to one another. The class for this test is a single lab's
repetitions of a given standard solution on the same day. Three coefficients are calculated, one for each
solution, and these are shown in Table B.24. As can be seen, for each solution there is a strong correlation
among the errors.
For comparison, a coefficient is calculated for Lab 101 alone, using the data from all three solutions,
and this is also shown in Table B.24. This value is not significant, which indicates that the concentrations
are indeed independent replicates.
The estimated a^ for each solution is calculated for each solution using the Lab 101 data alone, and
these estimates are shown in Table B.25. It is apparent that these values are higher than those obtained
from the full data set, and that the estimated variances in Table B.23 may have a low bias in them. If the
Lab 101 estimates are in fact better estimates of the true replication error, the effect on the within-and
between-laboratory standard deviation estimates would be relatively minor. The within-laboratory standard
deviation would be larger by approximately 1 Ib/scf X 10~7. The between-laboratory term is dominated by
the laboratory bias term, which is unchanged, and the coefficient of variation would go from the present
3.68% to slightly over 4%.
Table B.24. Intraclass Correlation Coefficients
Table B.25. Analytical Phase Repli-
cation Error, Lab 101
Source
Solution A
Solution B
Solution C
Lab 101, All solutions
r
0.993
0.995
0.732
0.022
Solution
A
B
C
~°R
2.78
5.78
31.22
49
-------
LIST OF REFERENCES
1. Cramer, H., Mathematical Methods of Statistics, 3rd Edition, The Macmillan Company, New York,
1970.
2. Dixon, W. J. and Massey, F. J., Jr., Introduction to Statistical Analysis, 3rd Edition, McGraw-Hill,
New York, 1969.
3. Environmental Protection Agency, "Standards of Performance for New Stationary Sources," Federal
Register, Vol. 36, No. 247, December 23, 1971, pp 24876-24893.
4. Hamil, H. F. and Camann, D. E., "Collaborative Study of Method for the Determination of Sulfur
Dioxide Emissions from Stationary Sources (Fossil Fuel-Fired Steam Generators)," Southwest
Research Institute report for Environmental Protection Agency, December 10, 1973.
5. Kendall, M.G. and Stuart, A., The Advanced Theory of Statistics, Vol. 2,2nd Edition, Griffin,
London,1967.
6. Searle, S.R., Linear Models, Wiley, New York, 1971.
7. Siegel, S., Nonparametric Statistics for the Behavioral Sciences, McGraw-Hill, New York, 1956.
8. Ziegler, R.K., "Estimators of Coefficients of Variation Using k Samples," Technometrics, Vol. 15,
No. 2, May 1973, pp 409414.
50
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO. 2.
EPA-650/4-75-003
4. TITLE AND SUBTITLE
Collaborative Study of Method for the Determination of Sulfuric Acid
Mist and Sulfur Dioxide Emissions From Stationary Sources
7. AUTHOR(S)
Henry F. Hamil Richard E. Thomas
David E. Camann
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Southwest Research Institute
8500 Culebra Road
San Antonio, Texas 78228
12. SPONSORING AGENCY NAME AND ADDRESS
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 2771 1
3. RECIPIENT'S ACCESSIOI«NO.
5. REPORT DATE
November, 1974 (date of approval)
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO
10. PROGRAM ELEMENT NO.
1HA327
11. CONTRACT/GRANT NO. |
68-02-0626
13. TYPE OF REPORT AND PERIOD COVERED jj
Task Order \
14. SPONSORING AGENCY CODE t
s
s
15. SUPPLEMENTARY NOTES
Statistical analyses are performed on data obtained in collaborative testing of EPA Method 8 (Determination of Sulfuric
Acid Mist and Sulfur Dioxide Emissions From Stationary Sources) and from ancillary tests performed in conjunction with
the analysis of the field samples. A collaborative test was conducted using four laboratory teams at a sulfuric acid plant.
A total of 14 sampling runs were made, and a total of 52 determinations. Using these data, estimates are made of the
precision that can be expected from a single team, and between two independent teams.
There was a tendency in these data for occasional high reported concentrations of sulfuric acid mist. On these samples,
there was noticed a concurrent tendency for low reported sulfur dioxide concentrations. Since it cannot be determined that
this phenomenon is unrelated to the method, these values are included in the data set to obtain the precision estimates. In
addition, a second analysis is done with the six highest H2S04/SO3 values removed, and the improvement in the precision
is noted.
Statistical analysis of the results of using the analytical part of the method on standard sulfate solutions provides estimates
of the variability associated with this phase alone. These results are compared to the results from an earlier study on EPA
Method 6 (Sulfur Dioxide) which uses the same barium-thorin titration procedure. Combined estimates for this analytical
procedure are presented.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
Air Pollution, 1302
Flue Gases
13. DISTRIBUTION STATEMENT
Release Unlimited
b.lDENTIFIERS/OPEN ENDED TERMS
Collaborative Testing
Methods Standardization
Sulfuric Acid Mist
19. SECURITY CLASS (This Report)
Unclassified
20. SECURITY CLASS (This page)
Unclassified
c. COSATI Field/Group
13-B
07-B
21 NO. OF PAGES
50 + prelims
22. PBICE
EPA Form 2220-1 (9-73)
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EPA Form 2220-1 (9-73) (Revert*)
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