EPA-650/4-74-028
MAY 1974
Environmental Monitoring Series
-fX-S-XwSSifCvI
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EPA-650/4-74-028
COLLABORATIVE STUDY OF METHOD
FOR THE DETERMINATION OF NITROGEN OXIDE
EMISSIONS FROM STATIONARY SOURCES
(NITRIC ACID PLANTS)
Prepared by
H.F. Hamil 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. Rodney 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
May 1974
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This report has been reviewed by the Environmental Protection Agency
and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
11
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SUMMARY AND CONCLUSIONS
This report presents the results obtained from a collaborative test of Method 7 promulgated
by the Environmental Protection Agency for determining the nitrogen oxide emissions trom
stationary sources. Method 7 specifies the collection of a grab sample in an evacuated flask con-
taining a dilute sulfuric acid-hydrogen peroxide absorbing solution and the colorimetric measure-
ment of the nitrogen oxides, except nitrous oxide, using the phenoldisulfonic acid procedure.
The test was conducted at u nitric acid plant using four collaborating laboratories. A total
of 22 samples were taken over a three-day period In addition, standard gas samples were taken,
and nitrate solutions whose true concentrations were unknown to the collaborators were prepared
for concurrent analysis. The concentrations determined by the collaborators from all three
phases of the test were submitted to statistical analysis to obtain estimates of the accuracy and
precision that can be expected with the use of Method 7.
The statistical analysis provides the basis for the following conclusions*
Accuracy -Samples of standard gas mixtures at three concentrations, 107, 344, and 784 ppm,
were taken and analyzed according to Method 7 Using the values determined by the collaborators,
we can say that the method is accurate at the 95 percent level of confidence
Precision-The precision of Method 7 is given in terms ol within-laboratory and between-
laboratory components and a laboratory bias component The precision estimates are derived
from the stack concentration determinations, with some adjustment Due to plant upset, there
was considerable variation in the actual NOX concentrations in the stack during the first day's
sampling. The fluctuation was reflected in the NOX concentrations values obtained by the col-
laborators and necessitated a correction in the data for the fluctuating mean However, the net
effect likely left the precision estimates obtained higher than the actual piecision values I Im-
precision components are shown to be proportional to the mean of the Method 7 determinations.
given by 6, and can be summarized as follows
(a) Within-laboratory The estimated within-laboratory standard deviation is 14 NX ',/ ol
6, and has 67 degrees of freedom associated with it
(b) Between-laboratoiy The estimated between-laboratory standard deviation is 18 471'/
of 6, with 3 degrees of freedom.
(c) Laboratory bias. From the above, we can estimate u laboratory bias standard deviation
of 10.49% of 5.
Analytical Procedure—The unknown nitrate solution data provides a basis for measuring the
accuracy and precision of the analytical procedure taken by itself. At three levels of concen-
tration, the procedure is shown to be accurate at the 95 percent level of confidence The witlnn-
laboratory standard deviation is not a function of the concentration, ju. and is estimated as
1.199 Mg/mC. The laboratory bias standard deviation is a linear function of the true concentration
and is estimated by 0 725 + (0.092)^. From an analysis of variance, the only consistently
significant factor affecting the precision of the concentrations obtained is the day-to-day vari-
ations within a given laboratory. This implies a need for recalibration of the spcctropliotoinctcr
on a daily basis to negate the effect on the values of drift.
Recommendations are made for the improvement of the precision of Method 7. and con-
siderations given for the use of the method in field testing.
111
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TABLE OF CONTENTS
LIST OF ILLUSTRATIONS jr
LIST OF TABLES v
I. INTRODUCTION I
II. COLLABORATIVE TESTING 2
A. Collaborative Test Site 2
B. Collaborators and Test Personnel • ... ... 6
C. Philosophy of Collaborative Testing . .... ... 6
III. STATISTICAL DESIGN AND ANALYSIS . . 7
A. Statistical Terminology 7
B. The Collaborative Test Plan . ...... 8
C. The Collaborative Test Data . . ^
D. The Accuracy of Method 7 . ... II
E. The Precision of Method 7 . . ... . . . 12
F. The Accuracy and Precision of the Analytical Procedure . . . 14
IV. COMPARISONS WITH PREVIOUS STUDY 16
V. RECOMMENDATIONS . . . .... 17
APPENDIX A-Method 7. Determination of Nitrogen Oxide Emissions From Stationary
Sources - • - 'tj
APPENDIX B-Statistical Methods .... .23
B.1 Preliminary Analysis of the Original Collaborative Test Data . 25
B.2 Significance of the Port Effect. . ... 26
B.3 Transformations . . . . 27
B.4 Empirical Relationship Between the Mean and Standard Deviation in the
Collaborative Test Data .... . 27
B.5 Underlying Relationship Between the Mean and the Standard Deviation 29
B.6 Estimating the Standard Deviation Components
B.7 The Nitrate Solution Data .... .... .... 33
B.8 Variance Components From the Nitrate Solution Data . ... 33
REFERENCES .... . . 37
IV
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LIST OF ILLUSTRATIONS
Figure Page
I Tail Gas Vent Line and Sample Manifold 3
2 Test Setup at Mobay Chemical Company Test Site 4
3 Collaborators Sampling at the Mobay Chemical Company Test Site 4
4 Schematic of Gas Standard Sample Preparation Train 5
5 Collaborative Test ot" Method 7, Instructions for Analysis of Unknown Nitrate
Solutions 10
B.I Intcrlaboratory Run Plot 29
B.2 Intralaboratory Collaborator Block Plot 30
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LIST OF TABLES
Table Page
1 Corrected Nitrogen Oxides Collaborative Test Data, NOX as NOS (Dry Basis)... 11
2 Nitrogen Oxide Emissions From NBS Samples 12
3 Confidence Intervals for Gas Sample Means 12
4 Accuracy of the Analytical Procedure 14
B.I Original Collaborative Test Data, NOX as NO2 25
B.2 Corrected Values for Block 1, Adjusted for Common Mean 26
B.3 Test for Port Effect 27
B.4 Data Transformation to Achieve Run Equality of Variance 27
B.5 Interlaboratory Run Summary 28
B.6 Intralaboratory Collaborator Block Summary 29
B.7 Reported Nitrate Solution Concentrations 34
B.8 Laboratory Day Averages for Nitrate Solution Data 34
B.9 Average Laboratory Nitrate Solution Concentration 34
B.10 Nitrate Solution Data Analysis of Variance 35
B ' F-Ratios and Probabilities 35
B.I 2 Variance Components of Nitrate Solution Data 36
VI
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I. INTRODUCTION
This report describes the work performed and results obtained on Southwest Research Institute
Project 01-3462-004, Contract No. 68-02-0626, which includes collaborative testing of Method 7
for nitrogen oxide emissions as given in "Standards of Performance for New Stationary Sources."(2)
This report describes the collaborative testing of Method 7 in a nitric acid plant, the statistical
analysis of the data from the collaborative tests, and the conclusions and recommendations based
on the analysis of data.
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II. COLLABORATIVE TESTING
A. Collaborative Test Site
'I IK- collaborative test of Method 7 in u nitric acid plant was conducted at Mobay Chemical
Company. liaytown. Texas. The nitric acid unit at Mobay Chemical Company utilizes a proprietary
process in which ammonia is catalytrcally oxidized. Due to the proprietary nature of the process,
no information concerning production rates, operational parameters, or unit design could he made
available lo Southwest Research Institute by Mobay Chemical Company for publication Lmission
data from the unit on-stream analyzer indicated normal NOX concentration in the vent gas duct
(Figure I) leading to the stack to be in the range of 200-250 ppm. We were assured by plant per-
sonnel that this NOX concentration placed them below the maximum pcrmissable emission levels
speciliecl by the New Source Performance Standards for nitric acid plants/2*
In Figure J is shown the configuration of the tail gas vent leading into the vertical stack and
the configuration of the sampling manifold. The sample manifold consisted of a ten-foot lenglli ol
2-inch ID stainless steel tubing, fitted with four sample outlet valves (Whitey® toggle valves) spaced
at two-toot centers. The sample valves were installed in the sample manifold m such a manner as
to have the sample inlet at the centroid of the sample manifold The sample manifold was fitted
with a stainless steel gauze diffuscr 2 inches from the 1/2-inch tubing sample inlet line, in order to
provide a mixing '/one to prevent channeling of the incoming sample. The sample manifold was
connected through a valve to the tail gas vent by means of a 1/2-inch stainless steel line The sample
manifold connection was at a point approximately three feet downstream from the sample tukeofl
for the on-stream analyzer
The tail gas vent on the unit was maintained at 3-4 psig which provided sufficient pressure head
to provide a high sample How rate through the sample manifold. The sample manifold was continually
purged with a moderate sample flow during the course of a day's sampling Approximately two min-
utes before a sample was taken, the sample flow rate was increased to a high flow rate to assme that
the gas in the sample manifold was representative of the gas in the tail gas vent. The exhaust gas
from the sample manifold was exhausted to atmosphere through a hydrogen peroxide bubbler to
scrub out nitrogen oxides. Figure 2 shows the test setup at Mobay, while Figure 3 shows the col-
laborators taking a sample.
The original collaborative test plan called for each collaborator to collect six samples (rotating
among sample points) on each of four days. However, on the first day of sampling, a minor explo-
sion, caused by rupture of a high pressure gas line, occurred in another unit in the plant Since the
nitric acid produced at Mobay is used internally as an intermediate in other processes, it was nec-
essary for plant personnel to reduce the nitric acid production. Only limited storage space in one
nitric acid tank was available to accept continued production. Arrangements were made with Mobay
to reduce the production rate m order that two more days of sampling could be conducted. As a
result, six samples were taken on the first day, and eight samples were taken on the second and
third days, respectively. On the fourth day, gas standard samples were taken by the collaborators at
the SwRI Houston laboratory. The gas standard samples were prepared at the time of sampling by
personnel from the National Bureau of Standards. The gas standard preparation tram is shown
schematically in Figure 4. The method used for producing the nitric oxide in air standards con-
sisted of metering a controlled, known small amount of a 0.98 mole percent NO in N2 mixture into
an air stream flowing at a known and much higher flow rate. The mixture passed through two
mixing chambers and into a sampling manifold from which the collaborators took their samples
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Top View
Stack
/
H202 Bubbler
Vent to Atmosphere
Pressure Regulator Valve
(3 to 4 psi)
Tail Gas Vent
\
v
A
$ ^^SRf
To On-Stream
NOX Analyzer
SS Gauze
Diffuser
"Sampling Point
FIGURE I. TAIl GAS VIAT I IM \\DSAMPLEMANIFOLD.
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FIGURE 2. TEST SETUP AT MOBAY CHEMICAL
COMPANY TEST SITE.
FIGURE 3. COLLABORATORS SAMPLING AT THE MOBAY
CHEMICAL COMPANY TEST SITE.
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1%NOinN2
Regulator with SS diaphragm
0-30 psi gauge
Ruby orifice
Flow controller
Trap (drierite and charcoal1
Rotameter
Mixing chamber No. 1
Mixing chamber No. 2
Samplmq manifold
12/5
Air Supply
FIGURE 4. SCHEMATIC 01 CAS STANDARD SAMPI I PREPARATION 1R\I\
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Tin cc concentration levels of nitrogen oxide standards were generated, and the collaborators took
three samples ol~ each standard
B. Collaborators and Test Personnel
The collaborators lor the Mobay nitric acid plant test were Or. Robert James and Mr. Thomas
Jay McMiLkle. Texas Air Control Board, State of Texas, Messrs. Quinno Wong and Randy Creighton.
Depaitment of Public Health. City of Houston, Houston Texas, Mr Mike Taylor, Southwest Research
Institute. Houston Laboratory. Houston. Texas and Mr. Ron Hawkins of Southwest Research Insti-
tute. San Antonio Laboratory, San Antonio. Texas.*
The standard gas samples were prepared and the concentrations verified under the supervision
of Mr. William D. Dorko, Chemist, Air Pollution Analysis Section, Analytical Chemistry Division.
The National Bureau of Standards, Washington, D.C.
The collaborative test was conducted under the supervision of Mr. Nolhe Swynnerton of South-
west Research Institute. Mr Swynnerton had the overall responsibility for assuring that the col-
laborators were competent to perform the test, that the test was conducted in accordance with the
collaborative test plan, and that all collaborators adhered to Method 7 as written in the Federal
C. Philosophy of Collaborative Testing
The concept of collaborative testing followed in the tests discussed in this report involves con-
ducting 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 II random experimental errors were observed, such as mismeasurement of
volume of absorbing solution, improper rinsing of flasks, etc , no interference was made by the test
supervisor Since such random errors will occur in the every day use of this method in the field, unduly
restrictive supervision of the collaborative test would bias the method with respect to the field test
results which will be obtained when the method is put into general usage However, if gross deviations
were observed, of such magnitude as to make it clear that the collaborator was not following the
method as written, these would be pointed out to the collaborator and corrected by the test super-
visor
While most of the instructions in the Federal Register are quite explicit, some areas are subject
to interpretation. Where this was the case, the individual collaborators were allowed to exercise
their professional judgement as to the interpretation of the instructions.
The overall basis for this so-called "real-world" concept of collaborative testing is to evaluate
the subject method in such a manner as to reflect the reliability and precision of the method that
would be expected in performance testing in the field.
"Throughout the remainder or this report, the collaborative laboratories are referenced by assigned code numbers as Lab 101. Lab 102
Lab 103. and Lab 104 These code numbers do not necessarily correspond to the above ordered listing of collaborators
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I. 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 leport. The procedures for obtaining estimates of the pertinent values
are developed and justified in the subsequent sections.
We say that \\nestimator, 6, is unbiased Jur a parameter 6 if the expected value of 0 is 0, or m
notational (orm,E(8) = 6. Let .v, ,x2 , . . .,xn be a sample of/i replicate method determinations.
Then we define
1 "
(1) A = — 2 A-, as tnc sample mean, an unbiased estimate of the true mean, 5,oJ the determination^
This term gives an estimate of the center of the distribution of the A-,'S.
1 "
(2) i2 = 5^ (v, - \ )2 as the sample variance, an unbiased estimate of the true raiiani c.
o- . This term gives a measure of the dispersion m a distribution.
(3) s =\ as the sample standard deviation, an alternative measure of dispersion, whn.li estimates
a. the true standard deviation
The sample standard deviation, s, however, is not unbiased for a,(I * so a correction liu toi needs
to be applied. The correction factor for a sample of size 11 is an , and the product of a,, and s is imhiaseil
for a That is, £'(a,,s) = a As n increases, the value of a,, decreases, going for example Irom c^ = I I 2X4.
«4 = 1 0854 toa,0 = 1.0281
We do tine
as the true tocf Intent oj variation for the distribution of the method determinations To estimate
tins parameter, we use -A sample coefficient oj vanation. 0, defined by
where |3 is the ratio of the unbiased estimates of a and 5, respectively. The coefficient of variation
measures the percentage scatter in the observations about the mean and thus is a readily under-
standable way to express the precision of the observations.
The modified experimental plan for this test called for 22 runs On each run, the collaborative
teams were expected to collect simultaneous samples from the stack in accordance with Method 7
Suite the actual NOX emission concentration m the stack fluctuates, one can in general ex pet. I ditferent
tiue concentrations for each run. To permit a complete statistical analysis, the individual inns aie
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gi on pod into />/<>< A.s. when.' each block has approximately the same true emission coiKenli.il ion
level
We can apply the statistical terms of the preceding paragraphs both to the collaborators' values
during a given inn and to each collaborator's values in a given block. In this report, statistical
results* Irom the hrst situation are referred to as run results Those from the second situation are
relerred to as lolluhorutoi block result* For example, a run mean is the average of each collaboiator's
loncentiutiuii level for the run as obtained by Method 7 A collaborator block coefficient of variation
is the ratio ol the unbiased standard deviation estimate to the sample mean for all of a collaborator's
runs grouped in the block.
The variability associated with a Method 7 concentration determination is estimated in terms of
the wi thin-laboratory and the between-laboratory precision components In addition, a laboratory
hias lomponent can be estimated. The following definitions of these terms arc given with respect to
a tun- utatk concentration,^-
• Wnhin-lahoratitiv The within-laboratory standard deviation, a, measuies the di\pcnutn;//
replicate single determinations made using Method 7 by one laboratory team (same held
operators, laboratory analyst, and equipment) sampling the same true concentration, p.
The value of a is estimated from within each collaborator block combination
• Between-laboratory-The between-laboratory standard deviation, a/,, measures the lolal
variability in a concentration determination due to simultaneous Method 7 determinations
by different laboratories sampling the same true stack concentration, JLI The between lab-
oratory variance, o\, may be expressed as
ol=al+ a2
and consists of a within-laboratory variance plus a laboratory bias variant e. o£ The between-
laboratory standard deviation is estimated using the run results.
Laboratory bia\— The laboratory bias standard deviation, o/, =\/o£ ~ °2 • 1S tnat portion ot
the total variability that can be ascribed to differences in the field operators, analysts and
instrumentation, and due to different manners of performance of procedural details left
unspecified in the method. This term measures that part of the total variability m a deter-
mination which results from the use of the method by different laboratories, as well as
from modifications in usage by a single laboratory over a period of time. The laboratory
bias standard deviation is estimated from the within-and between-laboratory estimates
previously obtained.
B. The Collaborative Test Plan
The collaborative test plan called for samples to be drawn on four successive days by four col-
laborative teams sampling simultaneously. The samples were to be taken through the four sample
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ports (Jescnbcil in Section II, and these were arbitrarily assigned the labels A, B, C, and I) Due to
the plant problems discussed earlier, however, the sampling period was shortened to three days.
While the ports are located so as to be as nearly equivalent as possible, the stack flow char-
acteristics can lead to a difference in concentrations dependent upon the port from which the
sample was taken. To offset this possibility, the teams rotated and sampled through different ports
on each run.
The starting port for each collaborator was chosen by a randomization method, and sub-
sequently each crew rotated in a systematic manner to an adjacent port While it would be more
desirable to re-randomize after each run, the difficulties involved in the movement of equipment and
in having four crews operating on a small platform at the same time made this impracticable
The Mobay plant had a split beam analyzer which monitored the NOX levels during operation.
These values were used as a basis for establishing blocks for the analysis of the data The values
are presented in Table Bl.
During the second day and the third day of sampling, the level reported by the on-stream
analyzei remained essentially constant. Each of these days, then, was used as a block of si/e X The
data from the first day's run were not homogeneous with respect to concentration level, but these
values were taken to be a block since other conditions were comparable throughout. The data were
then adjusted for a common mean level with regard to the on-stream analyzer, and these adjusted
values were used to obtain collaborator block variability estimates The result, then, was 22 runs
divided among three blocks where each day of samples constituted a block. The blocks were ol
size 6, 8, and 8, respectively
In addition to the 22 samples taken from the stack, samples were taken from standard gas
mixtures at the Southwest Research Institute Laboratory Three samples were obtained by eaeli
collaborator at each of three levels of NC\ concentration, under conditions which closely mirrored
those Lindei which the stack samples were drawn These standards were prepared and verified by per-
sonnel from the National Bureau of Standards, and were used to obtain a measure of the accuracy
of Method 7 at varying concentration levels.
To estimate the amount of variation in a test result due to the analytical procedure, three
standard solutions were prepared. The collaborators were instructed to analyze these in three
replicates on each of three days during which the test samples were being analyzed. A copy of the
instruction and reporting form is shown in Figure 5. These results should contain no variation
except that due to the laboratory work necessary to determine the concentration level.
C. The Collaborative Test Data
The collaborative test data upon which the analysis was based are shown in Table 1. These valuer
represent the concentrations reported by the collaborators as verified by preliminary calculation
checks and, in some cases, recalculated to correct errors in the reported values. In Appendix B I. the
originally reported data are shown and the rationale behind the recalculation explained
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A series of nitrate 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. Use a 10 ml aliquot and follow the procedure in
Section 5.2 (and 4.3) of Method 7 and report results as micrograms of
per ml of unknown solution.
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
Concentration, jig NO^ per ml
Solution A
Solution B
Solution C
*
FIGURE 5 COLLABORATIVE TEST OF METHOD 7, INSTRUCTIONS FOR
ANALYSIS OF UNKNOWN NITRATE SOLUTIONS
10
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TAULL 1 CORRI-.CThD NITROGLN OXIDLS COLLABORATIVE
1KST DATA,NON AS NO2 (DRY BASIS), Ibs/scf X 107
The values lor lab 102 in block 3
were treated as missing values, due to
fullure ol the analyst to neutrali/e the
samples prior to cvaponzution to dry-
ness, with resultant loss ot the nitrogen
containing species as HNO3. The values
of lab 102 in run 8 and lab 104 in run
7 were omitted from the analysis as
erroneous values due to the magnitude
of the difference between these values
and the other collaborators for those
runs, following an outlier test as shown
in Appendix B.I.
In these cases, no attempt is made
to substitute for these values in the
analysis. Rather than this, it is better
to work only with those values which
are the direct result of a Method 7 test.
Substituted values generally tend to
minimize the effect of the substitution
on the error terms, but by so doing may
inordinately decrease the estimate
Thus it is preferable to operate with
the missing results when the si/e ol
the test permits.
In Appendix B 2 the hypothesis
of no poit effect is tested I his test
is performed according to YoudenV5 '
rank test at the 5'/ level of significance
Differences among the sample values
due to the port from which the sample
was taken are not found to be significant. As a result, no allowance for a port factor is included
in the subsequent analyses.
D. The Accuracy of Method 7
In order to ascertain the accuracy of Method 7, samples were drawn from mixtures prepared
by personnel from the National Bureau of Standards. Three NOX concentration levels were used,
low, medium, and high, and these levels were generated by mixing a known amount of 0.98 mole
percent NO in N2 mixture into a controlled air flow. The samples were drawn into an evacuated
flask, and these were then analyzed according to Method 7.
The values obtained by the collaborators are presented in Table 2, with values for Lib 102 m
repetition 3 for the medium concentration and Lib 103 in repetition 3 for the high coiuentr.ilion not
reported due to analyst error. The actual concentration levels for the samples weie venlied by NBS
after the test, and these are also shown.
Hlock
1
2
3
Kun
1
•>
\
4
S
6
7
S
9
in
11
12
13
14
IS
16
17
18
19
20
21
22
Lib 101
IXil.i
335
448
254
12l>
251
203
105
112
112
108
107
107
93
112
119
US
120
144
127
133
120
163
Port
A
1)
r
1)
\
H
C
D
A
B
C
D
A
B
D
C
B
A
D
C
B
A
Uh 102
O.it.1
337
344
3ll(<
105
166
63
102
333*
104
103
62
89
98
102
2t
3t
3t
3t
3t
2f
2f
3t
Port
U
C
1)
A
It
C
D
A
B
C
D
A
B
C
A
D
C
B
A
D
C
B
L..H 103
D.iU
257
310
394
217
188
187
97
89
86
91
98
94
101
96
89
100
94
94
101
121
98
98
Port
C
1)
A
It
C
D
A
B
C
D
A
B
C
D
B
A
D
C
B
A
D
C
Lab 104
Data
203
410
391
279
255
230
45*
98
93
111
107
108
96
103
85
76
84
97
95
87
87
113
Port
D
A
»
C
D
A
B
C
D
A
B
C
D
A
C
B
A
U
C
B
A
D
*Vjlues eliiuin.iled Iriim I lie and lysis as outliers
f V.i lues regarded .is nnssint> due to unjlyst error
Mole I'A polity is 10 express .ill niLMsurcinunts in A^emy doiumenls in
menu nulls When iinplcnienlinu this pr.ii.liie. will result in undue cost or
dittiuilly in il.mty NIIU/KII' is providing conversion .ittors lor the
p.irluul.ir iioii-incirii units used in the document I'or this report, the factor
IS
10-' lb/scf= 1 6018 X lO'/ug/m3
11
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TABLE 2. NITROGEN OXIDE EMISSIONS
FROM NBS SAMPLES
(Parts Per Million)
1 CVl'l
107
344
784
Kepi-mum
1
•>
3
1
2
3
1
2
3
L.ihs
101
112
120
124
341
341
341
637
661
597
102
131
115
139
344
350
-
802
817
764
101
109
90
99
325
408
343
823
768
-
104
118
115
104
365
385
347
769
785
737
TABLE 3. CONFIDENCE INTERVALS FOR
GAS SAMPLE MEANS
Coiiccnlrjlion,
ppm
107
344
784
Mcjn
115
354
742
St Dcv
n
24
76
Si h.rror
4
7
21
'
2 201
2 228
2 228
<•!„,
KIM 21
U8-370
695-789
Confidence intervals around the sample mean for each concentration across the collaborators
are used to determine the accuracy of the NOX concentrations obtained. Values of the pertinent
statistics are given in Table 3. The method may be said to be accurate at each level ij the ui tual
concentration lies within the 95% confidence interval around the sample mean
For each of the concentrations, the true value does he in the confidence interval, tailing in the
low range for the 107 ppm and 344 ppm values, and in the high range for the 784 ppm value I mm
tins, then, we c.m conclude that in all three ranges, low, medium, and high, the method does pm\ide
.in accmatc estimate ol the true concenliation level. However, there is considciable scallei ainoiis.1 ilu-
obseivahons at the lughei concentrations, as reflected hy their standard deviations
E. The Precision of Method 7
Of prime importance in the evaluation of Method 7 is the estimation of the precision that is
associated with the determination of NOX concentrations. This precision is estimated in terms ol
between-laboratory and within-laboratory standard deviations, as previously defined
In analysing the data, the first consideration is to determine, if possible, the distributional nature
of the reported concentrations To accomplish this, the concentrations are transformed using two
common variance-stabilizing transformations, the logarithmic and the square root, and the degree ol
equality of variance obtained is determined In addition, the untransformed data are also tested, and
the three forms are compared in Appendix B 3. For the run data, the logarithmic transformation
produces the best results and is accepted as the most likely model for the data. This acceptance
implies that there is a proportional relationship between the true mean and standard deviation (3)
To further this argument, the sample mean and standard deviation arc examined by means of a
regression through the origin to see if the theoretical relationship proposed seems valid on an empn-
ical basis. The details are provided in Appendix B.4, and the least squares fit and the individual
points are shown in Figure B.I
The paired sample means and standard deviations exhibit an apparent linear trend, and an
investigation of the correlation terms confirms this. The coefficient of correlation for these values
is 0 936 which is a significant value at the 5 percent level of significance. The coefficient of deter-
mination for the no intercept model is 0 876, indicating that 87 6 percent of the change in magnitude
of the standard deviation is due to a change in the magnitude of the mean
12
-------
A similar analysis is used on the collaborator block mean and standard deviation, again using a
regression through the origin. The line which provides the least squares fit through the origin is shown
in Figure B.2. The value of the coefficient of correlation is 0.907 which also is significant at the 5 per-
cent level This gives a coefficient of determination tor the collaborator block data of 0 823.
Thus, on both a theoretical and an empirical basis, we can say that the mean and standard deviation
lor the run data are proportional to one another. In terms of the between-laboratory standard deviation
o/, , for the true determination mean, 6,
where fa is the true between-laboratory coefficient of variation. For the collaborator block data, on
an empirical basis, we can also say that there is a proportionality between the mean and standard
deviation. In terms of the within-laboratory component, a, and the true mean determination, 6,
where $ is the true within-laboratory coefficient of variation.
Thus, we can obtain estimates of o and a/, by estimating the proportionality factors, or coefficients
of variation, and expressing the estimates as percentages of the true mean determination In Appendix B 5
the technique for obtaining best estimates of the coefficients of variation is discussed, and it is demon-
strated that the resulting estimates are unbiased for the standard deviations of interest. We refer to
these estimates as a and a/, , and express them as
a=06
and
ob
where 0 and fa are the estimated coefficients of variation, and 5 represents the true mean ot the
determinations.
In Appendix B.6, the estimates of 0 and fa are obtained. The within-laboratory coefficient of
variation is|3 = (0.1488), which gives an estimated within-laboratory standard deviation of
a = (0.1 488)5
with 67 degrees of freedom.
Similarly, we obtain from the run data, fa = (0.1847), which gives an estimated between-laboratoi>
standard deviation of
with 3 degrees of freedom
= V/(0.1847)262 - (0.1488)262
OL = V(0.1847)2 - (0 1488)2
= (0 1094)6.
13
-------
F. The Accuracy and Precision of the Analytical Procedure
As previously discussed, the collaborators were given three standard nitrate solutions tor analysis
in conjunction with the collaborative test samples. The actual concentration was unknown lo the
collaborators, and this gave a basis for determining accuracy and precision for the lab procedine alone
The true concentration for solutions A, B, and C were 38.2, 7 2, and 22.3 Mg/mfi, respectively.
The test for accuracy was as for the gas samples in section 111, D, by constructing confidence inter-
vals around the sample mean values. The mean is the average of the nine individual determinations
for all four collaborators taken together and thus has an estimated variance of oi /4 + o2 /36. Using
the values in Appendix B.8 for each solution of MSi and o2r, we obtain the confidence intervals
shown in Table 4.
TABLE 4. ACCURACY OF THE
ANALYTICAL PROCEDURE
Solution
A
B
C
True
Concentration
MgNO,/mS
38.2
7 2
223
Sample
Mean
MgNO,/mfi
37.94
600
2221
Confidence
Interval
33.26<«i<4262
425
-------
The principal cause of differences among labs is shown in Appendix B 8 to be the day-to-day
variations in lab procedures. This is likely a result of drift in the spectrophotometer ubsorhaiuv icallings
It was noted that the collaborators tended to use a single absorbance curve for all the coiKciili.ilions
from the stack samples, the gas samples, and the standard solutions. With these results, aiul those in
the earlier study by Hanul and Camann,(3) it appears that daily recahbration is necessary to iciluce this
lab bias component
The investigation of the precision estimates obtained from the nitrate solution data revealed no
significant tendency of the within-laboratory components to rise as the concentration rises. This negates
the coefficient of variation approach. However, for each solution studied, the lab bias of the analytical
procedure is the primary contributor to the total variation. This suggests that if improvements in the
method are to be made, the analytical procedures are the most likely areas for revising or making additional
stipulations to the procedure.
15
-------
IV. COMPARISONS WITH PREVIOUS STUDY
The following comparisons can be made to the results obtained by Hamil and Camann in the
previous study on Method 7.*3)
The distributional characteristics of the data were essentially the same. In both cases, the log-
arithmic transformation proved to be marginally acceptable, while the linear and square root trans-
forms did not perform as well. In both cases, a linear dependency was established between mean
and standard deviation for the collaborative test data.
The accuracy tests conducted with the previous test proved to be inconclusive due to problems
resulting from the absence of oxygen in the gas standards but indicated that a reasonable amount of
accuracy could be expected. In following the recommendation that further accuracy tests be con-
ducted, the results of this study show that at all levels studied the method provides accurate estimates
of the true concentration levels, using a 5 percent level of significance.
Both the within-laboratory and between-laboratory standard deviation estimates were greater in
this report than in the previous one, but this was in large measure attributable to the contribution of
the first six runs. Because of this, and the fact that more observations were used to obtain the esti-
mates in the previous study, the true values are probably closer to those obtained by Hamil and Camann.
For the analysis of the unknown nitrate solutions, the only consistently significant factor was the
day within collaborator effect. This corresponds to the analysis done on data from lour solutions in the
power plant study. The variance components for these data could not be justified as suitable for a
coefficient of variation approach, and the withm-lab component, a2 , was independent of the concen-
tration level
16
-------
V. RECOMMENDATIONS
The following assessments ol und recommendations on Method 7 have been made as a lesull ot
the preceding results and comparisons.
(I) The calculation errors involved in a Method 7 determination and the varying luuuhei ol
significant digits carried are a major problem urea in evaluating the performance ot the
method To prevent these from unfairly influencing a performance test for compliance, a
standard computer program should be written for EPA to evaluate the test results based on
the raw data only This lecommendation has been previously made to EPA.
(2) In utilizing a calibration curve to translate absorbance into mass for determination of a
Method 7 result, the techniques vary from lab to lab By establishing a standardized
technique where a least squares line through the origin is generated, then the slope used to
calculate the mass, the results will be more self-consistent and reliable The use ol lines
drawn freehand and the inaccuracies involved in reading values from a graph lead to varia-
tions in the reported values that need not be there At least three significant digits should
be maintained when calculating the slope of the line.
(3) The day-to-day variations in lab procedure contributed significantly to the variation in the
analytical portion of the test A requirement should be made that the spcctropholoinclci
be recalibrated daily and a new calibration line drawn. This should somewhat negate the
effect of the drift on the determinations.
(4) Due to the many handling steps and chance for mishap, it is strongly recommended that an
aliquotmg section be inserted into the procedure. Aliquoting of samples is a basic proceduie
in analytical chcmisliy and would help in the determination of precision in the results It
would also guard against the loss of sample and data if mishap occurs m analysis, as
occurred in the analyses of these samples.
Enactment of these recommendations could greatly enhance the precision of Method 7 and
facilitate the use of the method in obtaining NOX concentrations.
17
-------
APPENDIX A
METHOD 7. DETERMINATION OF NITROGEN OXIDE
EMISSIONS FROM STATIONARY SOURCES
Federal Register, Vol. 36, No. 247
December 23,1971
19
-------
RULES AND REGULATIONS
METHOD 7—DETERMINATION OF NITROGEN OXIDE
EMISSIONS FROM STATIONARY SOtlRCKS
1. Principle and applicability.
I.I Principle A grab sample I> collected
In an evacuated flask containing a dilute
sulfurlc acid-hydrogen peroxide absorbing
•olutlon. and the nitrogen oxides, except
nitrous cxlilc, are measure colorlmetrlcally
using tbe phenoldlsulfonlc acid (PD6)
procedure.
1.3 Applicability. This method la applica-
ble (or the measurement of nitrogen oxide*
from stationary sources only when specified
bv the test procedures for determining com-
pliance wllh New Source Performance
Standards.
2. Apparatus
2.1 Sampling. See Figure 7-1.
2.1.1 Probe—Pyrex' glass, heated, with
filter to remove paniculate matter. Heating
IB unnecessary II the probe remains dry dur-
ing the purging period.
2.12 Collection flask—Two-liter, Pyrex,1
round bottom with short neck and 24/40
standard taper opening, protected against
Implosion or breakage.
1 Trade name.
3.1.3 Flask valve— T-bore stopcock con-
nected to a 34/40 standard taper Joint.
3.1.4 Temperature gauge—Dial-type ther-
mometer, or equivalent, capable of measur-
ing 2- F. Intervale from 25' to 126* F.
2.16 Vacuum line—Tubing capable of
withstanding a vacuum of 3 Inchea Hg abso-
lute pressure, with "T" connection and T-bore
stopcock, or equivalent.
2.1.0 Pressure gauge—U-tube manometer,
36 Inches, with 0.1-Inch divisions, or
equivalent.
2.1.7 Pump—Capable of producing a vac-
uum of 3 Inches Hg absolute pressure.
2.1.8 Squeeze bulb—One way.
2.2 Sample recovery.
2.2.1 Pipette or dropper.
2.2.2 Glass storage containers—Cushioned
for shipping.
2.2.3 Glass wash bottle.
2.3 Analysis.
2.S.1 Steam bath.
3.3.2 Beakers or casseroles—260 ml., one
for each sample and standard (blank).
2.3.3 Volumetric pipettes—1, 2, and 10 ml.
3.3 4 Transfer pipette—10 ml. with 0.1 ml.
divisions.
souurc tun
PHOBi
HASH VALVt'
T
FLASH
HASICSHIEICU.
GKOUND GLASS CONE,
STANDARD TAKft,
J SLEEVE NO. 24/40
OMMOOLASS
fOCKT. JNO. 124
Figure 7-1. Sampling Ir.iin, flask valve, and
FOAM ENCASEMENT
•Oil INC FLASH •
?IIIEH. HOUND-BOTTOM SHOUT
KITH } SUEVE NO. 24/40
2.3.S Volumetric flask—100 ml., one for
each sample, and 1.000 ml. for the standard
(blank).
2.3.0 Spectrophotometer—To measure ab-
sorbance at 420 nm.
2.3.7 Graduated cylinder—100 ml. with
1.0ml. divisions.
3J.fi Analytical balance—To measure to
0.1 mg.
3. Reagents.
3.1 Sampling.
3.1.1 Absorbing solution—Add 2.8 ml. of
concentrated H^3O, to 1 liter of distilled
water. Mix well and add 6 ml. of S percent
hydrogen peroxide. Prepare a fresh solution
weekly and do not expose to extreme heat or
direct sunlight.
3.2 Sample recovery.
3.2.1 Sodium hydroxide (IN)—Dissolve
40 g. NaOH In distilled water and dilute to 1
liter.
3 2.2 Red litmus paper.
3.2.3 Water—Delonlzed, distilled.
3.3 Analysis.
3.3.1 Fuming sulfurlc acid—15 to 18% by
weight free sulfur trloxlde.
3.3.2 Phenol—White solid reagent grade.
3.3.3 Sulfurlc acid—Concentrated reagent
grade.
3.3.4 Standard solution—Dissolve 0.5405 g.
potassium nitrate (KNO,) In distilled water
and dilute to 1 liter. For the working stand-
ard solution, dilute 10 ml. of the resulting
solution to 100 ml. with distilled water. One
ml. of the working standard solution Is
equivalent to 26 ug. nitrogen dioxide.
3.3.6 Water—Delonlzed, distilled.
3,3.6 Phenoldlsulfonlc acid solution—
Dissolve 25 g. of pure white phenol In 160 ml.
concentrated sulfurlc acid on a steam bath.
Cool, add 76 ml. fuming sulfurlc acid, and
heat at 100° C. for 2 hours. Store In a dark,
stoppered bottle.
4. Procedure.
4.1 Sampling.
4.1.1 Pipette 26 ml. of absorbing solution
Into a sample flask. Insert the flask valve
stopper Into the flask with the valve In the
•'purge" position. Assemble the sampling
train as shown In Figure 7-1 and place tbe
probe at the sampling point. Turn the flask
valve and tbe pump valve to their "evacuate"
positions Evacuate Hit- fl.v.k to at Icn.'.t :i
Inches Hg absolute pressure. Turn the pump
valve to Its "vpnL" position and turn oil the
pump. Check ilir mnnomclcr for any fluctu-
ation In the mercury level. If there Is ti visi-
ble change over tin- span of one mlnuii>.
check for leaks. Record the Initial volume.
temperature, and barometric, pro .sure Turn
the flask valve to Its "purge" position, nnrl
then do the same with the pump vnlvo
Purge the probe and the vacuum tube iiMm:
the squeeze bulb. If condensation occurs In
the probe and flask valve area, heat the probe
and purge until the condensation disappears
Then turn the pump valve to 1U "vent" posi-
tion. Turn the flask valve to Its "sample"
position and allow sample to enter the flask
for about 15 seconds. After collecting the
sample, turn the flask valve to Its "purge '
position and disconnect the flask from the
sampling train. Shake the flask fcr 5
minutes.
4.2 Sample recovery.
4.2.1 Let the flask set for a minimum of
16 hours and then shake the contents for 2
minutes. Connect the flask to a mercury
filled TJ-tube manometer, open the valve
from the flask to the manometer, and record
the flask pressure and temperature along
with the barometric pressure. Transfer the
flask contents to a container for shipment
or to a 250 ml benker for analysis. Rinse tin-
flask with two portions of distilled water
(approximately 10 ml.) and add rinse water
to the sample For a blank use 26 ml of ab-
sorbing solution and the same volume of dis-
tilled water as u..eci in ringing the flask. Prior
to shipping or artnlvsls. add sodium hydrox-
ide (IN} dropwlsc Into both the sample ami
the blank until alkaline to litmus paper
(about 25 to 35 drops In each).
4.3 Analysis.
4.3 1 If the sample has been shipped .n
a container, transfer the contents to a 'J.vi
ml. beaker using a small amount of distilled
water Evaporate the solution to dryness on a
steam bath and then cool Add 2 ml phenol-
dlsulfonlc acid solution to the dried residue
and triturate thoroughly with a glass rod
Make sure the solution contacts all the resi-
due. Add 1 ml. distilled water and four drops
of concentrated sulfurlc acid Heat the solu-
tion on a steam bath for 3 minutes with oc-
casional stirring. Cool, add 20 ml distilled
water, mix well by stirring, and add concen-
trated ammonium hydroxide dropwise wit h
constant stirring until alkaline to lltmur.
paper. Transfer the solution to a 100 ml
volumetric flask and wash the beaker three
times with 4 to 6 ml. portions of distilled
water. Dilute to the mark and mix thor-
oughly. If the sample contains solids, trans-
fer a portion of the solution to a clean, dry
centrifuge tube, and centrifuge, or filter a
portion of the solution. Measure the absorb-
ance of each sample at 420 nm. using the
blank solution as a zero Dilute the sample
and the blank with a suitable amount of
distilled water If absorbnnce falls outside the
range of calibration.
5. Calibration.
51 Flask volume. Assemble the flask and
flask valve and fill with water to the stop-
cock Measure the volume of water to •* 10
ml. Number and record the volume on the
flask
5.2 Spectrophotometer Add 0.0 to 16 0 ml
of standard solution to a series of beakers 'l»
each beaker add 25 ml. of absorbing solution
and add sodium hydroxide (IN) dropwise
until alkaline to litmus paper (about 35 to
35 drops). Follow the analysis procedure of
section 4.3 to collect enough data to draw a
calibration curve of concentration In pg NO
per sample versus absorbance.
6. Calculation*.
8.1 Sample volume.
21
-------
RULES AND REGULATIONS
where.
V.. = Sample volume at standard condl- Vt~ Volume of flask and valve, ml. T, = Filial absolute temperature nf flank
tlons (dry basis), ml. v.- Volume or absorbing solution, 25 ml. ¥.,i,^, .h~,i,,.- .- __ , • ~ > «. •,
_ AI^B^I.,*.* »A.vtnA*-nti,w ««• «4-«n«t««H« T, = Initial absolute temperature of flask.
T.,d= Absolut* temperature at standard pf_ Final absolute pressure of flask. «R.
conditions. 630" R. Inches Hg 6.2 Sample concentration Bead #g NO,
P. 14 = Pressure at standard conditions. P, = Initial absolute preesure of flask, for each sample from the plot of UK NO,
20 93 Inches Hg Inches Hg versus absorbance
equation 7-2
where*
C = Concentration of NO, as NO. (dry Standard Methods of Chemical Analysis. Book of ASTM Standards, Part 23. Phlladel-
basls), Ib /s c f 6th ed. New York. D. Van Nostrand Co., Inc., phia. Pa. 1968, ASTM Designation D-1608-60.
m = Mass of NO, In gas sample. «ig 1962. vol. 1, p. 329-330 p 726-729.
V.c=Sample volume at standard condl- Standard Method of Test for Oxides of Jacob. M B . The Chemical Analysis of Air
tlons (dry basis), ml. Nitrogen In Gaseous Combustion Products Pollutants. New York. N Y. Intersclence Pub-
7. References (Phenoldlsulfonle Add Procedure). In: 1968 Ushers, Inc. 1960, vol 10, p. 351-356
22
-------
APPENDIX B
STATISTICAL METHODS
23
-------
APPENDIX B. STATISTICAL METHODS
I his appendix consists of various sections which contain detailed statistical procedure's tinned
out in the analysis of the NOX collaborative study data. Reference to these sections has heen made
at various junctures in the Statistical Design and Analysis part of the body ol this report liach
Appendix B section is an independent ud hoc statistical analysis pertinent to a particular problem
addressed in the body of the report.
TABLE B 1 ORIGINAL COLLABORATIVE TEST DATA,
NOX ASNO2,lb/scfXl07
B.1 Preliminary Analysis of the Original
Collaborative Test Data
In order to insure that the results obtained
from the Method 7 test at the Mobay site were
indicative of the performance of the method
itself, preliminary recalculation ol the data was
performed. This serves to verify that the
collaborators had calculated their concentration
levels using the proper formulas and conversion
factors. In addition,when a particular laboutoiy
showed a consistent bias, possible causes were
investigated both by examining the colluhoratoi
work sheets and by contacting that laboratoiy
concerning their procedure The data us were
originally reported appear in Table B I. and Un-
verified or corrected data as used in the analysis
appear in Table I.
The values of lab 102 in runs I 5-22 were
eliminated from the analysis. The actual con-
centrations determined were treated as lost
values, due to the probable omission of the
neutralization step in the analytical procedure, which resulted in the loss of the nitrogen containing
species as HNO3 upon evaporation of the samples to dryness.
The reported values of lab 103 were almost uniformly lower than those by the other collabora-
tors, and possible causes for this were investigated by inspecting the work sheets provided. Lab 103
has set up an absorbance curve using five reference points. The line to match these points had been
drawn in such a manner as to pass nearly through three points and to essentially ignore the effect of
the other two The two points that did not contribute to the slope of the line, however, were above
the line, and their inclusion would have the effect of increasing the slope and raising all the values
A new curve was constructed using a least squares fit to these points through the origin. The slope
of this line times the absorbance provides the mass of each sample. It should be stressed that although
an adjustment of the data was made, it was made using the actual information obtained by the collab-
orators and in this light seems a valid procedure.
The values from lab 102 in run 8, and lab 104 in run 7 were regarded as suspicious clue to the
magnitude of the difference between those values and both the on-stream analyzer and the values
reported by the other collaborators during that run Using a test for outlying values given m Dixon
and Massey*1*, these values may be excluded from the analysis. The test is based on the ratio of
Run
1
2
3
4
5
6
7
8
9
10
II
12
13
14
15
16
17
18
19
20
21
22
Lab 101
328
444
247
328
258
209
105
111
111
108
106
107
92
III
118
116
118
142
128
134
119
160
Lab 102
377
344
306
305
166
14
102
333
104
102
62
89
98
102
-)
4
4
4
4
2
2
4
Lab 103
210
280
330
180
160
150
80
70
70
70
80
80
80
80
80
90
80
80
90
110
80
80
Lab 104
302
409
391
279
255
230
43
98
93
111
108
108
96
103
86
76
83
97
95
87
87
113
On-Stream
Analyzer
237
260
266
207
172
154
77
77
77
77
77
83
83
83
80
83
89
89
89
89
89
118
25
-------
the difference between the suspect value and its Closest value to the entire range of the sample. For
run 7, this becomes, using the corrected values from Table I,
97-45 52
and for run 8,
333- 112 221
r = = = 0.906.
333-89 244
These values may be said to be outlying if/- exceeds the tabled value for four observations at
the 95 percent level of confidence. From a table given in(' *, the critical value of r is 0.765, and thus
both values are rejected as outliers.
In these cases, there is no substitution for these values, but the analysis is done on the remaining
values only. In this manner, the final estimates are obtained only from actual Method 7 determinations,
made in accordance with the Federal Register.^
During the first six runs, the values read from the on-stream analyzer were fluctuating consider-
ably. This was due to the fact that a rupture disc blew, causing the plant to have to begin shutdown
during the fust day of the test. To obtain collaborator block variance estimates from these values,
it was necessary to make a compensating adjustment for the fluctuating mean value.
The value of the fourth run on day 1 on the on-stream analyzer of 207 appeared to be a good
central point of the first day's values. The adjustment used was to make a correction in the data for
the difference between the on-stream analyzer at that point and the value of 207. In this manner, the
differences between collaborators are maintained, while the block estimates are adjusted to a com-
mon mean value. The values of the first six runs adjusted for a mean of 207 are presented in Table B.2,
and the collaborator block values are taken from these. For betwecn-collaborator estimates, the origi-
nal data are used, as they appear in Table 1.
TABLE B 2 CORRECTED VALUES FOR
BLOCK I, ADJUSTED FOR
COMMON MEAN
B.2 Significance of the Port Effect
The sampling at the Mobay site was done through
four sample ports, assigned the labels A, B, C, and D.
Each collaborator sampled from only one port during
each run, and although the ports are as nearly identical
as possible, the pattern of the gas flow may lead to one
port showing a consistently higher or consistently lower
concentration than the others.
To test this possibility, a rank test proposed by Youden(S)
is used on the data Each port is assigned a rank during
each run, based on the reported concentration, one being the highest ranking concentration. These
ranks are then summed for each port, and the values compared to the limits of a 95% confidence
interval tabled by Youdcn
Table B.3 shows the details of the test. For the missing values of lab 103, the port was assigned
the lowest rank. This involved two observations from each data port, and it was felt that the effect
would be to maintain the relationship between the three good port observations.
Run
1
2
3
A
5
6
Ijb Idl
293
356
198
329
303
273
l.ih 102
330
274
238
305
200
85
Lib 103
225
263
306
217
227
252
Lab 104
177
326
304
279
308
309
26
-------
TABL1- B 1 TF.ST FOR
PORT EFFECT
Kun
1
2
3
4
5
6
7
8
9
10
11
12
13
14
IS
16
17
IK
19
20
21
22
Rjnk Sum
I'orl R.inks
A
2
2
1
2
2
1
3
1
1
1
3
4
4
2
4
2
3
1
4
2
3
1
49
II
1
1
2
4
4
2
4
4
2
2
1 5
3
2
1
2
3
1
4
2
3
1
4
535
C
3
3
4
3
3
4
1
3
4
3
1 5
1
1
3
3
1
4
3
3
1
4
3
595
\)
4
4
3
1
1
3
2
2
3
4
4
2
3
4
1
4
2
2
1
4
2
2
58
Youden's Confidence Interval 4 ports,
22 run*., (40, 70)
H0 No port efteci HA (not Ha)
Reject H0 if and only if a Rank Sum
falls outside Cl
Conclusion Adept H0, no significant
port effect
The highest port rank sum lor the Mobay site was loi port (',
witli a value of 5f) 5, and the low was port A. with a v.ilue ol 41). The
extreme values al a 5 pertvut significance level for the Icsl aie 40
and 70, and thus the values obtained are acceptable. No dilleiences
in reported NOX conccntution due to the port from which the
sample was taken are detectable, and as a result, the port factor is
not included in any further analysis.
B.3 Transformations
Transformations are applied to the test data for two purposes.
First, it can put the data into an acceptable form for performing an
analysis of variance. Secondly, it can provide a clue to the true
nature of the distribution of the sample data and thus provide a
model for the interpretation of the data.
The concentrations are analyzed under two common vaiunce
stabih/mg transformations and in their original (linear) lorm Foi
each, Barlletl's test for homogeneity of variance^ ^ is used to deter-
mine the adequacy of the two hansformations and the degiee ol
equality of variance present in the original data. The transtoim.itions
used weie the logarithmic and the square root The icsults obtained
for Bartlett's test are shown in Table B.4.
The test st.itistic is based on the chi-sqitare diMrihutinn and
the corresponding significance level is the probability of obtaining a
chi-square value at least that great due to chance alone Clearly
the logarithmic tiansformation provides the best fit to the daia.
even though this would be only marginally acceptable Those lesults
are consistent with those presented by Hamil and Camann'3' in
their study on Method 7
This acceptance of a logarithmic transformation as the most suitable model for the test data
indicates that a linear relations/up exists between the true mean and the true standaid deviation tor
the run data A proof of this is presented by Hamil and Camann.(3)
TABLE B 4 DATA TRANSFORMATION
TO ACHIEVE RUN EQUALITY
OF VARIANCE
Transformation
Linear
Logarithmic
Square Root
Test
Statistic
57980
36458
41 443
DP
21
21
21
Significance
Level
<001
002
001
B.4 Empirical Relationship Between the Mean and
Standard Deviation in the Collaborative Test Data
In order to properly analyze the data, it is necessary
to determine any underlying relationship between the
mean and standard deviation. We wish to do this for
both the interlaboratory run component and the intra-
laboratory collaborator block component on an empirical
basis.
Let us denote,
xlfk as the concentration reported b> / in block/ during run A
27
-------
1 p
V ik =~~
.v,yji, as the mean for run A: in block/, where p is the number of collaborators.
s)k =
'^£1
(xuk - x.ik)2 , as the standard deviation for run k, block/.
The values obtained for x.,k and s,k for each of the 22 runs are presented in Table B.5, along
with the coefficients of variation for each run. Asterisks denote those runs in which only three
collaborators values were used in the calculations.
TABLES 5. INTERLABORATORY
RUN SUMMARY
Block
1
2
3
Run
1
2
3
4
5
6
*7
*8
9
10
11
12
13
14
*15
*16
*I7
*I8
*19
*20
*21
*22
NOX as NO,
(Ib/scQ X 10*'
xlk
2830
3830
3362
2825
2150
1707
101 3
997
988
1032
935
995
970
1032
977
970
993
111 7
1077
113 7
101 7
124 7
slk
65 1
556
683
48.2
448
740
40
116
11 5
88
214
95
34
66
186
197
186
280
170
239
16.8
34 0
Coefficient of
l/nri i tion
v dl laliuii
02299
0.1452
02033
01706
02085
0.4333
00399
0 1163
0 1167
00853
02291
00952
0.0347
00639
0 1903
02028
0 1871
02511
0 1580
0.2099
0.1653
0.2730
* Values obtained using 3 determinations
There is an apparent linear relationship between the run
mean and standard deviation, and to test this idea, a standard
least squares regression line is fitted to the observed values. A
no intercept model is used, to include the origin (mean and
standard deviation both equal to zero). The regression line
thus generated and the individual points used are presented in
Figure B.I.
As a measure of the validity of the model, a correlation
coefficient, r, and coefficient of determination, r2 , are com-
puted for the data. For the no-intercept model.the correlation
coefficient is calculated according to the formula(4)
r = •
1=1
1=1
where x, represents a sample mean, y, represents the corre-
sponding standard deviation, and n is the number of points
used in the analysis.
For the run data, the value of r is 0.936, which is sig-
nificant at the 5 percent significance level. The value of r2 ,
then, is (0.936)2 = 0.876, indicating that over 87% of the variance in the means and the standard
deviations is related.
A similar analysis can be performed on the collaborator block data. We denote
1 xS
xii. = — j> xtlk, as the sample mean of collaborator i, block /, where n is the number of samples in
" *=i the collaborator block.
' as the samPle standard deviation of collaborator / in block /.
28
-------
I/I
fluo Swndtfd Q«vtMion
NT7 IBfttf
100
ISO
750 300
RunMMn. 10 ' Ib/icf
FIGURE B.I. INTERLABORATORY RUN PLOT
The values for the eleven collaborator block combinations are listed in Table B.6. No values are
shown for lab 102 in block 3 as no valid concentrations were reported in that group. Values with
asterisks were those based on less than the full number of observations for that block.
TABLE B.6. INTRALABORATORY
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
NOX as NO,
(Ib/scOx 10* 7
xn.
292.0
238.7
248.3
283.8
107.0
94.3
94.0
102.3
130.1
-
99.4
90.5
su
54.4
88.4
33.3
54.5
6.3
15.1
5.0
6.8
16.3
-
9.6
11.2
Coefficient of
Vsris tion
0.1862
0.3705
0.1340
0.1919
0.0587
0.1605
0.0533
0.0662
0.1249
-
0.0962
0.1236
"Collaborator blocks with missing values.
Once again, the standard deviation for the col-
laborator block data shows an apparent tendency
to increase linearly with the mean. The paired means
and standard deviations are presented in the graph in
Figure B.2. A least squares regression line is deter-
mined for these points and is also presented in
Figure B.2, to illustrate the degree of fit of the model.
The correlation coefficient for the intra-
laboratory data is 0.907 based on the 1 1 pairs,
x ij and Sjj. This value, again, is significant using
a 5 percent significance level. The value of r2 is
0.823, again indicating a high degree of association
between the sample mean and sample standard
deviation.
B.5 Underlying Relationship Between the Mean and
the Standard Deviation
In Appendix B.4, the empirical relationship
is established between the mean and standard devia-
tion of the collaborator block data. Let us denote :
29
-------
100 150 200 250 300
Collaborator Bloi-k Mean 10 ' Ib'ict
FIGURE B.2. INTRALABORATORY COLLABORATOR BLOCK PLOT
5, as the true mean of the distribution of the Method 7 determinations
a, as the true within-lab standard deviation.
and
(3 - - as the true coefficient of variation.
o
To estimate o, we use the relationship established in Appendix B.4.
*•// = bx'tj.
where b is the sample coefficient of variation. The sample standard deviation is a biased estimator
of the population value, but Ziegler(6) has shown that for a sample of size n, this bias may be effec-
tively removed by multiplying by a factor of
where F (a) is the standard gamma function. Thus we have
a = E(ctnsjj)
and substituting from above,
30
-------
attb£{xll)
where |3 = a,,b.
Similarly, in Appendices B.3 and B.4, the linear relationship between the run mean and run
standard deviation is established first on theoretical, then empirical grounds. Thus, we can say that
The true between-laboratory standard deviation is given by at, =\/ol + a2, where a£ represents the
true laboratory bias variance component. As before, Sy* is a biased estimator, and the correction factor
must be applied. We have
2 = E(ans,k )
= anE(s,k)
= anb'E(x.lk)
where /?/, =a,,b' .
From the above relationships, we find
and this gives us
where j3y is defined as \/|3^ — (3Z.
31
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B.6 Estimating the Standard Deviation Components
In Appendix B.5, we developed the relationships concerning the standard deviation components
for the run and the collaborator block components.
o/. =w.5
The standard deviation component o, lor the within-laboratory variability, and the standard dcvi.i-
tion OL , for the laboratory bias component, both follow the coefficient of variation hypothesis
To estimate these standard deviations, we obtain best estimates of the coefficients of variation and
express the standard deviations as percentages of the mean value, 5.
From Ziegler^6), the best estimate of a coefficient of variation is given by
k **• v
* 4=1*'
for k samples each of size n. For unequal sample sizes, «,, this may be extended as
where Cn, is the correction factor used to remove the bias on the sample standard deviation.
For the within-laboratory standard deviation, a, this estimate becomes
i=l /=!
where n,, is the number of runs in the collaborator block. The values used are those presented in
Table B.6, with the adjusted values in the first block as discussed in Appendix B.I . The estimated
coefficient of variation is J3 = (0.1 4882) which gives
a = 05 = (0.1 4882)6.
Similarly, from the run data we have
where n, is the number of runs in block /, and iifk is the number of collaborator values in block /.
run A. For the run data in Table B.5, the estimated fa isfa = (0.18468) which gives
a. =(0.18468)6
32
-------
Substituting these values into the second equation, we obtain
= v/(0.03411)-(0.02215)
= 0.10936.
Then the estimate for the lab bias standard deviation is
6L =(0.10936)6.
B.7 The Nitrate Solution Data
Three nitrate solutions were given to each of the collaborators to be analyzed m conjunction with
the collaborative test data. These solutions were analyzed in triplicate on each of three days and iiive
an indication of the effect of the analytical process on the Method 7 concentration deter minalioi^
The instruction and reporting form given to the collaborators is shown in Figure 5 The repoi led um-
centrations as determined by the lab analysts are shown in Table B.7.
In Table B.8, the values for each solution arc averaged for each day for each collabouiloi Horn
these, it is evident that fairly large discrepancies do occur in the results obtained hy the same l:ih I mm
day to clay. In Table B.9, the average over all three days for each solution is shown
There is no apparent tendency in the solution averages toward a single laboratory showing .1
consistently higher or consistently lower concentration than the other labs. The actuul concentra-
tion levels are also shown as a means of comparison. The tendency for all laboratories taken together
appears to be to show a low concentration with respect to the true value, at all three concentrations
B.8 Variance Components From the Nitrate Solution Data
An analysis of variance (AOV) was performed on the nitrate solution data to determine what
effects are significant contributors to the variability in the analysis. A separate analysis was> per-
formed on each set of solution data, and the resulting AOV tables are shown in Table B. 10.
The nitrate solution data is laid out in a two level nested design The model for this design is
a random ejfects model with
= Ji+7(+T,/f-
33
-------
TABLE B 7 REPORTED NITRATE
SOLUTION CONCENTRATIONS,
( ollabor.itnr
L.ih 101
Lab 102
Uh 1 03
Lab ] 04
Day
1
2
3
1
2
3
1
2
3
1
2
3
Kepi
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
1
2
3
1
2
3
1
2
3
Sol A
346
346
34 1
396
399
396
363
375
37 2
28 0
255
250
41 4
41 0
398
377
367
385
43
45
44
44
40
42
40
393
41 0
374
386
374
37 7
377
372
375
386
385
Sol B
6 1
6 0
58
80
7 1
82
86
66
60
5 5
80
4 3
78
86
82
55
62
60
70
70
7.0
80
75
75
60
63
5 5
4 8
2 2
3 7
4 2
36
4 8
3 7
1 5
3 2
Sol C
201
202
20 1
244
21 8
246
196
21 5
21 3
207
120
185
21 3
232
223
21 5
21 5
21 5
24
24
23
25
24
23
21 5
225
21 5
27 7
24 2
24 5
22 8
228
235
228
238
229
TABLE B 8. LABORATORY DAY
AVERAGES FOR NITKATh
SOLUTION DATA
/ig NO2/m»
Collaborator
Lah 101
Lib 102
Lib 103
Lab 104
Day
1
2
3
1
2
3
1
2
3
1
2
3
Sol A
144
397
370
26 2
407
376
44 (1
420
40 1
37 8
375
38 2
Sol It
6(1
78
7 1
5 9
8 2
59
70
7 7
59
36
4 2
28
Sol (
20 1
2U>
2(1 X
17 1
22 t
21 5
23 7
241)
21 8
255
230
232
TABLE B 9 AVERAGE LABORATORY
NITRATE SOLUTION
CONCENTRATION.
/JgNO2/mC
Collaborator
Lab 101
Lab 102
Lab 103
Lab 104
Actual
Solution A
37.0
348
42.0
378
382
Solution B
6.9
6.7
69
3.5
7 2
Solution ('
21 5
203
232
239
223
where
y,,k is the k\\\ repetition, on day/ for collaborator /, i = l,. . ., 4,y = 1, 2, 3, A' = 1, 2, 3
// is the overall mean.
7, is the effect of collaborator /.
TJ/, is the effect of day/ within collaborator/.
is the random error of replicate k for day / in collaborator /.
34
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TABLE B.10 NITRATE SOLUTION DATA
ANALYSIS OF VARIANCE
Then any null vicinal observation,
y,fic , is estimated by the equation
=A + C'( + £>//, +
where ft, C,. D,/,, and <'*///, are esti-
mates of ju, T,,T//I, and e/t/y/,, respec-
tively.
The overall mean is presented for
each solution across collaborators, along
with the mean squares obtained and
the expected mean squares for each
factor. Using the expected mean \quui c\
we are able to derive estimates of the
individual variance terms, us well as to
determine the correct ratios for the
F-tests of interest
The f''-ratio.\ are presented in
Table B.I 1 , along with their correspond-
ing degrees of freedom and significance
levels. Using u significance level lit S
percent, we can evaluate the effect of the factors involved in the analysis. For the lolluhnnifm Im-
tor. a significant effect was detected only at the low concentration, solution B. This result*, lioin
the values reported by lab 104, which were approximately half those of the other labs
TABLES II F-RATIOS AND PROBABILITIES The day within m/lahoKimi i-//,-, /
was significant for all solutions, howeu-i
This same occurrence has been iepoi led In
Hamil and Camann^1' in a previous si inly on
Method 7 and is an indication lh.it .uldili.m.il
variability is introduced into the deleimm.i-
tions by the day to day pimednul dilleiences
in the laboratory. The magnitude of I lie d.iv
component, o&, was on the sdine level .is the
replication component, a2f . for the I wo lowei
concentrations and greatly largei for the high
solution. Using the nitrate solution data, now, we can obtain estimates of the between JIK! \\-iiliui Inh
variance of a Method 7 determination due to the analytical process alone. For a2 . we use the lepln.ik
variance component aj . For the between-lab component, OQ, however, some modification is neces-
sary to obtain a result consistent with the definitions. For each solution, we obtain a runtime o/////025
«0005
1
35
-------
where
TABLE B 12 VARIANCE COMPONENTS
OF NITRATE SOLUTION DATA
M, Mg/10 ml
MSh
°b
Sol B
72
35706
Sol C
223
66904
Sol A
382
21 3270
Within Laboratory Variance
o* =o2
a, jug/ 10 nil
08094
08997
25664
1 6020
0.9381
09686
Labiiiaiarv Bias Variation
MSL
"1
27612
1 6617
50884
22557
20 3584
4 5120
For solutions A, B, and C, the variance components
are presented in Table B. 12. As before, /WS/, estimates
a\ + a2, so MSi = MS/, — a? is the lab bias component
The values obtained for the precision estimates are presented
in Table B.I 2 for the nitrate solution data. No justification
could be found for applying the coefficient of variation
approach to these estimates, as the within lab standard
deviation appears independent of the solution concentra-
tion level. As a result, the within lab and(lab bias components
are estimated by alternative techniques and presented in
Section III F.
36
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REFERENCES
I Dixon, W. .1 and Massey, K. J., Jr., Introduction To Statistical Analv.\is, 3rd l-.dilion McCuw-llill.
New York, l%9.
2. Environmental Protection Agency, "Standards of Performance for New Station.iiy Somces."
Federal Register, Vol. 36, No. 247, December 23, 1971, pp 24876-24893
3. Hamil, Henry F. and Camann, David E., "Collaborative Study of Method for the Dcternniialinn ol
Nitrogen Oxide Emissions from Stationary Sources," Southwest Research Institute report foi
Environmental Protection Agency, October 5, 1973.
4. Searle, S. R , Linear Models Wiley, New York, 197 1.
5. Youden.W. J., "The Collaborative Test," Journal of the AO AC, Vol. 46, No. 1, 1963. pp 55-(>2
6. Ziegler, R. K., "Estimators of Coefficients of Variation Using k Samples," Tecli name tries. Vol 1 S
No. 2, May 1973, pp 409-414.
37
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TECHNICAL REPORT DATA
(Please read Inunctions on the reverse before completing)
1 REPORT NO
EPA-650/4-74-028
3. RECIPIENT'S ACCESSIOr*NO.
4 TITLE AND SUBTITLE
Collaborative Study of Method for the Determination
Nitrogen Oxide Emissions from Stationary Sources
(Nitric Acid Plants)
of
5 REPORT DATE
May 1974
6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
Henry F. Hamil and R. E. Thomas
8 PERFORMING ORGANIZATION REPORT NO
Project No. 01-3462-004
9 PERFORMING ORGANIZATION NAME AND ADDRESS
Southwest Research Institute
8500 Culebra Road
San Antonio, Texas 78284
10 PROGRAM ELEMENT NO
1HA327
11 CONTRACT/GRANT NO
68-02-0626
12 SPONSORING AGENCY NAME AND ADDRESS
Environmental Protection Agency
Methods Standardization & Performance Evaluation Brand:
National Environmental Research Center
Research Triangle Park. N. C. 27711
13 TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
15 SUPPLEMENTARY NOTES
16 ABSTRACT
This reports presents the results obtained from a collaborative test of
Method 7 promulgated by EPA for determining the nitrogen oxide emissions from
stationary sources. Method 7 specifies the collection of a grab sample in an evac-
uated flask containing a dilute sulfuric acid-hydrogen peroxide absorbing solution
and the colorimetric measurement of the nitrogen oxides, except nitrous oxide,
using the phenoldisulfonic acid procedure.
The test was conducted at a nitric acid plant using 4 collaborating labora-
tories. A total of 22 samples were taken over a 3-day period. In addition,
standard gas samples were taken and nitrate solutions whose true concentrations
were unknown to the collaborators were prepared for concurrent analysis. The
concentrations determined by the collaborators from all three phases of the test
were submitted to statistical analysis to obtain estimates of the accuracy and
precision that can be expected with the use of Method 7.
17
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c COSATl Field/Group
18 DISTRIBUTION STATEMENT
19 SECURITY CLASS (This Report)
Unclassified
21 NO OF PAGES
40
Unlimited
20 SECURITY CLASS (Thispage)
Unclassified
22 PRICE
EPA Form 2220-1 (9-73)
38
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