COLLABORATIVE STUDY
of
REFERENCE METHOD FOR THE CONTINUOUS
MEASUREMENT OF CARBON MONOXIDE IN
THE ATMOSPHERE (NON-DISPERSIVE
INFRARED SPECTROMETRY)
Herbert C. McKee
Ralph E. Childers
Contract CPA 70-40
SwRI Project 01-2811
Prepared for
Office of Measurement Standardization
Division of Chemistry and Physics
National Environmental Research Center
Environmental Protection Agency
Research Triangle Park, N. C. 27709
May 1972
-------
COLLABORATIVE STUDY
of
REFERENCE METHOD FOR THE CONTINUOUS
MEASUREMENT OF CARBON MONOXIDE IN
THE ATMOSPHERE (NON-DISPERSIVE
INFRARED SPECTROMETRY)
Herbert C. McKee
Ralph E. Childers
Contract CPA 70-40
SwRI Project 01-2811
Prepared for
Office of Measurement Standardization
Division of Chemistry and Physics
National Environmental Research Center
Environmental Protection Agency
Research Triangle Park, N. C. 27709
May 1972
Approved
Herbert C. McKee
Assistant Director
Department of Chemistry
and Chemical Engineering
r
-------
SUMMARY AND CONCLUSIONS
This report presents information obtained in the evaluation and collaborative testing of a reference
method for measuring the carbon monoxide content of the atmosphere.
This method was published by the Environmental Protection Agency in the Federal Register,
April 30, 1971, as the reference method to be used in connection with Federal ambient air quality stan-
dards for carbon monoxide. Following minor editorial changes, the method was republished in the Federal
Register, November 25, 1971 . The former publication is reproduced as Appendix A of this report.
The method is based on the infrared absorption characteristics of carbon monoxide, using an instru-
ment calibrated with gas mixtures containing known concentrations of carbon monoxide. A similar method
based on the same principle has been published by the Intersociety Committee as Tentative Method
42101-04-69T in Health Laboratory Science, January 1970, Part Two, pp 81-86.
The method published in the Federal Register was tested, as a part of this program, by means of a
collaborative test involving a total of 16 laboratories. The test involved the analysis of both dry and
humidified mixtures of carbon monoxide and air over the concentration range from 0 to 60mg/m3. A
statistical analysis of the data of 15 laboratories provided the following results:
• The checking limit for duplicates is-0.5 mg/m3
• The repeatability is 1 .6 mg/m3
• The reproducibility varies nonlinearly with concentration with a minimum of 2.3 mg/m3 at a
concentration of 20 mg/m3 and ranges as high as 4.3 mg/m3 in the concentration range of 0 to
60 mg/m3
• The minimum detectable sensitivity is 0.3 mg/m3
The compensation for water vapor interference is satisfactory for drying agents and refrigera-
tion methods. The use of narrow-band optical filters alone may not provide adequate
comensation.
• The accuracy is totally dependent upon the availability of dependable calibration standards.
Based on the results of this collaborative study, the method produces results, on the average,
2.5 percent high.
In addition, this report presents other results with respect to the quality of calibration standards and
the minimum number of samples required to establish validity of results within stated limits.
in
-------
ACKNOWLEDGEMENT
The authors wish to express appreciation to the Project Officer, Mr. Thomas W. Stanley, and staff
member, Mr. John H. Margeson, of the Office of Measurement Standardization, for assistance in the plan-
ning and execution of the collaborative study.
The assistance and advice of Scott Research Laboratories, Plumsteadville, Pennsylvania, who prepared
and analyzed the test gases, is acknowledged.
The assistance and cooperation of the participating laboratories is also acknowledged with sincere
appreciation for the voluntary efforts of the staff members who represented each organization. The repre-
sentatives and organizations participating in one or more phases of the collaborative test program were as
follows:
Name
RichardS. Brief
R.G. Confer
Organization
Esso Research and Engineering Company
Linden, New Jersey
Franz J. Burmann
Jack A. Bowen
Environmental Protection Agency
Durham, North Carolina
Charles A. Cody
Southwest Research Institute
Houston, Texas
Ronald P. Dubin
Richard Wonderlick
Bureau of Air Pollution Control
Pennsylvania Department of
Environmental Resources
Harrisburg, Pennsylvania
Milton Feldstein
Bay Area Air Pollution Control District
San Francisco, California
Judith Garelick
Diane Berkel
Kenneth T. Irwin
Bureau of Air Pollution Control
Nassau Department of Health
Mineola, New York
Jefferson County, Kentucky
Air Pollution Control District
Louisville, Kentucky
Norman J. Lewis
Division of Environmental Quality
New Jersey State Department of Health
Trenton, New Jersey
IV
-------
Name
Organization
Peter K. Mueller
S.G. Kerns
Robert E. Pattison
F.D. Olmstead
Hisham M. Sa'aid
Roger B. McCann
R.K. Stevens
Dwight A. Clay
Bill Stewart
J.S.Payne
PhilipS. Tow
Air and Industrial Hygiene Laboratory
California State Department of Public
Health
Berkeley, California
Air Pollution Control Laboratory
Canton City Health Department
Canton, Ohio
Air Quality Section
Kentucky Air Pollution Control
Commission
Frankfort, Kentucky
Environmental Protection Agency
Research Triangle Park, North Carolina
Air Pollution Control
Texas State Department of Health
Austin, Texas
Sacramento County, California
Air Pollution Control District
Sacramento, California
Alvin L. Vander Kolk
Ken Smith
Standards and Analysis Sections
Michigan Department of Public Health
Lansing, Michigan
Grant S.Winn
Carl E. Kerr
Air Quality Section
Utah State Division of Health
Salt Lake City, Utah
-------
TABLE OF CONTENTS
Page
I. INTRODUCTION • • 1
II. COLLABORATIVE TESTING OF THE METHOD 1
A. Furnishing Test Samples and Calibration Gases . . . . 2
B. Selection of Collaborators . .... ... . . . 3
C. Collabortive Test Procedure . . .... ... ... 4
STATISTICAL DESIGN AND ANALYSIS
A. Summary of Design . . . . . . .... . . 4
B. Summary of Results . . . .... .... 5
LIST OF REFERENCES
LIST OF ILLUSTRATIONS
Figure Page
1 Repeatability and Reproducibility Versus Concentration . . ..... 6
LIST OF TABLES
Table Page
1 Reference Values for Carbon Monoxide Test Concentrations Used in Collaborative
Test, Parts per Million . . ... . . .... 3
vu
-------
I. INTRODUCTION
While carbon monoxide has received less atten-
tion than some other contaminants, it is found in
many of the urban areas of the world. Many different
sources of carbon monoxide exist in a typical city,
but by far the predominant source is motor vehicles.
As recent control measures reduce the emissions from
vehicles, other sources such as incinerators and var-
ious industrial operations will represent a larger per-
centage of the total.
Carbon monoxide has long been known to be
toxic at high concentrations, producing illness and
eventually death. At the lower levels of concentration
found in many urban atmospheres, carbon monoxide
may act to impair various bodily functions, although
the exact exposure conditions required to produce
such effects have not been definitely established.
Unlike most atmospheric contaminants, at-
tempts to measure carbon monoxide by a direct
chemical method have met with very limited success.
For industrial hygiene purposes, combustion pro-
cesses and colored indicator tubes have been used
satisfactorily. To measure the lower concentrations of
interest in urban air pollution, however, the only
satisfactory method which has received widespread
use is based on infrared absorption. Commercial in-
struments based on this principle have been available
for many years. The method involves detecting the
difference in absorption of infrared energy of the at-
mosphere being tested in a sample cell and a non-
absorbing gas in a reference cell. The difference is
sensed by selective detectors, sensitive only to carbon
monoxide, and amplified to provide an output signal.
The resulting signal is then used to operate a recorder
which provides a continuous record of carbon mon-
oxide levels over a period of time. Under normal at-
mospheric conditions, the only major interference
with this method is water vapor, which can be over-
come through the use of drying agents or other mea-
sures as discussed subsequently.
In order to obtain reliable data in measuring
carbon monoxide and other atmospheric
contaminants, the Environmental Protection Agency
(EPA) Office of Measurement Standardization (QMS)
has been working for some time to develop standard
methods which could be used by all persons making
air quality measurements. Following the development
of a tentative standard method, the final step in the
standardization process is a collaborative test, or in-
terlaboratory comparison, of the proposed standard
method. This procedure, also called "round-robin
testing," has been used to evaluate many different
methods of measurement in such diverse fields as
water chemistry, metallurgy, paint and surface coat-
ings, food and related products, and many others. A
test of this nature by a representative group of labora-
tories is the only way that the statistical limits of
error inherent in any method can be determined with
sufficient confidence.
This report presents the results of a collabora-
tive test of the carbon monoxide method conducted
by Southwest Research Institute and the Office of
Measurement Standardization, together with the sta-
tistical analysis of the data obtained. In this collabo-
rative test, standard samples contained in high-
pressure cylinders were prepared and carefully
analyzed to determine exact concentration. These
cylinders were then distributed to a representative
group of laboratories who participated in the test on
a voluntary basis. These samples were analyzed
according to the standard procedure as outlined in
the tentative method, after which the gas cylinders
were returned to the supplier for reanalysis to again
check the concentration levels. The results of the col-
laborative test were then analyzed statistically to
determine the accuracy and precision of the proposed
method.
II. COLLABORATIVE TESTING
OF THE METHOD
An important step in the standardization of any
method of measurement is the collaborative testing of
a proposed method to determine, on a statistical
basis, the limits of error which can be expected when
the method is used by a typical group of
-------
investigators. The collaborative, or interlaboratory,
test of a method is an indispensable part*-1) of the
development and standardization of an analytical pro-
cedure to insure that (1) the procedure is clear and
complete and that (2) the procedure does give results
with precision and accuracy in accord with those
claimed for the method. Among other organizations,
the Association of Official Analytical Chemists
(AOAC) and the American Society for Testing and
Materials (ASTM) have been active in the field of
collaborative testing and have published guidelines of
the proper procedure for conducting collaborative
tests and evaluating the data obtained/2~4) Publica-
tions of both organizations were used extensively in
planning and conducting the collaborative tests of
this method to measure carbon monoxide.
After the evaluation of various methods for pre-
paring test samples, a detailed collaborative test was
undertaken to obtain the necessary data to make a
statistical evaluation of the method. This section of
the report describes the various phases of the test
plan that was developed.
A. Furnishing Test Samples and Calibration
Gases
Many air contaminants must be measured at
concentrations in the fractional parts-per-million
range, and the use of test atmospheres in high-pres-
sure cylinders is not feasible at these low levels due to
reaction or adsorption effects which make it im-
possible to maintain an accurately controlled test
concentration. This is not true with carbon mon-
oxide, which is only of concern at levels in the parts-
per-million range. At these higher levels, and with
proper precautions, cylinder gas samples can be used
with a reasonable degree of confidence in the stability
of the samples. The stability should be checked by
periodic reanalysis where possible.
Test gases for this collaborative test were ob-
tained from Scott Research Laboratories, an organiza-
tion with wide experience in the generation, control,
and analysis of various gases for experimental pur-
poses. For each test concentration, a large master
cylinder containing carbon monoxide in dry synthetic
air was prepared and analyzed accurately by gas-solid
chromatography using helium ionization detection.
The chromatograph was calibrated with primary grav-
imetric gaseous standards prepared in glass. From
these master cylinders, smaller cylinders were filled
and individually analyzed by the same method. The
cylinders used had a chromium-molybdenum alloy in-
side surface of low iron content to minimize the loss
of carbon monoxide which has been reported to be
caused by the formation of iron carbonylA5' The
master cylinders were retained and the smaller cylin-
ders sent to the collaborative test participants.
At the conclusion of their analyses, the partici-
pants returned the cylinders to Scott Research Labor-
atories, who then reanalyzed the contents of each
cylinder having sufficient residual pressure. The date
of the first analysis was July 2, 1971; the date of the
reanalysis was January 21, 1972—203 days later. The
results are shown in Table I. They are shown in parts
per million as reported (divide by 0.873 to convert to
milligrams per cubic meter). The results have not
been converted in Table I in order to eliminate mis-
leading comparisons because of round-off errors due
to conversion. The converted values may be seen in
Table C-II of Appendix C.
Agreement between first and final analyses was
good for all but 3 or 4 of the 48 cylinders used. Most
collaborators completed their work within 30 days of
the first analysis; all work was complete within
80 days. Therefore, if any corrections were to be
applied, the result would be much closer to the first
analysis. No corrections were applied and the first
analyses were used as the reference values.
Since the infrared instrument produces a rela-
tive measurement, calibration with standard gases is
necessary in order to convert this measurement to a
measured concentration as described in the method
(Appendix A). This is done by the use of calibration
*Superscript numbers in parentheses refer to the List of References.
-------
TABLE I. REFERENCE VALUES FOR CARBON MON-
OXIDE TEST CONCENTRATIONS USED IN COLLAB-
ORATIVE TEST, PARTS PER MILLION
Assignee
Master
220
222
253
270
310
311
370
375
540
571
780
799
860
920
923
927
Master
220
222
253
270
310
311
370
375
540
571
780
799
860
920
923
927
Master
220
222
253
270
310
311
370
375
540
571
780
799
860
920
923
927
Cylinder
Number
W-18156
C-658
C-657
C-656
C-655
C-654
C-653
C-652
C-651
C-650
C-649
C-648
C-644
C-647
C-646
C-645
C-641
W-138035
C-674
C-673
C-672
C-671
C-670
C-669
C-668
C-667
C-666
C-665
C-664
C-659
C-663
C-662
C-661
C-660
W-138036
C-690
C-689
C-688
C-687
C-686
C-685
C-684
C-683
C-682
C-681
C-680
C-675
C-678
C-677
C-676
C-679
Initial
Analysis
7.50
7.29
7.47
7.40
7.33
7.43
7.49
7.48
7.20
7.42
7.45
7.35
7.36
7.13
7.48
7.48
7.36
25.5
26.1
26.4
26.3
26.1
26.0
26.0
26.1
26.4
26.1
26.2
26.0
26.4
26.1
26.0
26.3
26.3
45.5
45.9
45.5
45.7
45.6
45.6
45.9
45.5
45.7
45.7
45.7
45.6
45.7
45.7
45.7
45.7
45.7
Final
Analysis
7.47
7.27
_
7.21
7.53
_
7.52
6.54
7.46
7.44
7.33
7.33
5.50
7.28
7.57
7.22
25.2
26.8
—
—
26.2
26.0
26.3
—
26.2
26.1
26.4
26.0
26.2
26.4
25.9
25.9
26.3
45.5
45.7
_
-
45.7
45.7
45.6
-
45.6
-
45.7
45.7
45.7
45.6
45.8
45.4
45.2
Change
-0.03
-0.02
_
_
-0.12
0.10
0.04
-0.66
0.04
-0.01
-0.02
-0.03
-1.63
-0.20
0.09
-0.14
-0.3
0.7
_
—
0.1
0.0
0.3
—
-0.2
0.0
0.2
0.0
-0.2
0.3
-0.1
-0.4
0.0
0.0
-0.2
-
-
0.1
0.1
-0.3
-
-0.1
—
0.0
0.1
0.0
-0.1
0.1
-0.3
-0.5
Source: Scott Research Laboratories
gases representing 20, 40, 60, and 80 percent of the
range of the instrument. Such calibration gases are
available from a number of commercial suppliers, and
the participants were instructed to obtain the neces-
sary calibration gases from their usual sources.
Because of this calibration procedure, the
accuracy of the method is completely dependent on
the accuracy of the calibration gases used. For this
reason, all collaborators were instructed to take all
possible precautions to obtain calibration gases of suf-
ficient accuracy and to safeguard these materials from
contamination or deterioration in storage or use.
B. Selection of Collaborators
If a collaborative test is to achieve the desired
objective, it is desirable that the participants in the
test be representative of the large group that will ulti-
mately use the method being tested. Since air pollu-
tion measurements are of interest to many different
groups, it was desirable to include in the group of
collaborators a variety of governmental agencies, uni-
versities, industrial laboratories, and others. The final
selection of participants included two from federal
laboratories, twelve from state and local air pollution
control agencies, one from industry, and one from a
research institution. A complete list of the partici-
pants and their affiliation is given in the acknowl-
edgement.
Even more important than the type of labora-
tory is the degree of skill and experience of the per-
sons who participated. Each laboratory was asked to
assign a person to this test who had previous experi-
ence with the infrared method for measuring carbon
monoxide and was competent in carrying out mea-
surements by this method. This was done because the
emphasis was upon the capabilities of the method
rather than the performance of the laboratories. Each
laboratory had previous experience in the use of the
method and thus possessed a satisfactory infrared in-
strument and the necessary equipment for laboratory
processing of samples and calibration gases.
For purposes of familiarization, each partici-
pant was furnished a standard test sample for analysis
prior to the actual collaborative test. Results from
-------
these preliminary runs were used as an approximate
check on the experience and skill of each participant,
with the intention of eliminating any whose results
were grossly in error, thus indicating a lack of famili-
arity or experience with the method. No such elimi-
nation was necessary and, therefore, all of the partici-
pants originally selected were used in the actual
collaborative test which followed.
C. Collaborative Test Procedure
After the preliminary familiarization samples
were analyzed and the results obtained, test samples
for the actual collaborative test were distributed to
each participant. The national primary and secondary
air quality standard for carbon monoxide is
10 mg/m3 for 8 hr or 40 mg/m3 as a maximum 1-hr
concentration (both to be exceeded not more than
once per year). Therefore, test concentrations were
selected to indicate the variability of the method
within these ranges. This led to the selection of 8, 30,
and 53 mg/m3 as test concentrations for purposes of
collaborative testing.
In addition to examining the effects of concen-
tration on precision and accuracy, it was necessary to
realistically evaluate the effects of humidity on the
analysis. Therefore, in addition to analyzing the dry
test gases, each was analyzed after humidification.
The test gases were essentially saturated by passing
them through a midget impinger containing 15 m£
distilled water. Losses of carbon monoxide due to
absorption are negligible.
In order to estimate other random effects, each
of the three concentrations was analyzed in triplicate
on each of 3 days under both dry and humid condi-
tions. This resulted in a total of 810 separate determi-
nations-54 by each reporting laboratory. Section I-B
of Appendix B contains a more detailed discussion of
the experiment design, and Figure B-l graphically
shows the design.
The results of this test series were then used for
detailed statistical analysis, which is described in detail
in Appendix B and summarized in the next section.
111. STATISTICAL DESIGN
AND ANALYSIS
Several fundamental requirements must be met
in order to provide the maximum reliability of the
collaborative test. First, the conditions of the test
must be representative of a specified population; each
factor involved must be a representative sample of a
population about which inferences are to be drawn.
Second, the collaborative test must be unbiased; pre-
cautions must be taken to avoid the introduction of
any bias in the collaborative test procedure. It is im-
portant that the collaborators assume a responsibility
to try to eliminate any bias by carefully following the
instructions of the collaborative procedure and the
method. Every detail is important and even the
slightest departure from the specified procedures may
bias the results. Third, the results of the collaborative
test must be reproducible; that is, the conditions for
the test should be such that similar results would be
obtained if the collaborative test were repeated. The
fourth requirement involves the scope of the test; the
materials and conditions for which the analytical
method was designed must be included in the test.
Finally, the collaborative test must be practical and
economically feasible. Since funds and facilities are
never available for an unlimited testing program, it is
necessary to accept less than the ideal testing pro-
cedures in order to accomplish the program. Thus,
fundamental requirements may not be completely
fulfilled, since any practical compromise introduces
limitations on the inferences that can be drawn. If
pursued too far, compromises from practical con-
siderations may render the collaborative test useless.
Appendix B contains the complete and detailed
description of the design and analysis of the formal
collaborative test. The results of Appendix B are sum-
marized in this section.
A. Summary of Design
The primary purpose was to establish the reli-
ability of the method in terms of its precision and
accuracy. More emphasis was placed on the quality of
the method when properly used than upon the
-------
performance of the laboratories. At the same time, it
was necessary to retrieve information which would
allow the investigation of other aspects of the
method; therefore, intermediate data were obtained
relating to calibration curves.
The statistical planning of a program is limited
in scope and depends upon what information is
desired. The scope is limited by what a collaborating
laboratory can conveniently and economically accom-
plish, as well as by the number of collaborators that
can be accommodated. Under these limitations, it was
possible to examine the effects of laboratories, con-
centrations, and days upon the precision of the
method in addition to estimating the replication
error.
Of the 16 laboratories that took part in the test
program, 15 satisfactorily completed the test. These
laboratories constitute a random sample of a rather
large population of experienced laboratories. Three
different concentrations were analyzed by each labo-
ratory. The concentrations were nominally 8, 30, and
53 mg/m3 Each of the three concentrations was ana-
lyzed both dry and humidified, in triplicate, on each
of 3 separate days using independently prepared cali-
bration curves. This procedure resulted in a total of
810 individual determinations.
The collaborative test was designed to allow the
analysis of the results using the most efficient statisti-
cal methods available. The experiment was designed
so that the linear model analysis^3'6"8) could be used.
This analysis, as well as tests for outlying observa-
tions, is described in Appendix B.
B. Summary of Results
1. Procedural Errors
Since the emphasis was upon the quality
of the method and not upon the performance of the
laboratories, all arithmetic errors were corrected, and
the arithmetic error problem was evaluated quali-
tatively. Few instances of errors in arithmetic opera-
tions were noted. The method is relatively simple
and, consequently, is not vulnerable to arithmetic and
procedural errors.
2. Precision Between Replicates
The replication error (see Section II-A of
Appendix B for detailed definition) was shown to be
independent of concentration and humidity. The
standard deviation for variation between replicates is
equal to 0.17 mg/m3 Replication will not materially
assist in increasing the precision of the method, and
will, in general, be a waste of time and effort; how-
ever, replicates are often advisable to avoid gross
errors.
The checking limit for duplicates is
0.5 mg/m3; therefore, two replicates differing by
more than this amount should be considered suspect.
Section II-A of Appendix B contains more details re-
garding the replication error.
3. Humidity Effects
The humidity has no measurable effect
upon the precision or accuracy when drying or refri-
geration methods are used (see Section 3.1 of the
method in Appendix A). No data are available for the
saturation method. Optical filters alone do not appear
to be adequate; however, this conclusion is based on
very limited data. Section II-B of Appendix B con-
tains further details regarding humidity effects.
4. Precision Between Days
The standard deviation for variation be-
tween days for the same sample includes both the
replication error and a component for between-days
variation and is equal to 0.47 mg/m3 Two test results
on the same sample on different days by the same
laboratory should not differ by more than 1.3 mg/m3
The standard deviation for variation be-
tween days for different but similar samples includes
an additional term to account for heterogeneity
between samples. The corresponding standard devia-
tion is 0.57 mg/m3 If the test results on each of
these samples differ by less than 1.6 mg/m3-the re-
peatability of the method—there is no reason to be-
lieve there is any real difference between them.
-------
Section III-A-2 of Appendix B presents
more details regarding precision between days; in par-
ticular, a comparison of the means of different popu-
lations each analyzed by the same laboratory.
5. Precision Between Laboratories
The standard deviation for variation be-
tween laboratories includes terms representing addi-
tional, more complex, effects and is equal to the square
root of Vj(y) where V/(y) is given by
Vj(y) = 0.001007x? -0.0393*,- + 1.10
where the subscript/ is attached to signify the depen-
dence upon the concentration Xj which is the inde-
pendent variable.
5
Two test results on the same sample
should agree within the reproducibility which is
shown plotted versus concentration in Figure 1 along
with the repeatability for comparison. If the test re-
sults on two different samples differ by less than the
reproducibility, there is no reason to believe there is
any real difference between them.
Section III-A-3 of Appendix B includes
more details regarding the precision between labo-
ratories.
Various statistical methods are available
for the comparison of means or the comparison of a
mean and a fixed value.(9-H) These methods are
straightforward and are applied independently of the
results of this study. That is, whether or not a mean is
3
3
TJ
O
QC
£• 2
oc
I
I
I
I
I
Reproducibility
Repeatability
10
20 30
Concentration, mg/m
40
50
60
FIGURE 1. REPEATABILITY AND REPRODUCIBILITY
VERSUS CONCENTRATION
-------
significantly different from some fixed value is de-
pendent upon the actual standard deviation of the
sample population. The variance of the sample popu-
lation includes both the variance of the true values
and the variance due to the measurement method.
A limiting case is discussed in Appendix B under the
assumption that all variation is due to the measure-
ment method. The case is an extremely unlikely, if
not impossible, situation; however, a certain amount
of guidance can be obtained in terms of the numbers
of observations required to provide a specified degree
of agreement. These numbers are sufficient only to
compensate for the variation of the method. An addi-
tional quantity, dependent on the variation in the
true values, will always be required. Interested readers
may refer to Figures B-4 and B-5 and the respective
discussions in Section III-A-3 of Appendix B where
two illustrative examples are given.
6. Accuracy of the Method
There is a statistically significant bias in
the method based upon the results of this collabora-
tive test. The practical significance must be based
upon other criteria.
There is an approximately linear relation-
ship with the tendency for results to be, on the average,
2.5 percent high. (See Figure B-6 in Appendix B for a
graphic illustration.) Since the method uses the same
type materials for calibration as were used for reference
samples in this test, there remains little doubt that the
inaccuracy results almost entirely from the use of cali-
bration gases which exhibit significant variation with
respect to their specified content. Since results tend to
be high, the calibration gases must have a tendency to
be correspondingly low.
It cannot be overemphasized that the ac-
curacy of the method is almost totally dependent upon
the availability of sufficiently accurate calibration
standards.
Section III-B of Appendix B contains fur-
ther details regarding the accuracy of the method and
an examination of the quality of calibration gases.
7. Minimum Detectable Sensitivity
The minimum detectable sensitivity is de-
fined as "the smallest amount of input concentration
that can be detected as the concentration approaches
zero" (see Addenda B of the method in Appendix A).
The best estimate for this parameter is that based on
two standard deviations (replication error); therefore,
the minimum detectable sensitivity may be taken to
be 0.3 mg/m3 Obviously, it is also affected by other
criteria such as chart range and dimensions, recorder
performance, and instrument response. These charac-
teristics varied widely in the collaborative test.
LIST OF REFERENCES
1. Youden, W.J., "The Collaborative Test," Jour-
nal of the AOAC, Vol46, No. 1, pp 55-62
(1963).
2. Handbook of the AOAC, Second Edition,
October 1, 1966.
3. ASTM Manual for Conducting an Interlabora-
tory Study of a Test Method, ASTM STP
No. 335, Am. Soc. Testing & Mats. (1963).
4. 1971 Annual Book of ASTM Standards, Part 30,
Recommended Practice for Developing Precision
Data on ASTM Methods for Analysis and Test-
ing of Industrial Chemicals, ASTM Designa-
tion:El80-67, pp 403422.
5. Westberg, Karl; Cohen, Norman; and Wilson,
K.W.: "Carbon Monoxide: Its Role in Photo-
chemical Smog Formation," Science, Vol 171,
No. 3975, pp 1013-1015 (March 12, 1971).
6. Mandel, John, The Statistical Analysis of Ex-
perimental Data, John Wiley & Sons, New
York, Chapter 13, pp 312-362 (1964).
7. Mandel, J., "The Measuring Process," Tech-
nometrics, l,pp 251-267(1959).
-------
8. Mandel, J., and Lashof, T.W., "The Inter-
laboratory Evaluation of Testing Methods,"
ASTM Bulletin, No. 239, pp 53-61 (1959).
9. Dixon, Wilfred J., and Massey, Frank J., Jr.,
Introduction to Statistical Analysis, McGraw-
Hill Book Company, Inc., New York, Chap-
ter 9, pp 112-129 (1957).
10. Duncan, Ache son J., Quality Control and
Industrial Statistics, Third Edition, Richard D.
Irwin, Inc., Homewood, Illinois, Chapters XXV
and XXVI, pp 473-521 (1965).
11. Bennett, Carl A., and Franklin, Norman L., Sta-
tistical Analysis in Chemistry and the Chemical
Industry, John Wiley and Sons, New York,
Chapter 5, pp 149-164 (1954).
-------
Errata
Appendix A
Reference Method for the Continuous
Measurement of Carbon Monoxide in
the Atmosphere (Non-Dispersive
Infrared Spectrometry)
Page A-l, Section 1.1, lines 4 and 5
delete "split into parallel beams and"
-------
APPENDIX A
REFERENCE METHOD FOR THE CONTINUOUS MEASUREMENT
OF CARBON MONOXIDE IN THE ATMOSPHERE
(NON-DISPERSIVE INFRARED SPECTROMETRY)
Reproduced from Appendix C, "National Primary and Secondary Ambient Air
Quality Standards," Federal Register, Vol 36, No. 84, Part II, Friday,
April 30, 1971
-------
RULES AND REGULATIONS
- . -. @d $&mpl® and
! ,. i -i
APPENDIX C—REFERENCE. .METHOD FOR THE
CONTINUOUS MEASUREMENT OF CARBON
MONOXIDE IN THE ATMOSPHERE (NON-
DISPERSIVE INFRARED SFECTROMETRY)
1. Principle and Applicability.
1.1 This method IB based on the absorp-
tion of Infrared radiation by carbon mon-
oxide. Energy from a source emitting radia-
tion In the infrared region is split Into
parallel beams and directed through ref-
erence and sample cells. Both beams pass
into matched cells, each containing a selec-
D ii." •''•'•--• sii if! ti; it*
tive detector and CO. The CO In the cells
absorb Infrared radiation only at Its charac-
teristic frequencies and the detector Is sensi-
tive to those frequencies. With a nonatasorb-
ing gas In the reference cell, and with no
CO In the sample cell, the signals from
both detectors are balanced electronically.
Any CO introduced into the sample cell will
absorb radiation, which reduces the temper-
ature and pressure in the detector cell and
displaces a" diaphram. This displacement is
detected electronically and amplified to pro-
vide an output signal.
1.2 This method is applicable to the de-
termination of carbon monoxide In ambient
air, and to the analysis of gases under
pressure.
2. Range and Sensitivity.
2.1 Instruments are available that meas-
ure in the range of 0 to 58 mg./m.3 (0-50
p.p.m.), which Is the range most commonly
used for urban atmospheric sampling. Most
instruments measure in additional ranges.
2.2 Sensitivity is 1 percent of full-scale
response per 0.6 mg. CO/m.3 (0.5 p.p.m.).
3. Interferences.
3.1 Interferences vary between individual
instruments. The effect of carbon dioxide
Interference at normal concentrations is
minimal. The primary interference is water
vapor, and with no correction may give an
interference equivalent to as high as 12 mg.
CO/m.3 Water vapor interference can be
minimized by (a) passing the air sample
through silica gel or similar drying agents,
(b) maintaining constant humidity in the
sample and calibration gases by refrigera-
tion, (c) saturating the air sample and cali-
bration gases to maintain constant humid-
ity or (d) using narrowband optical niters
In combination with some of these measures.
3.2 Hydrocarbons at ambient levels do
not ordinarily interfere.
4. Precision, Accuracy, and Stability.
4.1 Precision determined with calibration
gases is ±0.5 percent full scale in the 0-58
mg./m.3 range.
4.2 Accuracy depends on Instrument
linearity and the absolute concentrations
of the calibration gases. An accuracy of ±1
percent of full scale in the 0-58 mg./m.8
range can be obtained.
4.3 Variations in ambient room tempera-
ture can cause changes equivalent to as
much as 0.5 mg. CO/m.8 per °C. This effect
can be minimized by operating the analyzer
in a temperature-controlled room. Pressure
changes between span checks will cause
changes in Instrument response. Zero drift
Is usually less than ±1 percent of full scale
per 24 hours, if cell temperature and pres-
sure are maintained constant.
5. Apparatus.
5.1 Carbon Monoxide Analyser. Commer-
cially available instruments should be in-
stalled on location and demonstrated, pref-
erably by the manufacturer, to meet or
exceed manufacturers specifications and
those described in this method.
5.2 Sample Introduction System. Pump,
flow control valve, and flowmeter.
5.3 Filter (In-line). A filter with a poros-
ity of 2 to 10 microns should be used to
Keep large particles from the sample cell.
5.4 Moisture Control. Refrigeration units
are available with some commercial Instru-
ments for maintaining constant humidity.
Drying tubes (with sufficient capacity to op-
erate for 72 hours) containing Indicating
silica gel can be used. Other techniques that
prevent the Interference of moisture are
satisfactory.
6. Reagents.
6.1 Zero Gas. Nitrogen or helium contain-
ing less than 0.1 mg. CO/m.s
6.2 Calibration Gases. Calibration gases
corresponding to 10, 20, 40, and 80 percent
of full scale are used. Oases must be pro-
vided with certification or guaranteed anal-
ysfls of carbon monoxide content.
6.3 Span Gas. The calibration gas corre-
sponding to 80 percent of full scale Is used
to span the instrument.
7. Procedure.
7.1 Calibrate the Instrument as described
In 8.1. All gases (sample, zero, calibration,
and span) must be introduced Into the en-
tire analyzer system. Figure Cl shows a
typical flow diagram. For specific operating
Instructions, refer to the manufacturer's
manual.
FEDERAL REGISTER, VOL. ,36, NO. 84—FRIDAY, APRIL 30, 1971
A-l
-------
8. Calibration.
8.1 Calibration Curve. Determine the
linearity of the detector response at the
operating flow rate and temperature. Pre-
pare a calibration curve and check the curve
furnished with the instrument. Introduce
zero gas and set the zero control to indicate
a recorder reading of zero. Introduce span
gas and adjust the span control to indicate
the proper value on the recorder scale (e.g.
on 0-58 mg./m.3 scale, set the 46 mg./m.3
standard at 80 percent of the recorder
chart). Recheck zero and span until adjust-
ments are no longer necessary. Introduce
intermediate calibration gases and plot the
values obtained. If a smooth curve is not
obtained, calibration gases may need
replacement.
9. Calculations.
9.1 Determine the concentrations directly
from the calibration curve. No calculations
are necessary.
9.2 Carbon monoxide concentrations in
mg./m.3 are converted to p.p.m. as follows:
p.p.m. C0 = mg. CO/m.3XO-873
10. Bibliography,
The Intech NDIR-CO Analyzer by Frank
McElroy. Presented at the llth Methods
Conference in Air Pollution, University of
California, Berkeley, Calif., April 1, 1970.
Jacobs, K. B. et al., J.A.P.C.A. 9, No. 2,
110-114, August 1959.
MSA LIRA Infrared Gas and Liquid Ana-
lyzer Instruction Book, Mine Safety Appli-
ances Co., Pittsburgh, Pa.
BecKman Instruction 1635B, Models 215A,
3 ISA and 415A Infrared Analyzers, Beckman
Instrument Company, Fullerton, Calif.
Continuous CO Monitoring System, Model
A 5611, Intertech Corp., Princeton, N.J,
Bendix—UNOR Infrared Gas Analyzers*
Ronceverte, W. Va.
A. Suggested Performance Specifications
for NDIR Carbon Monoxide Analysers:
Range (minimum) ------ 0-58 mg./m.B
(0-50 p.p.m.).
Output (minimum) _____ 0-10, 100, 1,000,
5,000 mv. lull
scale.
0.6 mg./m.B (0.5
RULES AND REGULATIONS
Output—Electrical signal which is propor-
tional to the measurement; intended for
connection to readout or data processing
devices. Usually expressed as millivolts or
milliamps full scale at a given impedance.
Full Scale—The maximum measuring limit
for a given range.
Minimum Detectable Sensitivity—The small-
est amount of Input concentration that
can be detected as the concentration ap-
proaches zero.
Accuracy—The degree of agreement between
a measured value and the true value; usu-
ally expressed as ± percent of full scale
Lag Time—The time interval from a step
change in input concentration at the in-
strument inlet to the first corresponding
change in the instrument output.
Time to 90 percent Response—The time in-
terval from a step change in the input
concentration at the instrument inlet to
a reading of 90 percent of the ultimate
recorded concentration.
Rise Time (90 percent)—The Interval be-
tween initial response time and time to 90
percent response after a step increase in
the inlet concentration.
Fall Time (90 percent)—The Interval be-
tween initial response time and time to
90 percent response after a step decrease
in the inlet concentration.
Zero Drift—The change in instrument out-
put over a stated time period, usually 24
hours, of unadjusted continuous opera-
tion, when the Input concentration is
zero; usually expressed as percent full
scale.
SAMPLE INTRODUCTIOM
Minimum detectable sen-
eitivity.
Lag time (maximum) —
Time to 9O percent re-
sponse (maximum).
Rise time, 90 percent
(maximum) .
Fall time, 90 percent
(maximum).
Zero drift (maximum) —
Span drift (maximum)--
p.pjn.).
15 seconds.
30 seconds.
15 seconds.
15 seconds.
3 percent/ week,
not to exceed
1 percent/ 24
hours.
3 percent /week,
not to exceed
1 percent/ 24
hours.
±0.5 percent.
3 days.
Precision (minimum) ___
Operational period (min-
Imum) .
Noise (maximum) _______ ±0.5 percent.
Interference equivalent l percent of full
(maximum) . scale.
Operating temperature 5-40° C.
range (minimum) .
Operating humidity range 10-100 percent.
(minimum) .
Linearity (maximum de- 1 percent of full
viation) . scale.
B. Suggested Definitions of Performance
Specifications:
Range — The minimum and maximum meas-
urement limits,
Span Drift—The change in instrument out-
put over a stated time period, usually 24
hours, of unadjusted continuous opera-
tion, when the input concentration is a
stated upscale value; usually expressed as
percent full scale.
Precision—The degree of agreement between
repeated measurements of the same con-
centration, expressed as the average devia-
tion of the single results from the mean.
Operational Period—The period of time over
which the instrument can be expected to
operate unattended, within specifications. •
Noise—Spontaneous deviations from a mean
output not caused by input concentration
changes.
Interference—An undesired positive or nega-
tive output caused by a substance other
than the one being measured,
Interference Equivalent—The portion of
indicated input concentration due to the
presence of an interferent.
Operating Temperature Range—The range
of ambient temperatures over which the
instrument will meet all performance
specifications.
Operating Humidity Range—The range of
ambient relative humidity over which the
instrument will meet all performance
specifications.
Linearity—The maximum deviation between
an actual instrument reading and the
reading predicted by a straight line drawn
between upper and lower calibration
points.
ANALYZER SYSTEM
SPAM
AND
CALIBRATION
!. R. ANALYZER
VENT-<-
VALVE
Figure C1. Carbon monoxide analyzer flow diagram.
FEDERAL REGISTER, VOL. 36, NO. 84—FRIDAY, AWIIL 30, 1971
A-2
-------
APPENDIX B
STATISTICAL DESIGN AND ANALYSIS
-------
TABLE OF CONTENTS
Page
I. INTRODUCTION B-l
A. Purpose and Scope of the Experiment B-l
B. Design of the Experiment • • ... B-l
C. Presentation of the Data B-2
II. STATISTICAL ANALYSIS B-3
A. Replication Error B-3
B. Humidity Effects . . . . B-5
C. Linear Model Analysis B-6
III. INTERPRETATION OF THE PARAMETERS B-12
A. Precision of the Method . . • • B-12
B. Accuracy of the Method . .... ... . . . . B-15
LIST OF REFERENCES . . B-20
B-i
-------
LIST OF ILLUSTRATIONS
Figure
B-1
B-2
B-3
B-4
B-5
R-fi
Control Charts for Means, Slopes, and Standard Errors of Estimate for
Repeatability and Reproducibility Versus Concentration .
Expected Agreement Between Two Means Versus Concentration for Various
Expected Agreement Between a Mean and a Fixed Value Versus Concentration
for Various Numbers of Observations (95 Percent Level of Significance) . .
Rial or Svstematir Frrnr VprsiK Hnnrfintration ... . ....
Page
B-2
. . B-9
. . B-12
B-16
. . B-17
B-18
LIST OF TABLES
Table Page
B-l Means and Standard Deviations for Each Cell of Data from the Collaborative Test . B-4
B-ll Differences Between Humidified and Dry Test Results ... . B-5
B-l 11 Test of Hypothesis That the Mean Difference Between Humidified and Dry Samples
Is Equal to Zero ... . . . . B-6
B-IV Means and Standard Deviations for Each Laboratory for Each Sample .... B-8
B-V Means, Slopes, and Standard Errors of Estimate for Linear Model Analysis B-9
B-VI Analysis of Variance for Linear Model . ... . . B-10
B-VII Summary of Results for Variance Components and Derived Quantities for Linear
Model Analysis . . . . . .... B-ll
B-VIII Sources of Variability and Their Relative Importance for the Linear Model Analysis . . B-ll
B-IX Standard Errors of Estimate for Calibration Curves Prepared from Calibration Gases
and from Reference Gases ... . ... B-19
B-ii
-------
APPENDIX B
STATISTICAL DESIGN AND ANALYSIS
I. INTRODUCTION
In the application of interlaboratory testing
techniques, the first step is to determine the exact
purpose of the program. There are many, and the
particular one must be established. All subsequent de-
tails of the program must be planned keeping the
prime objective in mind. This appendix describes the
design and analysis of the formal collaborative test of
the Reference Method for the Continuous Measure-
ment of Carbon Monoxide in the Atmosphere (Non-
Dispersive Infrared Spectrometry).
A. Purpose and Scope of the Experiment
The basic objective of the interlaboratory study
is to derive precise and usable information about the
variability of results produced by the measurement
method. This information is necessary to establish the
reliability of the method in terms of its precision and
its accuracy. More emphasis was placed on the in-
herent quality of the method when properly used
than upon the performance of the laboratories.
The statistical planning of the program, which
necessarily must be limited in scope, depends upon
what information is desired. The scope is limited by
what a collaborating laboratory can conveniently and
economically accomplish, as well as by the number of
collaborators that can be accommodated. Under these
limitations, it was possible to examine the effects of
laboratories, concentrations, days, and replication
upon the precision of the method, in addition to esti-
mating the effects of humidity upon the analysis. The
experiment was designed so that the analysis of vari-
ance technique could be used.
A total of 16 laboratories took part in the pro-
gram. An analyst representing each laboratory went
through the familiarization phase and subsequently
conducted the formal collaborative testing. These in-
dividuals and their affiliations have been identified
elsewhere in the main report. These laboratories con-
stitute a random sample from a rather large popu-
lation of experienced laboratories.
Three different concentrations were analyzed
by each laboratory. The concentrations were nomi-
nally 8, 30, and 53 mg/m3 These concentrations
were selected to approximate the low range, the inter-
mediate range, and the high range for the method.
Due to variations among the test gas cylinders, it was
not possible for each laboratory to have test atmo-
spheres having the exact values above; however, the
expected concentrations are known with confidence,
and the deviations of the observed values from the
expected values may be examined.
In addition to the analysis of the dry gases,
each of the three concentrations was analyzed after
humidification according to the technique illustrated
in the main report. This information was for the pur-
pose of testing the effectiveness of the various mois-
ture compensation options used in the method.
It was desirable to retrieve information which
would allow the investigation of various steps within
the method; therefore, emphasis was placed upon
obtaining intermediate data relating to calibration
curves, moisture compensation methods, instrument
ranges, instrument models, and sources of calibration
gas. As a result, a substantial amount of data was
obtained in addition to the end result of the analyti-
cal procedure.
B. Design of the Experiment
A properly planned collaborative test should
allow the analysis of the results by the analysis of
variance technique or by a procedure which incorpo-
rates this technique.U"5) In general, analysis of vari-
ance techniques are more efficient than the simpler
control chart techniques. Since the cost of statistical
analysis is small compared to the total cost involved
in a collaborative test, it is desirable to use the most
B-l
-------
efficient statistical methods available in analyzing the
results. High efficiency in data utilization is impor-
tant if the amount of data is limited.
The form of the analysis depends upon the sta-
tistical model under consideration. Several separate
statistical analyses were performed in order to deter-
mine the necessary parameters. Each of these analyses
will be described in detail in later subsections.
The overall design of the experiment can best
be shown by the diagram in Figure B-l. It can be seen
that one analyst in each of 15 laboratories analyzed,
in triplicate, each of three concentrations, both dry
and humidified, on each of three separate days, re-
sulting in a total of 810 individual determinations.
Independent calibration curves were used on each
day. The data are presented appropriately in the next
subsection. In collaborative testing, two general
sources of variability can be readily detected. First,
the variability between laboratories can be estimated.
This is frequently the largest source of variability and
is not under the control of the investigator. Second,
the within-laboratory variability can be estimated.
This source is under the control of the investigator to
the extent that the separate components which make
up this source may be identified separately. These
separate components, of varying magnitude and im-
portance, may be measured if the proper design has
been employed. Alternatively, the separate sources
may be confounded or lumped into a single variable
by altering the design. By employing the design
above, separate estimates could be made of the varia-
bility between days and of the variability between
replicates. These two components, appropriately
combined, constitute the within-laboratory source of
variability.
Additional assumptions and rationale for each
of the analyses listed previously will be stated later as
the analysis is described and applied. If appropriate,
the statistical model will be stated in the respective
discussion.
C. Presentation of the Data
The data resulting from the experiment are
rather voluminous; however, it is essential that these
data be tabulated for future reference. In addition to
their necessity as supporting information for the prob-
lem at hand, the data are also valuable academically as a
source of data for the development, evaluation, and
comparison of new statistical techniques. Therefore,
the more voluminous raw data will be found in Appen-
dix C. Data subsets and averages will be presented in
this appendix, as appropriate, along with the discussion
of the respective statistical analysis.
In presenting the data, all identifiable arithmet-
ic errors have been corrected. The data of Laboratory
1 1
L! Li L1B
(same as L^ )
1
DT D2 D3
(same as D-\ )
I
HI
I
HI
n
H2
1 2 3
FU R3
R2 R3
FIGURE B-l. DESIGN OF CARBON MONOXIDE METHOD EXPERIMENT. L, LABORATORIES;
D, DAYS; C, CONCENTRATIONS; H, HUMIDITIES; AND R, REPLICATES
B-2
-------
780 have been recalculated omitting an extremely sus-
picious calibration gas. The raw data from 15 of the 16
collaborating laboratories can be seen in Table C-I. One
laboratory failed to report complete and usable results.
It is not convenient to have a separate subsec-
tion concerning the tests for and disposition of out-
lying observations. Since there were several statistical
analyses and several types of outliers, the outlying
observations, if any, will be identified in the respec-
tive analysis.
II. STATISTICAL ANALYSIS
provides its own estimate of the replication error
with two degrees of freedom. The desired repli-
cation error is the combined estimate of these in-
dividual estimates, but the question is whether and
how these should be combined. Three factors must
be investigated in order to answer this question.
First, outlying observations must be identified and
dealt with. Second, it must be determined if the
replication error is a function of concentration.
Third, it must be determined if the replication
error is affected by humidity. The techniques for
each of these analyses are discussed in the follow-
ing paragraphs.
Because this study incorporates several statisti-
cal techniques, each with its own common notation,
certain complications involving consistency of mathe-
matical notation arise. To minimize the confusion, a
foldout notation guide is provided at the end of this
report. The symbols have been categorized according
to their respective use; however, duplicate entries
were avoided where there was no conflict or incon-
sistency. This guide will materially assist the reader
throughout this report and may be left folded out for
ready reference at any time.
A. Replication Error
To avoid ambiguity, the term replication must
be explicitly defined. In the context of this study,
replicates are defined to be successive determinations
with the same operator and instrument on the same
sample within intervals short enough to avoid change
of environmental factors, and with no intervening
manipulations other than zero adjustment. In general,
this will mean that time intervals between successive
replicates will be on the order of a few to several
minutes. Defined in this way, the replication error
will primarily reflect the effects of instrument charac-
teristics such as sensitivity, response time, and read-
out noise. The effects of changing environmental
factors will not be included.
The determination of the replication error is
straightforward from the data in Table C-l. Each cell
The means and standard deviations for each cell
are shown in Table B-I. The data from laboratories
not running replicates consistent with the previous
definition are marked with an asterisk and cannot be
used in the estimation of the replication error. The
data from laboratories not reporting results to the
nearest tenth of a milligram per cubic meter were also
omitted and are marked with a dagger. It would not
be consistent to estimate standard deviations of the
magnitudes involved from data rounded to the
nearest unit. Inspection of the remaining standard devi-
ations in Table B-I reveal several suspicious results.
These remaining data were tested for outliers by Coch-
ran's test*-6) applied to each column of standard devia-
tions in Table B-I. The observations thus identified as
outliers (99 percent level of significance) have been
marked with a double dagger in the table. The values at
the foot of each column of standard deviations indicate
the magnitude of the pooled estimate and its degrees of
freedom for the respective column. The pooled esti-
mates were computed according to usual practice/7)
These results indicate that the replication error is not
affected by concentration or by humidity within the
limits included in the test. Statistical tests and regres-
sion analysis, although hardly necessary, verify this
conclusion. Therefore, all individual estimates may be
pooled into the final estimate for the replication error
ae which is 0.17 mg/m3 (286 degrees of freedom).
Beyond this point, the individual values within
each cell are no longer required and all further analyses
of the data are made using only the cell averages.
B-3
-------
TABLE B-I. MEANS AND STANDARD DEVIATIONS FOR EACH CELL OF DATA FROM THE
COLLABORATIVE TEST. First figure in each cell is the mean and the second figure
is the standard deviation.
Laboratory
Code Number
220
222
253
270
310
311
370
375
540
571
780
799
860
920
927
Day
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
1
2
3
1
2
3
1
2
3
Mean
D.F.
Low Concentration
Dry
8.4 0.00
8.5 0.12
8.6 0.00
6.9 O.OOt
6.9 0.00*
6.9 O.OOf
8.0 O.OOf
9.2 O.OOt
8.0 O.OOf
7.3 0.64*
8.0 1.15*
8.8 0.69*
9.0 0.35$
9.1 0.17
9.1 0.31
9.1 0.21*
8.6 0.06*
9.5 0.12*
8.2 0.00
8.6 0.00
8.0 0.00
7.3 0.00
7.2 0.06
7.7 0.10
8.6 0.12
8.9 0.12
8.9 0.16
8.2 0.00
8.6 0.06
8.9 0.06
8.1 0.10
8.8 0.15
8.2 0.25
7.9 0.29
8.3 0.31
8.0 0.00
7.4 O.OOf
7.4 O.OOt
7.4 O.OOt
8.0 O.OOt
8.0 O.OOJ
8.0 O.OOf
8.9 0.00
8.9 0.00
8.9 0.00
0.13
26
Humid
8.6 0.00
8.6 0.06
8.7 0.06t
7.0 0.64*
7.4 0.00*
7.2 0.29f
8.0 O.OOf
9.0 0.35f
8.0 O.OOf
7.7 1.33*
8.0 0.00*
8.4 0.69*
8.3 0.31
8.8 0.12
8.8 0.00
9.5 0.15*
9.3 0.00*
9.7 0.25*
8.3 0.23
8.6 0.00
8.1 0.12
7.2 0.06
7.2 0.06
7.7 0.06
8.6 0.06
8.8 0.20
8.6 0.06
7.9 0.23
8.6 0.06
8.7 0.40
12.0 0.10
12.3 0.25
11.9 0.12
8.2 0.00
8.0 0.00
9.0 0.64f
7.4 O.OOf
7.4 O.OOf
7.4 O.OOt
8.0 O.OOf
8.0 O.OOt
8.0 O.OOJ
8.9 0.00
8.9 0.00
8.9 0.00
0.20
24
Intermediate Concentration
Dry
30.5 0.06
30.3 0.21
30.5 0.00
28.6 O.OOt
29.0 0.35*
29.0 0.69f
31.1 0.35f
32.1 O.OOf
30.9 O.OOt
30.5 0.64*
31.3 0.69*
31.7 0.69*
31.3 0.17
31.2 0.30
31.3 0.17
31.4 0.10*
31.5 0.06*
31.0 0.06*
30.6 0.00
30.6 0.00
30.0 0.35
30.3 0.12
29.6 0.00
30.8 0.17
30.3 0.29
30.5 0.15
30.5 0.06
29.4 0.32
30.2 0.35
30.6 0.17
30.7 0.21
30.5 0.15
30.5 0.23
29.9 0.00
29.5 0.31
31.1 0.17
30.4 O.OOt
30.4 O.OOt
30.4 O.OOt
30.2 0.64f
32.1 O.OOt
32.1 O.OOt
32.1 O.OOt
32.1 O.OOt
32.1 O.OOt
0.19
23
Humid
30.4 0.00
30.2 0.15
30.5 0.00
28.6 0.45*
29.8 0.60*
28.1 1.53t
30.9 O.OOt
32.1 O.OOt
30.9 O.OOJ
31.7 1.33*
32.1 0.00*
31.7 0.69*
30.3 0.23
30.6 0.25
31.4 0.17
31.2 0.06*
31.2 0.00*
30.9 0.10*
30.6 0.06
30.7 0.15
29.9 0.17
29.6 0.23
29.6 0.06
30.4 0.17
30.0 0.06
30.5 0.15
30.5 0.06
29.2 0.06
29.9 0.17
30.3 0.17
33.4 0.35
33.6 0.17
32.8 0.17
29.8 0.85 J
29.2 0.60J
31.0 0.17
30.4 O.OOt
30.4 O.OOt
30.4 O.OOt
30.5 0.64f
31.7 0.69t
32.1 O.OOt
32.1 O.OOt
32.1 O.OOt
32.1 O.OOt
0.15
25
High Concentration
Dry
53.2 0.23
52.3 0.35
53.3 0.00
52.7 O.OOt
53.1 0.35*
53.5 0.86f
53.8 O.OOt
53.8 O.OOt
53.8 O.OOt
56.5 2.66*
55.4 0.64*
55.0 0.00*
55.6 0.00
55.3 0.31
55.9 0.17
53.4 0.06*
54.3 0.10*
53.5 0.17*
54.4 0.00
54.2 0.00
53.4 0.12
54.1 0.00
53.4 0.20
54.2 0.06
53.1 0.17
52.8 0.42J
52.9 0.06
49.7 0.12
50.8 0.17
51.7 0.35
52.6 0.26
52.7 0.15
53.2 0.15
53.2 0.23
54.3 0.12
54.7 0.23
52.7 O.OOt
52.7 O.OOt
52.7 O.OOt
53.8 O.OOt
55.0 O.OOJ
55.0 O.OOt
55.0 O.OOt
55.0 O.OOt
55.0 O.OOt
0.17
22
Humid
53.4 0.06
52.3 0.35
52.8 0.12
52.7 0.00*
54.0 0.87*
53.3 O.OOt
53.8 O.OOt
54.8 0.35t
54.2 0.35f
56.1 1.96*
55.4 0.64*
55.0 0.00*
53.9 0.17
54.5 0.12
55.3 0.23
52.8 0.10*
53.4 0.06*
52.9 0.06*
54.4 0.00
54.2 0.06
53.4 0.12
53.4 0.59t
53.3 0.12
53.2 0.20
53.3 0.00
52.8 0.10
53.0 0.21
49.3 0.38
50.4 0.30
50.9 0.23
54.3 0.00
54.5 0.00
54.3 0.31
52.4 0.31
50.9 0.17
54.4 0.17
52.7 O.OOt
52.7 O.OOt
52.7 O.OOt
53.8 O.OOt
54.6 0.69f
53.8 O.OOJ
55.0 O.OOt
55.0 O.OOt
55.0 O.OOt
0.20
23
*Not consecutive replicates.
t Results not reported to nearest 0.1 mg/m3 -
:£ Outlying observations.
B-4
-------
B. Humidity Effects
Since humidity is a known interference, the ex-
periment was designed to measure the effectiveness of
the various methods of humidity compensation listed
in the method (see Section 3.1 of the method in
Appendix A). The result of the design was to provide
two levels for this factor-one dry and the other
essentially saturated. The technique for this humidifi-
cation step has been discussed in the main report.
Three of the four options for humidity com-
pensation listed in the method were used in the col-
laborative test. No potential collaborator reported the
use of option (c) which is "saturating the air sample
and calibration gases to maintain constant humidity."
Therefore, this option could not be included. Five
laboratories used option (a) using drying agents, and
six laboratories used option (b) using refrigeration.
Four laboratories used option (d) using narrow-band
optical filters. Two of these laboratories used optical
filters alone, and two used optical filters in combina-
tion with other methods. These laboratories will be
identified subsequently when the data are presented.
The effects of humidity can best be determined
by pairing the data within days and within concentra-
tions since they are not independent pairs. Statistical
techniques to analyze these differences test whether
the mean difference is significantly different from
zero.(8) In addition to analysis of all differences to-
gether, the three subclasses of humidity compensa-
tion methods may be analyzed separately to determine
whether there are differences in the effectiveness of
the respective humidity compensation methods.
The data are shown in Table B-II where the
entries are the differences in the means of the three
replicates for each humidity level. Each entry is iden-
tified according to its respective humidity compensa-
tion method as shown by the symbols and their
respective footnotes. These data can be shown to be
not normally distributed—either overall or within
concentrations. The data from two laboratories, 780
and 799, make the major contribution to non-
normality. These two laboratories used optical filters
and it is obvious that they are not completely
effective; however, the one large negative departure
for Laboratory 799 is probably an outlier. The data
for laboratories using optical filters are not further
analyzed due to the small number of laboratories
using this method; however, it appears that the use of
optical filters in combination with other methods
gives satisfactory results.
The data for options (a) and (b), which are nor-
mally distributed, are analyzed separately and the
TABLE B-II. DIFFERENCES BETWEEN HUMIDIFIED AND DRY TEST RESULTS. The figures for each day for each
concentration for each laboratory are the result of subtracting the dry result from the humidified result, each
the average of triplicates. Differences are in milligrams per cubic meter.
Laboratory
Code Number
220b
222b
25 3a
270b
310b
311d
370b
375a'd
540b
571a
780d
799a,d
860a
920a
927a
Low
Concentration
0.2 0.1 0.1
0.1 0.5 0.3
0.0 -0.2 0.0
0.4 0.0 -0.4
-0.7 -0.3 -0.3
0.4 0.7 0.2
0.1 0.0 0.1
-0.1 0.0 0.0
0.0 -0.1 -0.3
-0.3 0.0 -0.2
3.9 3.5 3.7
0.3 -0.3 1.0
0.0 0.0 0.0
0.0 0.0 0.0
0.0 0.0 0.0
Intermediate
Concentration
-0.1 -0.1 0.0
0.0 0.8 -0.9
-0.2 0.0 0.0
1.2 0.8 0.0
-1.0 -0.6 0.1
-0.2 -0.3 -0.1
0.0 0.1 -0.1
-0.7 0.0 -0.4
-0.3 0.0 0.0
-0.2 -0.3 -0.3
2.7 3.1 2.3
-0.1 -0.3 -0.1
0.0 0.0 0.0
0.3 -0.4 0.0
0.0 0.0 0.0
High
Concentration
0.2 0.0 -0.5
0.0 0.9 -0.2
0.0 1.0 0.4
-0.4 0.0 0.0
-1.7 -0.8 -0.6
-0.6 -0.9 -0.6
0.0 0.0 0.0
-0.7 -0.1 -1.0
0.2 0.0 0.1
-0.4 -0.4 -0.8
1.7 1.8 1.1
-0.8 -3.4 -0.3
0.0 0.0 0.0
0.0 -0.4 -1.2
0.0 0.0 0.0
^Passing the aii sample through silica gel or similar drying agent.
.Maintaining constant humidity in the sample and calibration gasses by refrigeration.
Using narrow-band optical filters in combination with other measures.
B-5
-------
TABLE B-IH. TEST OF HYPOTHESIS THAT THE MEAN DIFFERENCE
BETWEEN HUMIDIFIED AND DRY SAMPLES IS EQUAL TO ZERO
Statistic
Number of
Observations
Mean
Difference
Standard
Deviation
t-value
Degrees of
Freedom
Drying Agents
Concentration*
A
15
-0.05
0.10
-1.82
14
B
15
-0.07
0.18
-1.62
14
C
15
-0.12
0.50
-0.93
14
All
45
-0.08
0.31
-1.75
44
Refrigeration
Concentration*
A
18
-0.01
0.30
-0.16
17
B
18
-0.01
0.54
-0.04
17
C
18
-0.16
0.53
-1.24
17
All
54
-0.06
0.47
-0.90
53
*A is low concentration, B is intermediate concentration, C is high concentration, and All is all concentrations combined.
results are summarized in Table B-III. No values of
the t-statistics^8) are significant at the 95 percent
level of significance; therefore, the hypothesis of
mean differences equal to zero is accepted. Both
methods of moisture compensation appear to be
equally satisfactory in comparison with the precision
capabilities of the method.
An analysis of variance of the differences in
Table B-II (omitting Laboratories 780 and 799) indi-
cates a significant variation between laboratories with
respect to the variation between days. Both the varia-
tion between laboratories and the variation between
days appear to be dependent upon concentration;
however, the data are erratic in this respect and the
results are inconclusive.
Using the previously determined replication
error and the preliminary estimates of the precision
between days (0.3, 0.4, and 0.5 mg/m3 for the low,
intermediate, and high concentrations, respectively),
an examination of the significance of the magnitude
of individual differences can be made. According to
these estimates, differences of less than 0.9, 1.2, and
1.4 mg/m3 for the low, intermediate, and high con-
centrations, respectively, may be accounted for
95 percent of the time by chance alone. Excluding
Laboratories 780 and 799, relatively few observations
exceed these amounts.
The humidity has no measurable effect upon
the accuracy of the method and does not appear to
contribute significantly to the precision.
C. Linear Model Analysis
The assumption made in linear model analysis is
that systematic differences exist between sets of
measurements made by different observers in differ-
ent laboratories, and that these systematic differences
are linear functions of the magnitude of the measure-
ments. Hence, the technique is called "the linear
model."(1>3~5) The linear model leads to a simple
design, but requires a special method of statistical
analysis, geared to the practical objectives of collabo-
rative tests.
The general design is as follows: to each of p
laboratories, q materials have been sent for test, and
each laboratory has analyzed each material n times.
Now, the n determinations made by the ith labora-
tory on the ]th material constitute what will be de-
noted as the "ij cell." The n replicates of any particu-
lar cell are viewed as a random sample from a theore-
tically infinite population of measurements within
that cell. The laboratories, however, are not con-
sidered as a random sample from a larger population
of laboratories, but are considered as fixed variables.
Therefore, the inferences involving the variability
among laboratories is limited, at least theoretically, to
B-6
-------
those laboratories participating in the test. The set of
values which corresponds to the q materials is viewed
as a fixed variable, but each material is considered to
be a random selection from a population of materials
with the same "value." This model allows for noncon-
stant, nonrandom differences between laboratories.
The method is not as sensitive to outliers as is the
conventional analysis of variance where even a single
outlier may result in an unusually large interaction
term.
This collaborative test has a nested design in
order to allow the differentiation between the repro-
ducibility of results made almost simultaneously and
that of results obtained on different days. The term
replicate in the paragraph above includes both the
replication error as it has been previously defined in
this appendix as well as the within-laboratory be-
tween-days precision yet to be determined.
In view of the results of the analysis of humid-
ity effects discussed in the previous subsection, it is
appropriate to combine the data from both dry and
humidified test concentrations in this linear model
analysis. Since humidity has no apparent effect on
either precision or accuracy, there is no reason not to
combine the data.
The data in Table B-IV provide the basis for the
determination of the between-days precision as well
as for the subsequent linear model analysis. The
means and standard deviations have been computed
as follows:
k=w
ytj
C +
w
k=w
4-=-
w- 1
(B-l)
(B-2)
where
(B-3)
Each yfjk is rounded to 0.1 mg/m3 before subsequent
use in Equation (B-l) or (B-2). For the particular
model, there are p = 15 laboratories, q = 6 concentra-
tions or samples, w = 3 days, and n = 3 replicates. The
values of c,y are shown in Table C-II of Appendix C
and the values of c, are 8, 30, and 53 mg/m3 for the
low, intermediate, and high concentrations, respec-
tively. The reference values are the same for both dry
and humidified samples; hence there are only three
values whereas q is equal to 6.
The foregoing treatment is necessary in order to
remove the variations due to the differences in indi-
vidual test gas concentrations within a given concen-
tration level. In estimating the replication error or the
between-days precision, such treatment was not
necessary; however, it was required for subsequent
analysis involving variations between laboratories.
The data in Table B-IV are arranged by column
for samples and by rows for laboratories with two
entries for each cell—the upper is the mean and the
lower is the standard deviation. Inspection of the
standard deviations reveals some suspiciously high
values which must be tested to determine whether
they are outliers. Each standard deviation has
w — 1 degrees of freedom, and each column may be
examined by Cochran's test/6) One observation thus
identified as an outlier (99 percent level of signifi-
cance) has been marked with an asterisk. The values
at the foot of each column show the value for the
pooled estimate for the column and also the respec-
tive degrees of freedom computed in accordance with
usual practice/7)
Further examination of the pooled estimates
for each column by regression analysis indicates that
there is no significant correlation of standard devia-
tion with concentration. Therefore, all individual
estimates may be pooled into a single value equal to
0.45 mg/m3 (178 degrees of freedom).
The value of 0.45 mg/m3 corresponds to F(e),
which is the replication variance in the context of the
general linear analysis modelA^-S) \i can be
partitioned into the between-days precision and the
B-7
-------
TABLE B-IV. MEANS AND STANDARD DEVIATIONS FOR EACH LABORATORY FOR EACH SAMPLE. Upper number in
each cell is mean and lower number is standard deviation. Values in milligrams per cubic meter.
Laboratory
Code Number
220
222
253
270
310
311
370
375
540
571
780
799
860
920
927
Pooled Estimate
D.F.
Dry
Low
Concentration
8.1
0.10
6.3
0.00
7.9
0.69
7.6
0.75
8.6
0.06
8.5
0.45
7.7
0.31
7.2
0.26
8.3
0.17
8.1
0.35
8.0
0.38
7.7
0.21
7.2
0.00
7.4
0.00
8.5
0.00
0.34
30
Medium
Concentration
30.5
0.12
28.7
0.23
31.3
0.64
31.3
0.61
31.5
0.06
31.5
0.26
30.5
0.35
30.0
0.60
30.5
0.12
30.1
0.61
30.8
0.12
30.0
0.83
30.5
0.00
31.7
1.10
32.0
0.00
0.50
30
High
Concentration
53.3
0.55
54.0
0.40
54.5
0.00
56.4
0.78
56.4
0.30
54.1
0.49
54.9
0.53
54.6
0.44
53.6
0.15
51.4
1.00
53.6
0.32
54.8
0.78
53.4
0.00
55.3
0.69
55.7
0.00
0.52
30
Humidified
Low
Concentration
8.2
0.06
6.6
0.20
7.8
0.58
7.6
0.35
8.1
0.29
8.9
0.20
7.7
0.25
7.2
0.29
8.2
0.12
7.9
0.44
11.7
0.21
8.0
0.53
7.2
0.00
7.4
0.00
8.5
0.00
0.30
30
Medium
Concentration
30.5
0.15
28.6
0.87
31.2
0.69
31.9
0.23
31.0
0.57
31.3
0.17
30.5
0.44
29.7
0.46
30.4
0.29
29.8
0.56
33.5
0.42
29.8
0.92
30.5
0.00
31.6
0.83
32.0
0.00
0.53
30
High
Concentration
53.2
0.55
54.2
0.65
55.0
0.50
56.3
0.56
55.4
0.70
53.4
0.32
54.9
0.53
54.0
0.10
53.7
0.25
50.9
0.82
55.2
0.12
53.3
1.76*
53.4
0.00
54.8
0.46
55.7
0.00
0.47
28
*Outlying observation.
replication error as defined in this study according to
the relationship
V(e) = o}>
(B-4)
To reduce confusion as much as possible, V(e) will be
used to denote the variance for replication in the con-
text of linear model analysis, and a\ will be used to
denote the variance for replication as defined in this
study. Solving Equation (B-4) with V(e) = 0.45,
ae =0.17,and« = 3yieldscT£, = 0.44 mg/m3 (161 de-
grees of freedom) for the value of the standard devia-
tion for between-days precision. The effects of environ-
mental factors and calibration procedures are included
in this error term.
Since there was no significant correlation of be-
tween-days precision with concentration, there was no
B-8
-------
need to make any transformation of scale, and the
following linear model analysis was thus made upon
the means in Table B-IV.
On the assumption of linear relationships
among the p laboratories, it follows that the values
obtained by each laboratory are linearly related to
the corresponding average values of all laboratories.
Each of the means in Table B-IV may be plotted ver-
sus its respective column mean. This should be a
linear function, and the points corresponding to each
line may be represented by three parameters: a mean;
a slope; and a quantity related to the deviation from
linearity, the standard error of estimate. These param-
eters are determined by a least-squares regression
analysis, and the results are shown in Table B-V. The
data of Laboratory 780 have been eliminated from
this analysis because of the large differences between
dry and humidified samples. The linear model analy-
sis by itself will reveal any other laboratory outliers.
TABLE B-V. MEANS, SLOPES, AND STANDARD
ERRORS OF ESTIMATE FOR LINEAR MODEL
ANALYSIS. (Omitting Laboratory 780) Data in
milligrams per cubic meter.
Laboratory
Code Number
220
222
253
270
310
311
370
375
540
571
799
860
920
927
Mean
Mean
30.63
29.73
31.28
31.85
31.83
31.28
31.03
30.45
30.78
29.70
30.60
30.37
31.37
32.07
30.93
Slope
0.9697
1.0248
1.0083
1.0482
1.0226
0.9686
1.0150
1.0129
0.9762
0.9277
0.9936
0.9932
1.0244
1.0148
1.0000
Standard Error
of Estimate
0.13
0.74
0.34
0.26
0.44
0.37
0.27
0.32
0.16
0.44
0.59
0.35
0.47
0.20
0.41*
*Pooled estimate.
A plot of the lines represented by the means
and slopes from Table B-V would result in a rela-
tively tight bundle of straight lines, each line rep-
resenting a particular laboratory. Only the lines for
Laboratories 222 and 571 depart from the cluster
enough to be recognized; therefore, the plot was
not reproduced in this report. Both the means and
the slopes approximate normal distributions, and
no outliers can be detected in either.
Inspection of the standard errors of estimate
from Table B-V reveals one suspiciously high value;
however, these standard errors of estimate have an
approximate chi-square distribution and no outliers
can be identified.
These data may be more easily compared from
the graphic presentation in Figure B-2 where they
have been sorted into an ascending order relative to
the means. This sorting often reveals effects not read-
ily visible otherwise. Control limits, based upon
deviation from linearity, are shown for the means and
the slopes. These 95 percent control limits indicate
several points to be "out of control." This indicates
that the differences between laboratories cannot be
n 0.75
E
571 222 360 375 799 220 540 370 311 253 920 310 270 927
Laboratory Number
FIGURE B-2. CONTROL CHARTS FOR MEANS, SLOPES,
AND STANDARD ERRORS OF ESTIMATE FOR
LINEAR MODEL ANALYSIS.
(Omitting Laboratory 780).
B-9
-------
accounted for by experimental error alone. Exami-
nation of Figure B-2 reveals which laboratories
showed the greatest departures from the overall
mean, which laboratories showed the greatest depar-
ture from unit slope, and which laboratories were re-
sponsible for the greatest deviations in linearity.
When viewing this figure, it is important to watch for
relationships between the parameters.
The next step is an analysis of variance which
was performed according to the technique of
Mandel/3) and the results are shown in Table B-VI.
The interested reader may consult the appropriate
reference for the theory and details of the analysis.
The next step in linear model analysis is to de-
termine whether a correlation exists between the
means and the slopes. Such a correlation, if it exists,
is a valuable feature in the interpretation of the data.
The correlation between these two parameters is sig-
nificant at 90 percent but not at the 95 percent level
of significance; therefore, an approximate correlation
exists, and the slopes and the means are not com-
pletely independent. This significantly positive corre-
lation indicates a tendency for concurrence of the
lines at a point below the overall mean of
30.9 mg/m3 If the lines were exactly concurrent,
there would exist a particular value of concentra-
tion—the point of concurrence—at which all labora-
tories obtained the same result. An F ratio of the
mean square for nonconcurrence to V(n) from
Table B-VI is highly significant; therefore, the concur-
rence is not absolute, and there remains a significant
amount of variability between laboratories even at
the point at which all laboratories tend to agree best.
This point lies in the vicinity of zero.
The variance components may now be com-
puted from the data in Table B-VI, and again the
technique of Mandel(3) was used. A summary of re-
sults for variance components and derived quantities
is shown in Table B-VII.
It is now necessary to introduce and define the
concept of a test result.^ A test result is defined as
the average of m replicates, where m is the required
number of replicate measurements specified by the
method. The particular method does not specify any
more than one replicate; therefore the value of m is
taken to be one. Thus, a test result is defined as a
single measurement and V(e) is given by Equation
(B-4) with n = m = 1.
The four sources of variability have been calcu-
lated for several values of concentration and are shown
in Table B-VIII. Also shown are the fractions of the
total variance accounted for by each source. Compari-
son of V(e) and K(X), each of which is constant, would
indicate that the precision of the method could be im-
proved by decreasing V(e). However, V(e) is largely
composed of the variation between days, which is large
in comparison with the replication error; therefore, in-
creasing the number of replicates will not materially
assist in improving the precision of the method. The
between-laboratory variability is larger than the within-
laboratory variability throughout the table,which indi-
cates significant sources of variation between the labo-
ratories. These sources of variation are undoubtedly
related to the accuracy of the calibration gases used
in the collaborating laboratories.
The repeatability and reproducibility^9) must
now be defined and computed. The repeatability is "a
TABLE B-VI. ANALYSIS OF VARIANCE FOR LINEAR MODEL
Source of Variation
Laboratories
Concentrations
Laboratory x Concentration
Linear
Concurrence
Nonconcurrence
Deviation from Linear
Sum of Squares
42.6987
30284.1677
35.9206
27.0714
7.4996
19.5718
8.8491
Degrees
of Freedom
13
5
65
13
1
12
52
Mean Square
3.2845
6056.8335
0.5526
2.0824
7.4996
1.6310
0.1702
B-10
-------
TABLE B-VII. SUMMARY OF RESULTS FOR VARI
ANCE COMPONENTS AND DERIVED QUANTI-
TIES FOR LINEAR MODEL ANALYSIS. Data
in milligrams per cubic meter.
where V(rj) is given by
Components
Within Laboratories
°l
°b
K(e) = a'D + a\ln
VM
VM = VM + V(e)lw
Between Laboratories
V(u.)
V($)
K(6)
at
X
Derived from
Collaborative Test,
n = w = 3
0.0289
0.1936
0.2025
0.1027
0.1702
0.5191
0.000884
0.000754
0.02207
30.9
For Computations
Based on a Test Result,
n - w ~ 1
0.0289
0.1936
0.2225
0.1027
0.3252
0.5191
0.000884
0.000754
0.02207
30.9
quantity that will be exceeded only about five per-
cent of the time by the difference, taken in absolute
value, of two randomly selected test results obtained
in the same laboratory on a given material. "(9) The
reproducibility is "a quantity that will be exceeded
only about five percent of the time by the difference,
taken in absolute value, of two single results made on
the same material in two different, randomly selected
laboratories. "(9) These parameters are computed by
the formulas
Repeatability = 2.77 VF(T?)
Reproducibility = 2.77 V^/C
(B-5)
(B'6)
(B-7)
where V(e) is given by Equation (B-4) for n = m = 1
and Vj(y} is given by
V,(y) = (l+ay/)
Between
laboratories
(B-8)
Within
laboratories
where the index; is attached to the variance symbol
to signify its dependence upon yf- which is given by
-Y. = x —x (R-9}
i] Aj A \L> ?)
where Xj is the level of concentration at which Vj(y)
is desired. Substituting the derived values into Equa-
tion (B-8) and simplifying, the following equation is
obtained.
Vf(y) = 0.001007*? - 0.0393^. + 1.10 (B-10)
Users may choose between Equation (B-8) or (B-10)
or the graphic presentation shown in Figure B-3 in
which the repeatability and the reproducibility have
been plotted for a range of values of concentration.
TABLE B-VIII. SOURCES OF VARIABILITY AND THEIR RELATIVE IMPORTANCE
FOR THE LINEAR MODEL ANALYSIS
X
0
5
10
15
20
25
30
35
40
45
50
55
60
\/F(e) Pet.*
0.45 19
0.45 22
0.45 26
0.45 28
0.45 29
0.45 28
0.45 25
0.45 22
0.45 18
0.45 15
0.45 12
0.45 10
0.45 9
•JV(\) Pet.*
0.32 10
0.32 11
0.32 13
0.32 14
0.32 15
0.32 14
0.32 13
0.32 11
0.32 9
0.32 8
0.32 6
0.32 5
0.32 4
Vd + <*7)2 K(M) Pet.*
0.23 5
0.31 10
0.39 19
0.47 31
0.55 43
0.63 54
0.71 62
0.79 66
0.86 67
0.94 66
1.02 64
1.10 62
1.18 60
V72V(fi) Pet.*
0.85 67
0.71 56
0.57 42
0.44 27
0.30 13
0.16 4
0.03 0
0.11 1
0.25 6
0.39 11
0.52 17
0.66 22
0.80 27
N/FOO
1.04
0.95
0.89
0.85
0.83
0.85
0.90
0.97
1.06
1.16
1.28
1.40
1.53
*Percent of total variance.
B-ll
-------
_£
OJ
E
I" 3
!Q
'o
~a
o
Q.
0)
oc
o
2- 2
Reproducibility
Repeatability
I
I
I
I
10 20 30 40 50
2
Concentration, mg/m
FIGURE B-3. REPEATABILITY AND REPRODUCIBILITY VERSUS CONCENTRATION
60
III. INTERPRETATION OF THE
PARAMETERS
cases and selected from a group of g means, then the
a allowance for any comparison is
The results of the previous section may now be
used to answer some fundamental questions—thus ful-
filling the objectives of this collaborative test. Unless
otherwise stated below, a 95 percent level of signifi-
cance is assumed.
A. Precision of the Method
The most general method to test class means is
the studentized range A ^"^^ If an estimate of the
standard deviation s is based on v degrees of freedom
and is independent of the class means to be com-
pared, and if these class means are computed from TV
(B-ll)
where x\ is the highest class mean and x2 is the low-
est class mean. The value of q is obtained from the
appropriate tabledH> 13) interest will center around
g = 2 because most often the interest is in comparing
two class means. In computing checking limits for
duplicates, N is of course equal to 1 and the test is
identical to ASTM recommended practiceX14)
An obvious limitation is that the means must all
contain the same number of observations. When this
B-12
-------
is not the case, the standard normal deviate is ade-
quate*-15) and use can be made of the equation
-*2|is the absolute value of the difference
in the two class means x1 and 3c2 , and Nl and 7V~2 are
the numbers of observations in Xi and 5c2 , respec-
tively. The results from this equation are the same as
Equation (B-ll) when N = N^ = 7V2 and v is large.
The results are adequate if N^ and JV2 are relatively
large (20 or more).
To test whether the true value of a mean is
lower than a specified fixed value, the maximum per-
missible difference is
which is a one-sided test where x is the mean, ;U0 is
the fixed value, and N is the number of observations
in x.
These techniques will be applied as appropriate
to the three sources of variation below. The treat-
ment will be in more depth for the precision between
laboratories, which is of more practical interest.
1. Precision Between Replicates
We have already concluded that replica-
tion will not materially assist in increasing the preci-
sion of the method. Replication will, in general, be a
waste of time and effort; however, replicates are
often advisable to avoid gross errors. The expression
for the checking limit for duplicates uses ae and
Equation (B-l 1) yielding
Rr
2.77(0.17) = 0.5
(B-l 4)
where .Rmax is the maximum permissible range be-
tween duplicates. Two such replicates should be con-
sidered suspect if they differ by more than
0.5 mg/m3
2. Precision Between Days
One situation involves within-laboratory
comparisons of the same sample. It is of interest
when comparing measured values on the same sample
analyzed on separate days. The estimate of the stan-
dard deviation in Equation (B-ll) must now include
the variation between days in addition to the replica-
tion error. The expression for Rmax, the maximum
permissible range between two test results, is
/?max=2.77VF(e)=1.3
(B-l 5)
where V(e) is given by Equation (B-4) for n = m = 1.
Two such test results should be considered suspect if
they disagree by more than 1.3 mg/m3
A separate and distinct case arises for
within-laboratory comparisons of two samples. Sup-
pose it is desired to compare the results from a single
laboratory on two different but similar samples ana-
lyzed on different days. The samples may have the
same concentration but may differ in other inter-
fering properties such as humidity. It must be
assumed that the heterogeneity between the two
samples with respect to interfering properties is essen-
tially the same as that shown in the collaborative test.
Therefore, the estimate of F(X) is the appropriate
measure for the possible heterogeneity of the two
samples. Thus, the standard deviation estimate for
Equation (B-ll) must now include F(A) as well. The
resulting expression for -Rmax, the maximum permis-
sible range between the test results on each sample is
R max = 2.77VF(A)+F(e) = 1.6
(B-l 6)
Therefore, the maximum permissible difference be-
tween a single test result on each of the samples is
1.6 mg/m3. If two such test results differ by less than
1.6 mg/m3 there is no reason to believe that there is
any real difference between them.
There may also be some occasions where it
will be necessary to compare the means for each
of two given sampling stations, where each mean
was obtained by the same analyst, and consisted
of a known number of test results. The number of
observations in each mean will not usually be
equal. Their standard deviations will not usually be
equal, and one or both may not be normally
distributed. Where they are normally distributed,
standard tests such as the t-test(17) may be applied.
B-13
-------
A limiting case may be investigated if
it is assumed that two means 3ci and x2 are nor-
mally distributed with ai = cr2 = \/V(\) + V(e) =
0.57 mg/m3. This is an unlikely, if not impossible,
situation which could only result from absolutely
constant concentrations at each of the sampling
stations. Under these assumptions, we may apply
Equation (B-12) and obtain
(B-17)
where ^max is the maximum permissible range be-
tween means jct and x2 containing N\ and 7V2 ob-
servations, respectively. If the range exceeds Rmax,
the means are significantly different and do not
belong to the same population.
Under the same limiting assumptions, a
mean 3c containing TV observations may be com-
pared with some fixed value /j0 and it may be
stated whether the true value of 3c is less than MO •
Equation (B-13) may be applied to this case result-
ing in
(B-18)
where .Rmax is the maximum permissible range be-
tween x and MO- If 3c -ju0 is less than.Rmax, then the
true value of jc is less than /u0.
3. Precision Between Laboratories
Probably the most frequent comparison
to be made will be that involving observations of two
different laboratories. When a comparison is made be-
tween results obtained in different laboratories, the
variance F(X) is always included in the comparison,
regardless of whether this comparison involves a
single material or different materials. While it is true
that the interfering properties for a single material are
constant, the response of different laboratories to the
same interfering property may not necessarily be the
same. The variability of this response is exactly what
is measured by F(A). The estimate of the standard
deviation for Equation (B-l 1) now contains the
effects of variations in the means and the slopes of
the response lines for the laboratories. The required
estimate is the square root of V/(y) which may be
obtained from either Equation (B-8) or (B-10). The
resulting expression for jRmax, the maximum permis-
sible difference between a test result from each of
two different laboratories, is
(B-19)
This comparison is complicated by the dependence of
between-laboratory variability on the concentration.
Rmax is identical to the reproducibility given by
Equation (B-6) and plotted in Figure B-3. Two such
test results may not be considered to belong to the
same population if they differ by more than ^?max.
Conversely, the two test results are not significantly
different if they differ by less than Rm ax.
Frequently, it will be necessary to com-
pare the means for each of two given sampling sta-
tions. Each mean may be the result of observations
by one or more different laboratories. Each mean
may contain a different number of observations, each
a test result. Their standard deviations will not
usually be equal, and one or both may not be nor-
mally distributed. Where they are normally dis-
tributed, standard tests such as the t-test^17) may be
applied.
Similar to the preceding subsection, a
limiting case may be investigated if it is assumed that
the two means 3cj and 3c2 containing NI =7V2 =N
observations are normally distributed with
PI = ^2 = VP/O")- Here again, this is an unlikely, if
not impossible, situation which could only result
from absolutely constant concentrations at each
sampling station. Nevertheless, a certain amount of
guidance can be derived. If Equation (B-ll) is applied
to this case, the result is
(B-20)
where RmaK is the maximum permissible range be-
tween the means 3ci and 3t2. If the range exceeds
.Rmax, the means are significantly different and do
not belong to the same population.
B-14
-------
Under the same assumptions as above,
with the exception that N1 may not equal /V2 but
both are relatively large, Equation (B-12) is used,
yielding
Rearranging Equation (B-23) and solving
R»
1 1
— + — (B-21)
N, N,
max is the maximum permissible range be-
where R
11.
tween Xj and x2. If the range exceeds /?max, the
means are significantly different and do not belong to
the same population.
It is interesting to pursue this line of rea-
soning further in terms of the number of samples
required to detect a specified difference under the
limiting assumptions. Rearranging Equation (B-20)
and solving for TV, the result is
(B-22)
This expression now gives the minimum number of
observations N for any desired agreement Rmax be-
tween two means at any level of concentration x,-.
These results are best illustrated in Figure B4. This
figure shows the agreement versus the concentration
level for a family of sample sizes. Superimposed on
the curve are constant percentage agreement lines for
comparison purposes. For example, if agreement
better than 5 percent at a concentration of 15 mg/m3
is desired, a minimum of 10 observations would be
required.
Under the same limiting assumptions, it is
possible to compare a mean x containing N observa-
tions with some fixed value MO and be able to state
whether the true value of x is less than MO. Equa-
tion (B-13) is used for this type case yielding
Rr
= -1.645
Vfiy)
N
(B-23)
where R is the maximum permissible range be-
tween x and MO- If* -Mo is less than,Rmax,
true value of x is less than MO •
then the
for N yields
N=
1.645
(B-24)
This equation is exactly analogous to Equa-
tion (B-22). N is the minimum number of obser-
vations required to attain the agreement -Rmax under
the limiting assumptions. Figure B-5, which is ana-
logous to Figure B-4, best illustrates the resulting rela-
tionships. For example, a minimum of two observa-
tions would be required to establish that the true
value of x is less than 20 mg/m3, while the actual
value is 19 mg/m3 (a 5-percent difference). Stated
differently, given a set of two observations with a
mean of 19 mg/m3, there exists a 95 percent confi-
dence that the true mean is less than 20 mg/m3
B. Accuracy of the Method
In the discussion of accuracy, an additional
concept must be introduced—the reference value of
the measured property for the system under consider-
ation. Mandel(18) discusses three types of reference
values of which the "assigned value" applies for this
collaborative test. The reference values for the
samples included in the study are the values provided
for these samples by the supplier of those samples.
This does not necessarily mean that these values are
considered absolutely correct, but it does mean that
there is a reasonable degree of confidence in the qual-
ity of such materials from this source.
If the reference value is represented by R and
the mean of the population of repeated measure-
ments is M, then the bias or systematic error is M - R.
The error for an individual measurement x would be
x —R. Inaccuracy is thus measured by the magnitude
of p.-R 01 x -R. A method is accurate if M - R is
not significantly different from zero.
A definite and statistically significant in-
accuracy exists; however, its practical significance
must be interpreted with respect to other criteria.
This inaccuracy is best illustrated in Figure B-6. The
B-15
-------
1, mg/m3
FIGURE B4. EXPECTED AGREEMENT BETWEEN TWO MEANS VERSUS CONCENTRATION FOR VARIOUS
NUMBERS OF OBSERVATIONS (95 Percent Level of Significance). EACH MEAN HAS N OBSERVATIONS
WITH A STANDARD DEVIATION EQUAL TO (0.001007x5 - 0.0393*, + 1.10)0-5
B-16
-------
01
E
o
10
20
30
, mg/mc
40
50
60
FIGURE B-5. EXPECTED AGREEMENT BETWEEN A MEAN AND A FIXED VALUE VERSUS CONCENTRATION
FOR VARIOUS NUMBERS OF OBSERVATIONS (95 Percent Level of Significance). THE MEAN HAS N
OBSERVATIONS WITH A STANDARD DEVIATION EQUAL TO (0.001007M20 - 0.0393,u0 + 1.10)0-5
B-17
-------
3 -
-2
O
^vLLLKJJ
20 30
Concentration,
40
60
FIGURE B-6. BIAS OR SYSTEMATIC ERROR
VERSUS CONCENTRATION
departures of individual laboratory averages from
their respective reference values as well as the depar-
tures of overall averages from their respective values
have been plotted versus concentration. The large
open circles are overall averages at each level of con-
centration in the collaborative test. The small circles
are individual laboratory values. The overall averages at
each level are the mean of 14 laboratory averages, each
of which is the average of 1 8 observations (three repli-
cates on each of three days for each of two samples).
The standard error of the overall means is represented
by the solid lines, and the standard error of the indi-
vidual means is represented by the dashed lines. The
standard errors have been plotted with reference to
zero so that observations failing outside these lines are
significantly different from zero.
Several of the individual laboratory means
are significantly different from zero, mostly at the
higher concentrations and nearly all on the high
side. The overall means are significant at the two
higher levels of concentration. This relationship is
nearly linear and the results tend to be, on the
average, 2.5 percent high.
The method uses the same type materials for
calibration as were used for reference samples in this
test. There is little doubt, therefore, that the inaccu-
racy results primarily, if not completely, from the use
of calibration gases which exhibit significant variation
with respect to their specified concentration. Since
the results tend to be high, the calibration gases must
have a tendency to be correspondingly low.
Caution should be exercised in the use of these
measures of accuracy. Although calibration gas
sources were randomly selected, it is known that
some standards used by different laboratories were
prepared and analyzed at the same time by the same
supplier. Nevertheless, it cannot be overemphasized
that the accuracy of the method is almost totally
dependent upon the availability of sufficiently accu-
rate standards.
In order to further examine the accuracy of the
calibration gases used by the individual collaborators,
some additional analyses were made. The first of
these investigated the individual calibration curves
and compared them with calibration curves con-
structed from the reference sample data. Since the
chart readings for each calibration curve were re-
corded, the parameters of each curve could be com-
puted. The standard error of estimate was computed
for each calibration curve by a least-squares regression
analysis of chart readings on calibration gas concen-
tration. The average standard errors of estimate for
each laboratory are shown in Table B-IX, where they
have been grouped into instrument ranges and sub-
grouped into calibration gas sources. They are in units
of chart divisions and, for purposes of comparison, a
chart division for the 0 to 58-mg/m3 (0 to 50 ppm)
range is approximately equal to 0.6 mg/m3, and a
chart division for the higher range is approximately
equal to 1.2 mg/m3. These standard errors of esti-
mate are measures of nonlinearity of the calibration
curves.
In order to provide individual comparisons, the
^n~ analysis was performed on the reference samples
and their respective chart readings as though they
were actually calibration gases. These are also shown
in Table B-IX. Inspection reveals some unusually large
same ana
B-18
-------
TABLE B-IX. STANDARD ERRORS OF ESTIMATE FOR CALIBRATION CURVES
PREPARED FROM CALIBRATION GASES AND FROM REFERENCE GASES
Laboratory
Code Number
571
370
375
799
310
311
222
220
253
540
860
920
780
927
270
Instrument*
A
B
A
A
A
A
C
D
B
A
B
A
A
B
A
Rangef
0-58
0-58
0-58
0-58
0-58
0-58
0-116
0-116
0-116
0-116
0-116
0-116
0-116
0-116
0-116
Water Vapor
Compensation^
a
b
a&d
a&d
b
d
b
b
a
b
a
a
d
a
b
Calibration
Gas Source*
A
B
B
C
D
D
E
A
A
A
A
B
C
F
E
Standard Error of Estimate
Calibration
1.0**
1.0**
2.5**
4.3**
1.8**
1.2**
1.2ft
0.7ft
0.4ft
0.4ft
O.Off
1.6ft
3.7ft
1.3ft
2.4ft
Reference
1.2**
1.1**
0.7**
0.9**
0.9**
1.2**
1.9ft
0.2ft
0.5ft
0.3ft
O.Sff
0.5ft
0.4ft
0.2ft
0.5ft
*Coded to obscure identity.
t Milligrams per cubic meter.
jSee Section 3.1 of method in Appendix A.
**Chart divisions- 1 chart division is approximately equivalent to 0.6 mg/m3
ffChart divisions- 1 chart division is approximately equivalent to 1.2 mg/m3
values in the calibration gas data. In the majority of
cases, the standard error of estimate for the calibra-
tion gases is larger than the corresponding value for
the reference samples. It is evident that the calibra-
tion gases are more variable than the reference
samples; the question remains, to what can this vari-
ability be ascribed?
To explore this matter further, each calibration
gas was "analyzed," using its respective chart reading
and the "calibration curve" prepared from reference
samples. Such a treatment corresponds to giving the
collaborator the concentrations of the reference
samples and asking him to prepare a calibration curve
from them and then analyze his own calibration gases
as if they were unknown samples. This is most in-
formative since these "analytical results" may be
compared with the specified value for the calibration
gases. Unusually large differences would point to a
suspicious calibration gas.
Following this procedure, some of the large
standard errors of estimate can be explained by one
suspicious calibration gas. Some notable examples of
differences more than 10 percent are (^Labora-
tory 799-a higher value than quoted for 23 mg/m3
(20 ppm) calibration gas, (2) Laboratory 270-a
much lower value than quoted for 91 mg/m3
(80 ppm) calibration gas, (3) Laboratory 780-alower
value than quoted for 46 mg/m3 (40 ppm) calibration
gas, and (4) Laboratory 927—a lower value than
quoted for 23 mg/m3 (20 ppm) calibration gas. Other
cases of high standard errors of estimate could not be
attributed to a single suspicious calibration gas. Several
other cases of differences of 10 percent were observed
along with numerous cases of 5-percent differences.
Absolute magnitudes of "analyzed" values minus
quoted values ranged from -10.2 to +3.3 mg/m3
It should be noted, however, that some labora-
tories did not use suspicious calibration points in com-
puting their results for the reference samples and pre-
ferred to use their judgment based on the calibration
curve as a whole, sometimes drawing nonlinear calibra-
tion curves. While this practice can often minimize in-
accuracy, it can also lead to worse situations. For in-
stance, Laboratory 780, upon inspection of its calibra-
tion curve, thought the 91 -mg/m3 (80 ppm) point to
be out of line and chose not to use it when actually the
46-mg/m3 (40 ppm) calibration gas was at fault.
Utmost care should be taken in obtaining high-
quality calibration gases and protecting them from de-
terioration. If smooth calibration curves are not ob-
tained, calibration gases may be at fault and should be
replaced.
B-19
-------
LISTOF REFERENCES
1. ASTM Manual for Conducting an Inter-
laboratory Study of a Test Method, ASTM STP
No. 335, Am. Soc. Testing & Mats. (1963).
2. 1971 Annual Book of ASTM Standards, Part 30,
Recommended Practice for Developing Pre-
cision Data on ASTM Methods for Analysis
and Testing of Industrial Chemicals, ASTM
Designation: E180-67, pp 403422.
3. Mandel, John, The Statistical Analysis of Ex-
perimental Data, John Wiley & Sons, New
York, Chapter 13, pp 312-362 (1964).
4. Mandel, J., and Lashof, T.W., "The Interlabora-
tory Evaluation of Testing Methods," ASTM
Bulletin, No. 239, pp 53-61 (1959).
5. Mandel, John, "The Measuring Process," Tech-
nometrics, l,pp 251-267 (1959).
6. Dixon, Wilfred J., and Massey, Frank J., Jr., In-
troduction to Statistical Analysis, McGraw-Hill
Book Company, Inc., New York, Chapter 10,
pp 180-181 (1957).
7. Ibid, Chapter 8, pp 109-110.
8. Ibid, Chapter 9, pp 112-129.
9. Mandel, John, "Repeatability and Reproduci-
bility," Materials Research and Standards, Am.
Soc. Testing & Mats., Vol 11, No. 8, p8
(August 1971).
10. Duncan, Acheson J., Quality Control and In-
dustrial Statistics, Third Edition, Richard D.
Irwin, Inc., Homewood, Illinois, Chapter XXXI,
pp 632-636 (1965).
11. Ibid, p 909.
12. Bennett, Carl A., and Franklin, Norman L., Sta-
tistical Analysis in Chemistry and the Chemical
Industry, John Wiley and Sons, Inc., New York,
Chapter 4, p 111(1954).
13. Ibid, p 185-189.
14. 1971 Annual Book of ASTM Standards, op cit,
p411.
15. Dixon and Massey, op cit, p 120.
16. Ibid, pp 114-115.
17. Ibid, pp 123-124.
18. Mandel, John, The Statistical Analysis of Ex-
perimental Data, John Wiley & Sons, New
York, Chapter 6, pp 104-105 (1964).
B-20
-------
APPENDIX C
TABULATION OF ORIGINAL DATA
-------
TABLE C-I-a. OBSERVED VALUES FOR DRY SAMPLES FOR COLLABORATIVE
TEST OF CARBON MONOXIDE METHOD, MILLIGRAMS PER CUBIC METER
Laboratory
Code Number
Day 1
Day 2
Day 3
Low Concentration
220
222
253
270
310
311
370
375
540
571
780
799
860
920
927
8.4 8.4 8.4
6.9 6.9 6.9
8.0 8.0 8.0
8.0 6.9 6.9
9.4 8.8 8.8
8.9 9.3 9.0
8.2 8.2 8.2
7.3 7.3 7.3
8.5 8.5 8.7
8.2 8.2 8.2
8.2 8.0 8.1
7.7 8.2 7.7
7.4 7.4 7.4
8.0 8.0 8.0
8.9 8.9 8.9
8.4 8.4 8.6
6.9 6.9 6.9
9.2 9.2 9.2
9.2 8.0 6.9
8.9 9.2 9.2
8.7 8.6 8.6
8.6 8.6 8.6
7.2 7.2 7.1
9.0 9.0 8.8
8.6 8.6 8.7
8.9 8.6 8.8
8.6 8.2 8.0
7.4 7.4 7.4
8.0 8.0 8.0
8.9 8.9 8.9
8.6 8.6 8.6
6.9 6.9 6.9
8.0 8.0 8.0
9.2 9.2 8.0
9.4 8.8 9.2
9.4 9.6 9.6
8.0 8.0 8.0
7.6 7.8 7.7
8.9 8.9 8.8
8.9 8.9 9.0
8.0 8.5 8.2
8.0 8.0 8.0
7.4 7.4 7.4
8.0 8.0 8.0
8.9 8.9 8.9
Intermediate Concentration
220
222
253
270
310
311
370
375
540
571
780
799
860
920
927
30.5 30.5 30.6
28.6 28.6 28.6
30.9 30.9 31.5
29.8 30.9 30.9
31.2 31.2 31.5
31.5 31.4 31.3
30.6 30.6 30.6
30.2 30.2 30.4
30.6 30.1 30.1
29.3 29.2 29.8
30.9 30.6 30.5
29.9 29.9 29.9
30.4 30.4 30.4
29.8 30.9 29.8
32.1 32.1 32.1
30.1 30.4 30.4
29.2 29.2 28.6
32.1 32.1 32.1
32.1 30.9 30.9
31.5 30.9 31.2
31.5 31.4 31.5
30.6 30.6 30.6
29.6 29.6 29.6
30.5 30.7 30.4
30.4 30.4 29.8
30.7 30.5 30.4
29.8 29.2 29.4
30.4 30.4 30.4
32.1 32.1 32.1
32.1 32.1 32.1
30.5 30.5 30.5
28.6 29.8 28.6
30.9 30.9 30.9
32.1 32.1 30.9
31.2 31.2 31.5
30.9 31.0 31.0
30.4 29.8 29.8
30.9 30.9 30.6
30.5 30.6 30.5
30.7 30.4 30.7
30.2 30.6 30.6
31.2 30.9 31.2
30.4 30.4 30.4
32.1 32.1 32.1
32.1 32.1 32.1
High Concentration
220
222
253
270
310
311
370
375
540
571
780
799
860
920
927
53.3 53.3 52.9
52.7 52.7 52.7
53.8 53.8 53.8
59.6 55.0 55.0
55.6 55.6 55.6
53.4 53.3 53.4
54.4 54.4 54.4
54.1 54.1 54.1
53.3 53.0 53.0
49.6 49.6 49.8
52.7 52.8 52.3
52.9 53.3 53.3
52.7 52.7 52.7
53.8 53.8 53.8
55.0 55.0 55.0
52.7 52.1 52.1
53.3 53.3 52.7
53.8 53.8 53.8
56.1 55.0 55.0
55.6 55.2 55.0
54.3 54.4 54.2
54.2 54.2 54.2
53.2 53.4 53.6
52.5 53.3 52.7
51.0 50.7 50.7
52.9 52.6 52.7
54.4 54.2 54.4
52.7 52.7 52.7
55.0 55.0 55.0
55.0 55.0 55.0
53.3 53.3 53.3
53.3 52.7 54.4
53.8 53.8 53.8
55.0 55.0 55.0
55.8 56.1 55.8
53.6 53.3 53.6
53.5 53.3 53.5
54.2 54.2 54.3
52.9 52.9 52.8
51.5 52.1 51.5
53.2 53.0 53.3
55.0 54.6 54.6
52.7 52.7 52.7
55.0 55.0 55.0
55.0 55.0 55.0
C-l
-------
TABLE C-I-b. OBSERVED VALUES FOR HUMIDIFIED SAMPLES FOR COLLABORATIVE TEST OF
CARBON MONOXIDE METHOD, MILLIGRAMS PER CUBIC METER
Laboratory
Code Number
Day 1
Day 2
Day 3
Low Concentration
220
222
253
270
310
311
370
375
540
571
780
799
860
920
927
8.6 8.6 8.6
7.4 6.3 7.4
8.0 8.0 8.0
9.2 6.9 6.9
8.6 8.0 8.2
9.7 9.5 9.4
8.6 8.2 8.2
7.2 7.2 7.3
8.6 8.5 8.6
7.8 7.8 8.2
11.9 12.1 12.0
8.2 8.2 8.2
7.4 7.4 7.4
8.0 8.0 8.0
8.9 8.9 8.9
8.6 8.7 8.6
7.4 7.4 7.4
9.2 9.2 8.6
8.0 8.0 8.0
8.9 8.7 8.7
9.3 9.3 9.3
8.6 8.6 8.6
7.3 7.2 7.2
8.6 9.0 8.8
8.6 8.6 8.5
12.5 12.3 12.0
8.0 8.0 8.0
7.4 7.4 7.4
8.0 8.0 8.0
8.9 8.9 8.9
8.7 8.7 8.6
6.9 7.4 7.4
8.0 8.0 8.0
8.0 8.0 9.2
8.8 8.8 8.8
9.7 9.4 9.9
8.0 8.0 8.2
7.8 7.7 7.7
8.6 8.7 8.6
8.2 8.9 8.9
12.0 11.8 11.8
9.7 8.6 8.6
7.4 7.4 7.4
8.0 8.0 8.0
8.9 8.9 8.9
Intermediate Concentration
220
222
253
270
310
311
370
375
540
571
780
799
860
920
927
30.4 30.4 30.4
28.6 28.1 29.0
30.9 30.9 30.9
33.2 30.9 30.9
30.0 30.4 30.4
31.3 31.2 31.2
30.6 30.6 30.7
29.3 29.7 29.7
30.1 30.0 30.0
29.2 29.2 29.3
33.7 33.4 33.0
30.6 29.9 28.9
30.4 30.4 30.4
29.8 30.9 30.9
32.1 32.1 32.1
30.4 30.2 30.1
29.2 30.4 29.8
32.1 32.1 32.1
32.1 32.1 32.1
30.6 30.9 30.4
31.2 31.2 31.2
30.9 30.7 30.6
29.7 29.6 29.6
30.5 30.4 30.7
30.1 29.8 29.8
33.7 33.4 33.7
29.8 29.2 28.6
30.4 30.4 30.4
30.9 32.1 32.1
32.1 32.1 32.1
30.5 30.5 30.5
27.5 29.8 26.9
30.9 30.9 30.9
32.1 32.1 30.9
31.5 31.2 31.5
30.8 30.9 31.0
30.1 29.8 29.8
30.5 30.5 30.2
30.5 30.4 30.5
30.4 30.4 30.1
32.9 32.9 32.6
30.9 30.9 31.2
30.4 30.4 30.4
32.1 32.1 32.1
32.1 32.1 32.1
High Concentration
220
222
253
270
310
311
370
375
540
571
780
799
860
920
927
53.4 53.4 53.5
52.7 52.7 52.7
53.8 53.8 53.8
58.4 55.0 55.0
54.1 53.8 53.8
52.7 52.9 52.8
54.4 54.4 54.4
53.2 54.1 53.0
53.3 53.3 53.3
49.5 49.6 48.9
54.3 54.3 54.3
52.3 52.1 52.7
52.7 52.7 52.7
53.8 53.8 53.8
55.0 55.0 55.0
52.7 52.1 52.1
53.3 53.8 55.0
55.0 54.4 55.0
55.0 55.0 56.1
54.6 54.4 54.6
53.4 53.5 53.4
54.2 54.3 54.2
'53.4 53.4 53.2
52.7 52.8 52.9
50.4 50.1 50.7
54.5 54.5 54.5
51.0 50.7 51.0
52.7 52.7 52.7
55.0 55.0 53.8
55.0 55.0 55.0
52.9 52.7 52.7
53.3 53.3 53.3
53.8 54.4 54.4
55.0 55.0 55.0
55.2 55.6 55.2
52.9 52.9 52.8
53.3 53.3 53.5
53.0 53.4 53.2
53.2 52.8 52.9
51.0 50.6 51.0
54.6 54.4 54.0
54.6 54.3 54.3
52.7 52.7 52.7
53.8 53.8 53.8
55.0 55.0 55.0
C-2
-------
TABLE C-II. REFERENCE VALUES FOR CARBON MONOXIDE TEST
CONCENTRATIONS USED IN COLLABORATIVE TEST,
MILLIGRAMS PER CUBIC METER
Laboratory
Code Number
220
222
253
270
310
311
370
375
540
571
780
799
860
920
923
927
Low
Concentration
8.4
8.6
8.5
8.4
8.5
8.6
8.6
8.2
8.5
8.5
8.4
8.4
8.2
8.6
8.6
8.4
Intermediate
Concentration
29.9
30.2
30.1
29.9
29.8
29.8
29.9
30.2
29.9
30.0
29.8
30.2
29.9
29.8
30.1
30.1
High
Concentration
52.6
52.1
52.3
52.2
52.2
52.6
52.1
52.3
52.3
52.3
52.2
52.3
52.3
52.3
52.3
52.3
C-3
-------
NOTATION
Foldout for Ready Reference
-------
NOTATION
(a) Principal Variables: (may also be used as sub-
scripts)
y = measurements,
L = laboratories,
M = materials or concentrations,
D = test days, and
e = replication errors.
(b) Qualifying Subscripts:
i = a particular laboratory,
/ = a particular material,
k = a particular test day, and
m = a particular replication error.
(c) Number of Levels of Variables:
p = number of laboratories,
q = number of materials,
w = number of test days, and
n = number of replicates.
(d) Statistical Notation:
the reference value for the jth ma-
terial for the ith laboratory,
the average of all c^ for material /,
average of all replicates by labora-
tory i on material j on day k, and
average of all yiik by laboratory z
on material/.
(e) Measures of Variability:
(g) Regression Analysis:
x
y
a
s
R
population standard deviation,
sample estimate of a,
range (largest measurement minus
smallest measurement), and
variance of random variable y.
(f) Analysis of Variance:
DF = degrees of freedom,
SS = sum of squares,
MS = mean square, and
EfMS) = expected value of mean square.
independent variable,
dependent variable,
slope of a straight line,
residual (observed value minus fit-
ted value), and
correlation coefficient.
(h) L inear Model A nalysis:
Xj = average of all y^ for material /,
3e = average of all Xj,
a = the slope of the line /?,- versus ju,-,
j3,- = slope of the line y^ versus Xj,
Jj = Xj-X,
6,- = scatter of the ith point about the
line /3,- versus M,-,
e = replication error,
Tj(y = scatter of the jth point for the ith
laboratory about the line y(J- versus
Xj,
\ = that part of T? which is not ac-
counted for by e and
Hi = average of allj^ for laboratory i.
(i) Qualifying Superscripts:
•^ = a sample estimate of a population
parameter,
= a mean, and
= = a mean of means.
(j) Hypothesis Testing:
g = number of items from which range
is obtained,
N = number of cases from which a
mean is computed,
q = a variable that has a studentized
range distribution,
s = independent estimate of standard
deviation,
ta = the a point of a f distribution,
z = a variable that has a normal distri-
bution with zero mean and unit
standard deviation,
a = level of significance,
M = mean of a universe,
Mo = hypothetical value of p. that is
being tested,
v - degrees of freedom, and
CT = population standard deviation.
------- |