COLLABORATIVE STUDY
of
REFERENCE METHOD FOR DETERMINATION
OF SULFUR DIOXIDE IN THE ATMOSPHERE
(PARAROSANILINE METHOD)
Herbert C. McKee
Ralph E. Childers
Oscar Saenz, Jr.
Contract CPA 70-40
SwRI Project 21-2811
Prepared for
Office of Measurement Standardization
Division of Chemistry and Physics
National Environmental Research Center
Environmental Protection Agency
Research Triangle Park, N. C. 27709
September 1971
SOUTHWEST RESEARCH INSTITUTE
SAN ANTONIO CORPUS CHRIST! HOUSTON
-------
COLLABORATIVE STUDY
of
REFERENCE METHOD FOR DETERMINATION
OF SULFUR DIOXIDE IN THE ATMOSPHERE
(PARAROSANILINE METHOD)
Herbert C. McKee
Ralph E. Childers
Oscar Saenz, Jr.
Contract CPA 70-40
SwRI Project 21-2811
Prepared for
Office of Measurement Standardization
Division of Chemistry and Physics
National Environmental Research Center
Environmental Protection Agency
Research Triangle Park, N. C. 27709
September 1971
Approved:
7N~~~
Herbert C. McKee
Assistant Director
Department of Chemistry
and Chemical Engineering
SOUTHWEST RESEARCH INSTITUTE - HOUSTON
3600 SOUTH YOAKUM BOULEVARD, HOUSTON, TEXAS 77006
-------
SUMMARY AND CONCLUSIONS
This report presents infonnation obtained in the evaluation and collaborative testing of a reference
method for measuring the sulfur dioxide content of the atmosphere. Different variations of this method
have been used extensively by many laboratories since the original publication in 1956, and it has been
found to be reliable and reasonably free of interferences.
This method was recommended as a tentative standard method by the Intersociety Committee, a
cooperative group now consisting of representatives of nine scientific and engineering societies. * It was
published as Tentative Method 42401-01-69T in Health Laboratory Science, January 1970, Part Two,
pp 4-12. It was then tested, as a part of this program, by means of collaborative tests involving a total of
eighteen laboratories.
A statistical analysis of the data of fourteen laboratories provided the following results, based on the
analysis of pure synthetic atmospheres using the 30-min sampling procedure and the sulfite calibration
method prescribed-
.
The standard deviation for replication varies linearly with concentration from 7 Jlgfm3 at zero
to 17 Jlgfm3 at 1000 Jlgfm3
.
The standard deviation for within-laboratory variation (repeatability) varies linearly with con-
centration from 15 Jlgfm3 at zero to 36 Jlgfm3 at 1000 Jlgfm3
.
The standard deviation for between-laboratory variation (reproducibility) varies linearly with
concentration from 29 Jlgfm3 at zero to 70 Jlgfm3 at 1000 Jlgfm3 .
.
No systematic error, bias, or inaccuracy was detected.
.
The lower limit of detection is 25 Jlgfm3 (95 percent confidence level).
In addition, this report presents other results with respect to the use of control samples and reagent
blank samples, the minimum number of samples required to establish validity of results within stated limits,
and the statistical evaluation of various steps included in the method.
These results show that the method can give satisfactory results only when followed rigorously by
experienced laboratory personnel.
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 sulfur dioxide. That publication is reproduced as Appendix A of this report.
* Air Pollution Control Association
American Chemical Society
American Conference of Governmental Industrial Hygienists
American Industrial Hygiene Association
American Public Health Association
American Society for Testing and Materials
American Society of Civil Engineers
American Society of Mechanical Engineers
Association of Official Analytical Chemists
The Intersociety Committee receives partial financial support through EPA Contract 68-02-0004.
iii
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ACKNOWLEDGEMENT
The authors wish to express appreciation to the Project Officer, Mr. Thomas W. Stanley, and staff
members of the Office of Measurement Standardization, for assistance in the planning and execution of the
collaborative study. The assistance ofMr. John H. Margeson and others of the OMS staff in providing space,
facilities, and training contributed significantly to the success of the Method Familiarization Session. Also
acknowledged are the efforts of Mr. Clarence A. Boldt, Jr., of Southwest Research Institute, who con-
ducted the bulk of the laboratory evaluation of the method and assisted in preparation for the Method
Familiarization Session.
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
Organization
Robert M. Bethea
Texas Tech University
Lubbock, Texas
James S. Caldwell
Environmental Protection Agency
Cincinnati, Ohio
Gary Carlson
St. Louis County Health Department
Clayton, Missouri
Emil R. deVera
Air & Industrial Hygiene Laboratory
California Department of Public Health
Berkeley, California
B. l. Ferber
Bureau of Mines
United States Department of the Interior
Pittsburgh, Pennsylvania
Harriet Klinger
Gary Air Pollution Control Division
Gary, Indiana
W. D. Langley
Texas A&M University
College Station, Texas
Harold E. Meyer
Galveston County Air Control Division
Texas City, Texas
M. Rodney Midgett
Environmental Protection Agency
Research Triangle Park, North Carolina
iv
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Organization
Name
Gordon D. Nifong
Bethlehem Steel Corporation
Bethlehem, Pennsylvania
Walter Oyung
Bay Area Air Pollution Control District
San Francisco, California
Robert E. Pattison
Air Pollution Control Laboratory
Canton City Health Department
Canton, Ohio
Rolf A. Paulson
Institute for Materials Research
National Bureau of Standards
Washington, D.C.
M. J. Rohlinger
Air Pollution Control Laboratory
State of Illinois
Springfield, Illinois
Karl Schoenemann
Air Pollution Chemistry Laboratories
Los Angeles County Air Pollution
Control District
Los Angeles, California
F. Wopat, Jr.
Shell Oil Company
Wood River Refinery
Wood River, Illinois
Sandra Wroblewski
Department of Air Pollution Control
City of Chicago
Chicago, Illinois
Karl J. Zobel
Environmental Protection Agency
Research Triangle Park, North Carolina
v
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I.
II.
III.
TABLE OF CONTENTS
INTRODUCTION. . .
. . . .
. .. .. . .
.. .. . . .. . .
. . . .
COLLABORATIVE TESTING OF THE METHOD
. . . . .. .. . .
. . . .
. . . . . . .
A.
B.
C.
D.
Generation of Test Atmospheres. . . . . . . . . . .. ....,.
Selection of Collaborators. . . . . . . . . . . .. .....,......
First Collaborative Test. . . . . . . . . . . . . . . . . . . . . . . . . . .
Familiarization Session and Second Collaborative Test. . . . .. ........
STATISTICAL DESIGN AND ANALYSIS
. . . .
. . . . . . . . . . . ..
A.
B.
C.
D.
Outlying Observations.. ........ ""'" ....,..
Analysis of Variance . . . . . . . . . . .. ...,......
Various Sources of Error Within the Analytical Method. .. .,.......
Appl ication of the Results . . . . . . . . . .
LIST OF REFERENCES. . . . . . .
Figure
2
. . . . . . . .
. . . .
LIST OF IllUSTRATIONS
Specifications for Permeation Tube System Used in Collaborative Tests
Replication Error, Repeatability, and Reproducibility Versus Concentration
for Three Different Methods of Data Analysis.. .........
. . . . . .
vii
Page
2
2
4
4
5
5
7
7
9
I I
13
Page
3
8
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I. INTRODUCTION
Sulfur dioxide is one of the more common
atmospheric pollutants which result from the activi-
ties of man. Many urban areas throughout the world
experience some degree of pollution from this con-
taminant due to the burning of sulfur-containing
fuels, with less prevalent but occasionally severe prob-
lems due to emissions from industrial and other
sources. In a few limited areas, volcanoes or sulfur
springs add a natural source to the many man-made
sources which exist. Sulfur dioxide in sufficiently
high concentrations can be objectionable in many
ways, including adverse effects on human health,
damage to vegetation, corrosion of metals and other
materials, and formation of haze which restricts visi-
bility. During short-term episodes involving high con-
centrations, detrimental effects can occur in a few
hours. At lower levels, long-range chronic effects can
also occur over long periods of time, although the
documentation of these is more difficult.
Because of the many different adverse effects
which can occur, sulfur dioxide has traditionally
received a major share of attention as an atmospheric
pollutant. For this reason, methods to measure sulfur
dioxide concentrations in the atmosphere have been
known for many years, although some of the
methods used in the past possessed serious disadvan-
tages. Perhaps the chemical method most widely used
in the past decade or more has been the
pararosaniline method, also known as the West-Gaeke
method from the original publication9)* The
method is essentially a colorimetric technique, in
which sulfur dioxide is removed from the air by
absorption in a liquid solution, followed by reaction
with pararosaniline dye to form a color proportionate
to the amount of sulfur dioxide present, after which
the color is then measured in a conventional labora-
tory spectrophotometer. As with most colorimetric
methods, results are compared with a calibration
curve developed from a chemically pure standard
material in order to obtain quantitative results.
*Superscript numbers in parentheses refer to the List of References.
The pararosaniline method can be used by any
laboratory equipped for conventional colorimetric
analysis by merely adding the absorbers necessary for
atmospheric sampling and a few other items of equip-
ment. As with other colorimetric methods, careful,
precise laboratory technique is required if accurate
results are to be obtained, but this method is no more
difficult to carry out than many other colorimetric
methods that are widely used for a variety of pur-
poses.
Since the original publication, many research
investigations have been conducted to develop varia-
tions of this method aimed at minimizing inter-
ferences, increasing accuracy, and in other ways
improving on the basic method. Because of these
many investigations, a number of different variations
of the original method have been published. Most of
these vary in only minor details, such as the method
used in purifying the reagent dye, the method of
plotting calibration curves, and similar details. Except
for various minor effects on precision, most of the
differences do not exert a major effect on the results
if the same procedure is used for preparing the cali.
bration curve and for analyzing samples. However, to
obtain the degree of precision which is possible, all
details of the method as published in Appendix A of
this report should be adhered to rigidly.
In order to obtain comparable data so that
interlaboratory comparisons of results would be
possible, the Office of Measurement Standardization
(OMS) has been working for some time to develop
standard methods which could be used by all persons
making air quality measurements. A number of
scientific and engineering societies have also been
active in the development of standard methods,
including several of those now participating in the
Intersociety Committee whose members are listed in
the Summary and Conclusions.
Following the development of a tentative stan-
dard method by the Intersociety Committee, the final
-------
step in the standardization process is to conduct a
collaborative test, or interlaboratory 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 coatings, food and related products,
and many others. A test of this nature by a
representative group of laboratories is the only way
that the statistical limits of error inherent in any
method can be determined with sufficient con-
fidence. This report presents the results of a series of
collaborative tests of the pararosaniline method con-
ducted by Southwest Research Institute and the
Office of Measurement Standardization, together
with the statistical analysis of the data obtained. In
planning for the collaborative test, it was also
necessary to develop methods for generating test
atmospheres so that each laboratory participating in
the collaborative test could have an assured test
atmosphere for experimental purposes. The informa-
tion obtained in the development of these procedures
is also presented as background information relating
to the collaborative test program and as information
helpful in understanding the capabilities and limita-
tions of this standard method.
II. COLLABORATIVE TESTING OF
TH E 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 investi-
gators. The collaborative, or interlaboratory, test of a
method is an indispensable part(2) of the develop-
ment and standardization of an analytical procedure
to insure that (1) the procedure is clear and complete,
and that (2) the procedure does give results with pre-
cision 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 Mate-
rials (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.(3-S) Publica-
tions of both of these organizations were used
extensively in planning and conducting the collabora-
tive tests of this method to measure sulfur dioxide.
After the development of techniques for gen-
erating test atmospheres, 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.
Generation of Test Atmospheres
In order to facilitate interlaboratory compari-
son of results, a method must be evaluated by a
collaborative test in which each of the various partici-
pants works in his own laboratory. Therefore, it was
necessary to develop a procedure whereby each
participant could generate a standard test atmosphere
in his own laboratory for use in collaborative testing.
Several methods are available for doing this, including
dilution of cylinder gases into plastic bags, successive
dilution stages using purified air, and others.
Fortunately, the recent development of calibrated
permeation tubes provided a more accurate and
reproducible method of generating test atmospheres,
and this method was chosen for the investigations
reported here. A major advance in this field is the
recent availability of certified permeation tubes for
sulfur dioxide from the National Bureau of
Standards.(6) By using these certified tubes, and con.
trolling all experimental conditions which influence
the rate of permeation, each laboratory could be
assured of an accurate primary standard to use in
evaluating the test method.
The permeation tubes used consist of a small
cylindrical tube of Teflon containing liquid sulfur
dioxide. The rate of diffusion of sulfur dioxide
through the walls of the cylinder depends only on
temperature and is reproducible within a reasonable
temperature range. The certification available from
the National Bureau of Standards covered the range
2
-------
0- to 15.Qlmin flowmeter
1 to 2% accuracy
Purified Compressed Air
or Cylinder Air
Rubber or Tygon Tubing
Tygon Tubing
Constant-Temp. Bath
:to. 1°C
68 em
Thermometer
Permeation Tube
Kjeldahl Mixing
Bulb (Large)
Vent to Hood
Glass Manifold
-----.1
15.0~
em
Connector (For Sampling Train)
FIGURE I. SPECIFICATIONS FOR PERMEATION TUBE SYSTEM USED
IN COLLABORATIVE TESTS
of 20° to 30°C and provided sufficient accuracy if
temperature control to within 0.1 °c was maintained.
If the rate of permeation is controlled accur-
ately through controlling the temperature, the only
other variable controlling the concentration of the
test atmosphere is flow rate. By passing air through
the permeation tube apparatus at a controlled flow
rate, and thus diluting the sulfur dioxide which
passed through the walls of the tube by diffusion, the
concentration of sulfur dioxide in the final air stream
could be accurately controlled. A special apparatus
was developed for this purpose which is illustrated in
Figure 1. Major portions of this system were fabri-
cated from pyrex glass, and temperature control was
achieved by enclosing the permeation tube holder in a
water jacket supplied by circulating water controlled
to within 0.1 °c. Purified air used for dilution was
measured accurately with calibrated rotameters.
The apparatus consisted primarily of a con-
denser capable of accommodating a permeation tube
and a 0.1 °c thermometer, a large KjeldaW trap to be
used as a mixing bulb, and a manifold with Teflon
stopcocks for sampling. The glassware is connected
by ground-glass ball joints. Associated parts for the
system include a calibrated flowmeter covering the
range of 0 to 100 cc/min with an accuracy of 5 per-
cent, a flowmeter covering the range of 0 to 15 Q/min
with an accuracy of 1 to 2 percent, a OJ °c
thermometer, and a constant-temperature bath
equipped with a circulating pump to continuously
supply water to the condenser. The bath must
be capable of maintaining the temperature within
:t0.1 or. Cylinder air or compressed air, purified
by carbon fIlters and driers (e.g., silica gel, molec-
ular sieve), and cylinder nitrogen are required to
complete the system.
A sulfur dioxide permeation tube obtained
from the National Bureau of Standards was inserted
into the condenser and the system assembled as
shown in Figure 1. Nitrogen was passed continuously
through the condenser housing the permeation tube
3
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and the 0.1 °c thermometer at a rate of 50 cc/min. It
is advisable to maintain this flow through the system
continuously in order to avoid sulfur dioxide accumu-
lation in the condenser tube. The temperature in the
system was adjusted to the desired temperature
(usually 25.0°C). After the permeation tube had been
equilibrated 24 hr, the dilution air was introduced
into the system and the flow adjusted to produce the
desired test atmosphere. Up to one-half of the total
flow of the system may be sampled. The concentra-
tion of sulfur dioxide in the standard atmosphere
generated was calculated according to the formula
found in Section 8.2.2.2 of the method (see Appen-
dix A). In order to conserve dilution air, it was shut
off at the end of a sampling day; however, the con-
stant-temperature bath and purge nitrogen gas were
normally left on.
Following the development of this system, the
permeation tube holder and other components were
fabricated and the necessary equipment for a com-
plete system was supplied to each participant in the
collaborative test series for use in his own laboratory.
Complete instructions were also supplied for using
this system to generate test atmospheres.
B.
Selection of Collaborators
If a collaborative test is to achieve the desired
objectives, it is necessary that the participants in the
test be representative of the large group that will
ultimately make use of the method being tested.
Since air pollution measurements are of interest to
many different groups, it was desirable to include in
the group of collaborators a variety of governmental
agencies, universities, industrial laboratories, and
others. The final selection of participants in all of the
testing which was performed included five partici-
pants from federal laboratories, nine from state and
10 c a 1 air pollution control agencies, two from
industry, and two from universities. A complete list
of the participants and their affiliation is given else-
where in this report.
Even more important than the type of la\>ora-
tory is the degree of skill of the persons who partici-
pated. Each laboratory was asked to assign a person
to this test who had previous experience with the
pararosaniline method and was competent in carrying
out determinations by this method. This was done to
avoid errors and greater variation in results which
might be produced by a group of inexperienced
workers. Each laboratory had previous experience in
the use of the method and thus possessed the
necessary equipment for collection of samples,
preparation and standardization of solutions, and
analysis by the colorimetric method used.
C.
First Collaborative Test
For the first collaborative test, permeation
tubes were furnished to seventeen collaborating
laboratories, together with the special holders, cali-
brated flowmeters, and other equipment described
previously to be used to generate test atmospheres.
One permeation tube was furnished for use in
familiarization runs plus two tubes to be used for test
purposes. Nominal test concentrations used were 130
and 780 f.l.g/m3 (approximately 0.04 and 0.3 ppm).
Participants were instructed to set up the equip-
ment for generation of test atmospheres, complete a
number of familiarization runs, and then analyze
samples obtained with the two tubes furnished for
test purposes. When the results were received, it was
found that many of the participants had deviated in
one way or another from the desired procedure and it
was necessary to normalize the data and recalculate
results to produce a set of "adjusted" data. If very
rigorous statistical and procedural requirements had
been adopted, it would have been necessary to dis-
card data obtained from fifteen of the sixteen labora-
tories completing the test and reporting results. In
order to salvage as much useful information as
possible from this test series, the adjustment of data
was used and included such changes as the following:
(1)
Elimination of calibration points higher
than 24 f.l.g of sulfur dioxide (see method,
Appendix A, Section 2.3), eight labora-
tories.
4
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(2)
Insertion of a zero-zero point on the cali-
bration curve for those laboratories (nine)
which plotted net absorbance and failed
to recognize (all nine) that a zero-zero
point exists.
After adjusting the data, only about one-half of
the participants (nine out of seventeen) submitted
results that could be used for statistical analysis. The
remainder included laboratories which did not sample
at the specified rate, some who used the wrong tem-
perature for the permeation system, or those which
were rejected on statistical grounds as outliers.
Following this adjustment and recalculation of
the data, a statistical analysis was performed on the
remaining subset of data from nine laboratories. The
results of this statistical analysis appeared to be
straightforward and reasonable, in view of the
expected results and the previously published infor-
mation concerning the precision and reliability of the
method. However, it was felt that any test in which
almost one-half of the data could not be used was
hardly valid to provide a rigorous statistical analysis
concerning the capabilities of the method as it was
intended to be used. Therefore, it was concluded
from this test that the method is inherently satis-
factory but is extremely vulnerable to misinterpre-
tation, as shown by the large number of participants
that failed to follow the method as specified and by
the large number of outliers. Therefore, additional
work was undertaken to provide a better test of the
tentative method, and these steps are described sub-
sequently.
D.
Fa mil i a r i zation Session and Second
Collaborative Test
In order to be sure that all participants fol-
lowed all details precisely in generating test atmos-
pheres and in carrying out the analysis by the tenta-
tive .method, a familiarization session was held to
review the entire procedure with the participants. The
session was held at the EPA training laboratory in
Durham, North Carolina, over a 3-day period. All
details of the method and test procedure were
reviewed, and each participant conducted alllabora-
tory operations in the training laboratory. Data from
these test runs were reviewed qualitatively, but no
detailed statistical analysis of the data was under-
taken. However, the results did appear to be consis-
tent with previous test results.
Following the familiarization session, the
participants were again given permeation tubes and
instructions for a complete collaborative test series,
with each again working in his own laboratory. The
value of this familiarization session is shown by the
fact that all participants in this test series returned
usable data, in distinct contrast to the original series
in which mistakes in procedure invalidated much of
the data obtained. The results of this test series were
then used for detailed statistical analysis, and this
series is considered to provide the best evaluation
available of the method being tested.
III. 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
important that the collaborators assume a responsi-
bility to try to eliminate any bias by carefully follow-
ing 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
5
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necessary to accept less than the ideal testing pro-
cedures in order to accomplish the program. Thus,
fundamental requirements may not be completely
fulf1lled, 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.
The conditions for the test were very carefully
prescribed. The method was tested for 30-min
sampling using the calibration procedure with sulfite
solution (see Sections 7 and 8, respectively, of the
method in Appendix A). The collaborative test pro-
cedure required that a separate calibration curve be
prepared for each separate day. In addition, certain
reagents were specified to be made fresh each day.
Stability was not the only criterion, since it was
desired to include the variation associated with these
operations in the between-days within-laboratories
variation (repeatability). These specific reagents are
identified below followed by the respective section
n umber in the method (see Appendix A). The
reagents prepared fresh were as follows: sulfamic acid
(6.2.1), formaldehyde (6.2.2), standardized sulfite
solution for preparation of working sulfite-TCM solu-
tion (6.2.8), and working sulfite-TCM solution
(6.2.9). A sufficient quantity of pararosaniline solu-
tion conforming to the specifications of the method
(see Section 6.2.10.2 of the method in Appendix A)
was supplied to each collaborator in the test.
Appendix B contains the complete and detailed
description of the design and analysis of the formal
collabora tive test which followed the Method
Familiarization Session. The results of Appendix B
are summarized in this section.
The primary purpose was to establish the reli-
ability of the method in terms of its systematic varia-
tion, 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
various steps within the method; therefore, inter-
mediate data were obtained relating to calibration
curves, control samples, and blanks.
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. The main experiment, as well as secondary
experiments, was designed so that the analysis of
variance technique could be used.
Fourteen laboratories took part in the final test
program. An analyst representing each laboratory
attended the Method Familiarization Session and sub-
sequently conducted the formal collaborative testing.
These individuals and their aff1liations have been
identified elsewhere in this report. These laboratories
constitute a random sample of a rather large popula-
tion of experienced laboratories. Three different con-
centrations were analyzed by each laboratory. The
concentrations were nominally 150, 275, and
820 Jlgfm3 . These concentrations, in addition to hav-
ing practical significance, were selected to approxi-
mate the low range, the optimum range, and the high
range for the method. Each of the three concentra-
tions was analyzed in triplicate on each of three
separate days using independently prepared reagents,
standards, and calibration curves. This resulted in a
total of 378 individual determinations.
The collaborative test was designed to allow the
analysis of the results using the most efficient statis-
tical methods available. The form of the analysis
depends upon the statistical model under considera-
tion. The experiment was designed so that the data
could be analyzed according to three different models
or techniques which are listed and described in
Appendix B. In addition to providing a comparison of
the techniques, this approach also provided the
opportunity to use the technique the results of which
were most convenient to apply. It was shown that
excellent agreement was obtained, and that an
analysis of variance with the data for all concentra-
tions analyzed together (with data transformation)
6
-------
provided the most convenient and useful application
of the results.
Supplementary or secondary experiments were
incorporated to evaluate errors associated with
various steps within the method. Each of these
supplementary experiments was designed so that the
data could be analyzed by the analysis of variance to
determine whether variations between days and
between laboratories were significant. The results of
each of these experiments will be discussed below.
A.
Outlying Observations
In accordance with the experiment design, the
full plan was carried out satisfactorily and without
any missing data. Two cases of atypical results were
present. These were dealt with in accordance with the
discussion and conclusions in Appendix B. A logical
substitute was made for each case to allow the
remainder of the data for the laboratory to be uti-
lized.
Since the emphasis was upon the quality of the
method and not upon the performance of the labora-
tories, all arithmetic errors were corrected, and the
arithmetic error problem was evaluated qualitatively.
Only three of the fourteen laboratories submitting
results exhibited any errors. Four instances of
inadvertent errors in arithmetic operations were
noted and corrected. The method contains complex
calculational procedures and consequently is vul-
nerable to arithmetic and procedural errors. However,
the majority of the collaborators demonstrated the
capability to handle this complexity. There is no
reason to believe that a careful checking procedure
could not eliminate this problem.
The results, after the disposition of the two
outlying observations, are believed to be an excellent
data base for the statistical analyses to follow. The
data are believed to be representative and unbiased.
The number of outliers was small, especially in com-
parison with the first test where nearly two-thirds of
the laboratories produced one or more atypical
results, many of which could not be corrected to
obtain usable data.
B.
Analysis 01 Variance
In Appendix B, three analyses are described and
the results discussed. The first two are classic analysis
of variance cases. The first handles each concentra-
tion separately, while the second combines all con-
centration data into a single analysis, and includes the
evaluation and application of the necessary data
transforma tion to allow this treatment. The third
case, the linear model an.alysis, does not strictly con-
stitute a classic analysis of variance case but does
involve the technique.
The comparison of methods is best made by
referring to the results in graphic form shown in
Figure 2. This figure compares the replication error,
the repeatability*, and the reproducibility'" for each
method of statistical analysis. First, the overall agree-
ment between these methods is very good. The agree-
ment for the replication error is exact because the
methods have this much in common. The point esti-
mates seem to imply a minimum for repeatability and
reproducibility in the midrange of concentration. The
other methods, because of their fundamental assump-
tions, do not recognize any minimum. In this respect,
the results are inconclusive, and an experiment incor-
porating many more intermediate concentrations
would be required to verify such a condition. In con-
sideration of the optimum absorbance range of most
spectrophotometers, such a minimum could be
entirely possible.
The point estimates are therefore of limited use
*The terms "repeatability" and "reproducibility" have been in use for many years, and it has not always been clear from the
context of each publication just what is the precise definition. A very recent publication (Mandel, John, "Repeatability and
Reproducibility," Materials Research and Standards, Am. Soc. Testing & Mats., Vol 11, No.8, p 8, (August 1971)] clears the
confusion by giving rigid definitions. While the use of these two terms in this report is not exactly consistent with the definitions
of Mandel, they are, nevertheless, well defined and are easily relatable.
7
-------
80
0 Concentrations handled separately
-- Concentrations handled together
70 with data transformation.
Linear model with data
transformation
"
60 (/
Reproducibility
50
M
E
.......
C)
::t
r::.'
.Q
....
.!!! 40
>
OJ
CI
"C
~
co
"C
r::.
co
....
(f)
30 0
20
10
o
o
Repeatability
o
Replication
200
400
600
1000
800
Concentration, p.g/m3
FIGURE 2. REPLICATION ERROR, REPEATABILITY, AND REPRODUCIBILITY VERSUS
CONCENTRATION FOR THREE DIFFERENT METHODS OF DATA ANALYSIS.
8
-------
since we must also make inferences between these
points. The other two methods of analysis provide for
objective estimates at other concentrations. The
second method, the analysis of variance with concen-
trations handled together, has the advantage of a
simple expression for the standard deviations as a
function. of concentration. The linear model expresses
the standard deviations as a function of concentra-
tion; however, the function is more complex. The
linear model has an advantage because of its ability to
describe and compare the various sources of error
more thoroughly. The linear model is less sensitive to
outlying observations.
On the basis of the preceding discussion, it was
concluded that the analysis of variance handling all
concentrations together (with data transformation)
offers the most convenient and practical method of
expressing the replication error, the repeatability, and
the reproducibility as a function of concentration. All
subsequent treatment of these parameters will be
made accordingly.
c.
Various Sources of Error Within the
Analytical Method
No study would be complete without at least a
superficial examination of certain steps within the
analytical procedure. This subsection deals with the
determination of the existence and the estimation of
the magnitude of some of these sources of error.
1.
Calibration Curves
The experiment was designed so that
complete data for each and every calibration curve
were retrieved. Each individual absorbance-concen-
tration point for each day for each laboratory was
recorded. These voluminous data are not reproduced
here. The purpose of this secondary experiment was
to examine the deviations from linearity of the
curves, to examine the distribution of the slopes of
these curves, and to evaluate the variability in slope
between days and between laboratories.
From these data, the slopes, the inter-
cepts, and the standard errors of estimate were com-
puted using the least squares technique. There were
fourteen laboratories and 3 days, thus yielding a table
of 42 entries for each parameter. These data are
shown in Table C-III in Appendix C.
We will first examine the standard errors
of estimate of these calibration curves. The overall
mean standard error of estimate was found to be
0.010 absorbance unit (41 degrees of freedom). At an
average slope of 0.030 absorbance unit per microgram
sulfur dioxide, this corresponds to 0.33 /J.g of sulfur
dioxide. Thus, the lower limit of detection for sulfur
dioxide (see Section 7.1.1 of the method in Appen-
dix A) at the 95 percent level of confidence is
2.02 X 0.33 or 0.67 /J.g, representing a concentration
of 22 /J.g/m3 for a 30-Q air sample. This is in excellent
agreement with the 25-/J.g/m3 limit claimed for the
method (see Section 2.2 of the method in Appen-
dix A). Other independent estimates of the lower
detection limit will be made later.
The overall linearity of the calibration
curves was not examined explicitly since the method
proposes a straight line relationship (see Section 2.1
of the method in Appendix A). A qualitative
examination was made resulting in the general con-
clusion that the upper end of the calibration curves
contributed most heavily to the standard error of esti-
mate. This does not necessarily imply nonlinearity
but suggests increasing inaccuracy in absorbance read-
ings at the higher end. These effects could be mini-
mized by using a weighted least squares tech-
nique(7-8) in which the relative deviations are
minimized rather than the absolute deviations. In
view of the magnitude of the overall precision of the
method, this refinement, although no more difficult
or complex than the conventional least squares tech-
nique, is probably not justified.
The data for the slopes of the calibration
curves were normally distributed with the possible
exception of Laboratory 926, whose slopes appeared
to be atypically low. These data were subjected to an
analysis of variance involving two factors-labora-
9
-------
tories and days. The variation between laboratories
was significant (95 percent level of significance) with
respect to the variation between days. The com-
ponent of variance due to laboratories constituted
about 80 percent of the total variance. The standard
deviation of the slope for variation between days was
0.00082 absorbance unit per microgram (28 degrees
of freedom) while the corresponding standard devia-
tion for between-laboratories variation was
0.00195 absorbance unit per microgram (13 degrees
of freedom). The overall mean slope was
0.0298 absorbance unit per microgram. The 95 per-
cent confidence interval was therefore 0.0298 t
0.0017 for within-laboratories and 0.0298 t 0.0042
for between-laboratories. The overall mean is in excel-
lent agreement with that claimed for the method, and
the within-laboratory confidence interval corresponds
almost exactly to the claim for the method (see Sec-
tion 6.2.10.1 of the method in Appendix A). The
important observation is that the variation between
laboratories is approximately 2.5 times as much as
the variation within laboratories, which partially
accounts for the relatively poor interlaboratory pre-
cision demonstrated previously.
These calibration curves were further
investigated with respect to the absorbance-axis inter-
cept (see Table C-III in Appendix C). The absolute
magnitude of the intercept as well as its respective
deviation from the zero-standard absorbance was
investigated. The variation between laboratories was
significant (95 percent level of significance) with
respect to the variation between days for the absolute
magnitude of the intercept. The component of
variance due to laboratories contributed two-thirds of
the total variance. The standard deviation of the
intercept, for variation between days, was
0.013 absorbance unit (28 degrees of freedom), while
the corresponding standard deviation for variation
between laboratories was 0.022 absorbance unit
(13 degrees of freedom). The overall mean was
0.163 absorbance unit. The 95 percent confidence
intervals were therefore 0.163 t 0.026 for within-
laboratories and 0.163 t 0.048 for between-labora-
tories. Since the reagent blank is temperature
sensitive, it is not surprising to find significant inter-
laboratory variation. The overall mean of 0.163 is
comparable to the value suggested as a guide by the
method (see Section 6.2.10.1 of the method in
A ppendix A); however, because of temperature
effects, no rigid comparison is valid.
The deviations of the zero-absorbance
standards from the intercepts of the calibration
curves were analyzed, and the effects due to labora-
tories were found to be not significant (95 percent
level of significance). The overall mean was not
significantly different from zero. The standard devia-
tion (pooled estimate with 41 degrees of freedom)
was 0.006 absorbance unit corresponding to a 95 per-
cent confidence interval of to.O 11 absorbance unit.
This is well below a value of 0.03 specified in the
method (see Section 8.2.1 of the method in
Appendix A).
2.
Control Samples
The method prescribes that a control
sample, consisting of an aliquot of standard sulfite
solution, is to be included with each set of determina-
tions (see Section 7.2.2 of the method in
Appendix A). The results of all of these control
samples were analyzed.
Some laboratories ran more control
samples than others and one laboratory (788) did not
run any. A set of data was constructed consisting of
three randomly selected control samples for each of
twelve laboratories. Most laboratories had analyzed
three control samples (one each day), except Labora-
tory 578 which analyzed only one. Consequently,
Laboratories 578 and 788 were not included in this
analysis.
The data consisted of a table of 36 values
(twelve laboratories X 3 days), which were the result
of subtracting the amount taken from the amount
found, both in micrograms of sulfur dioxide. These
data are shown in Table C-IV in Appendix C. All data
were of the approximate same order of magnitude,
allowing this approach. The differences were
normally distributed.
10
-------
The analysis of variance found the
between-laboratory variability to be significant
(95 percent level of significance) with respect to the
within -laboratory variability. The between-laboratory
variance accounted for 42 percent of the total
variance while the within-laboratory variance
accounted for the remaining 58 percent. The standard
deviation for within-laboratory variation was 0.4 J.1.g
(24 degrees of freedom), and the standard deviation
for between-laboratory variation was 0.5 J.1.g
(11 degrees of freedom). The overall mean was found
to be insignificantly different from zero. The 95 per-
cent confidence interval for within-laboratory varia-
tion was therefore 1:.0.77 J.1.g, and the corresponding
interval for between-laboratory variation was
1:.1.08 J.1.g. In terms of concentration, for a 30-Q air
sample, these values become 26 J.1.gfm3 and 36 J.1.gfm3 ,
respectively. The first figure is another independent
estimate of the lower limit of detection and also veri-
fies the claim for the method (see Section 2.1 of the
method in Appendix A).
The method (see Section 7.2.2 of the
method in Appendix A) specifies that a control
sample be run with each set of determinations, but
does not set any specifications regarding the results
obtained. If the difference (in micrograms of sulfur
dioxide) between the amount taken and the amount
found exceeds 0.8 J.1.g, either the control sample or
the calibration curve is suspect and should be checked
accordingly.
3.
Reagent Blanks
The method prescribes that a reagent
blank is to be included with each set of determina-
tions (see Section 7.2.2 of the method in Appen-
dix A). An analysis of all reagent blanks run along
with samples was made, and the differences between
the blank and the intercept of the calibration curve
were analyzed. All data were normally distributed,
except that from Laboratory 788 which contained an
unusually high and an unusually low difference.
These data are shown in Table C-V in Appendix C. In
this case, a graphic analysis was made by plotting the
results on normal probability graph paper. All results,
including those of Laboratory 788, were within
1:.0.04 absorbance unit, and 95 percent of the results
were within 1:.0.03 absorbance unit. The overall mean
was zero. These results conform to the criteria set
forth in the method (see Section 7.2.2 of the method
in Appendix A) and also with the results from Sec-
tion 1II-C-1 above which compared the intercept of
the calibration curve with the zero-absorbance stan-
dard (reagent blank).
D.
Application of the Results
A more detailed application of results is given
in Appendix B. In this subsection, the various mea-
sures of precision are summarized. Unless otherwise
stated below, a 95 percent level of significance is
assumed. The results apply for 30-min sampling and
the use of the calibration procedure with sulfite solu-
tion.
The expressions for the replication error (aE),
the within-laboratory (single-replicate, single-analyst)
variation (repeatability) (aD), and the between-
laboratory (single-replicate, single-day, single-analyst)
variation (aL) from Figure 1 are restated as follows:
aE = (0.7 + O.OOly) (10)
aD = (0.7 + O.OOly) (21)
aL = (0.7 + O.OOly) (41)
where y is the concentration in J.1.gfm3 . All statements
regarding the precision of the method are derived
from these expressions. With these equations, the pre-
cision for any desired case can be computed. Some of
the simpler cases are shown below.
Replication will not materially assist in increas-
ing the precision of the method, and will, in general,
be a waste of time and effort. Nevertheless, a measure
of acceptability of replicates should be provided. The
expression for the checking limits for duplicates is
Rmax = (2.77) (0.7 + O.OOly) (10)
where Rmax is the maximum permissible difference
11
-------
between duplicates. Two such replicates should be
considered suspect if they differ by more thanRmax.
Agreement between duplicates better than
5 percent cannot be expected below 900 p.gfm3
Agreement better than 10 percent cannot be
expected below 300 p.gfm3, and agreement better
than 20 percent cannot be expected below
100 p.gfm3 .
To compare two single-replicate observations
made by the same analyst on the same sample on
different days, the following expression is used:
Rmax = (2.82) (0.7 + O.OOly) (21)
where Rmax is the maximum permissible difference
between the two results. Two such values may not be
considered to belong to the same population if they
differ by more than Rm ax' Conversely, the two
values are not significantly different if they differ by
less thanRmax'
The method cannot detect a difference smaller
than 10 percent between two observations by the
same analyst in the range of 0 to 1000 p.gfm3 A
difference of 20 percent or less may be detected
above 300 p.gfm3, and a difference of less than
50 percent may be detected above 100 p.gfm3
As an example of the futility of replication, the
factor 21 in the equation above would be reduced to
20 for duplicates, approximately the same for tripli-
cates, and to 19 for an infinite number of replicates.
To compare two single-replicate observations
made by different laboratories on the same sample,
the following expression is used:
Rmax = (3.06) (0.7 + O.OOly) (41)
where Rmax is the maximum permissible difference
between the observations. Two such values may not
be considered to belong to the same population if
they differ by more than Rmax. Conversely, the two
values are not significantly different if they differ by
less thanRmax.
The method cannot detect a difference of less
than 20 percent between single-replicate observations
of two laboratories in the range of 0 to 1000 p.gfm3 .
At a level of 100 p.gfm3, a difference of less than
100 percent is not detectable.
Various statistical methods are available for the
comparison of means or the comparison of a mean
and a fixed value.(9-11) These methods are straight-
forward and are applied independently of the results
of this study. That is, whether or not a mean is
significantl:y different from some fixed value is depen-
dent upon the actual standard deviation of the sample
population. The variance of the sample population
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 assump-
tion that all variation is due to the measurement
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 com-
pensate 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 B4 and B-5 and the respective
discussions in Section B-V of Appendix B where two
illustrative examples are given.
Three independent estimates of the lower limit
of detection were made. These are in very good agree-
ment, and it is not too important which one is used;
therefore, a value of 25 p.gfm3 is proposed as a
practical figure. A single determination less than this
value is not significantly different from zero. Whether
the mean of several observations, each a single deter-
mination, is significantly different from zero is depen-
dent upon the number of observations and their dis-
tribution, regardless of the magnitude of the mean.
Recorded results of a determination using this
method should carry no more than two significant
digits. Originators or recorders of data should assume
the responsibility of appending confidence limits
(95 percent) to their data.
12
-------
The overall average deviations from the
expected values for each concentration tested were
not significant, and therefore no systematic error,
bias, or inaccuracy was detectable.
LIST OF REFERENCES
1.
West, P.W., and Gaeke, G.C., "Fixation of Sul-
fur Dioxide as Sulfitomercurate III and Sub-
sequent Colorimetric Determination," Anal.
Chern. 28, pp 1816 (1956).
2. Youden, W.J., "The Collaborative Test,"
Journal of the AOAC, Vol 46, No.1, pp 55-62
(1963).
3.
1968 Book of ASTM Standards, Part 30,
Recommended Practice for Developing Pre-
cision Data on ASTM Methods for Analysis and
Testing of Industrial Chemicals, ASTM Designa-
tion: E180-67, pp 459-480.
4. Handbook of the AOAC, Second Edition,
October 1, 1966.
5.
ASTM Manual for Conducting an Interlabora-
tory Study of a Test Method, ASTM STP
No. 335,Am. Soc. Testing & Mats. (1963).
6.
National Bureau of Standards, "New Sulfur
Dioxide Permeation Tube," NBS Technical
News Bulletin, p 106 (April 1971).
7. Cook, Peter P.., and Grady, Roger A., "Analysis
of Flow Sensor Calibration Data," Instruments
and Control Systems, Vol 44, No.4,
pp 101-102 (April 1971).
8.
Southwest Research Institute, Houston, Texas,
Computer Subroutine WTLSQ for Weighted
Least Squares Regression Analysis, Unpublished
(1971).
9.
Dixon, Wilfred J., and Massey, Frank J., Jr.,
Introduction to Statistical Analysis, McGraw-
Hill Book Company, Inc., New York,
Chapter 9, pp 112-129 (1957).
10.
Duncan, Acheson 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.,
Statistical Analysis in Chemistry and the
Chemical Industry, John Wiley and Sons,
New York, Chapter 5, pp 149-164 (1954).
13
-------
APPENDIX A
REFERENCE METHOD FOR THE DETERMINATION
OF SULFUR DIOXIDE IN THE ATMOSPHERE
(PARAROSANILINE METHOD)
Reproduced from Appendix A, "National Primary and Secondary
Ambient Air Quality Standards," Federal Register, Vol 36,
No. 84, Part II, Friday, April 30, 1971.
-------
ApPENDIX A.-REFERENCE :METHOD FOR TUE
DETERMINATION OF SULFUR DIOXIDE IN THe
ATMOSPHERE (PARAROSANILINE METHOD)
1. Principle and Applicability. 1.1 Sulfur
dioxide Is absorbed from air In a solution of
potassium tetrachloromercurate (TCM). A
dlchlorosulfitomercurate complex, which re.
slsts oxidation by the oxygen In the air, ,S
formed (1, 2). Once formed, this complex Is
stable to strong oxidants (e.g., ozone, oxides
of nitrogen).. The complex Is reacted with
pararosanUine and formaldehyde to form In-
tensely colored pararosan1l1ne methyl sul-
fonic acid (3). The absorbance of the solu-
tion is measured spectrophotometrically.
1.2 The method Is applicable to the meas-
urement of sulfur dioxide In ambient air
using sampling periods up to 24 hours.
2. Range and Sensitivity. 2.1 Concentra-
tions of sulfur dioxide In the range of 25 to
1.050 /
-------
properly standardized.
6.2.10.2 Preparation of stock Solution. A
specially purified (99-100 percent pure) so-
lution of pararosaniline, which meets the
above specifications, Is commercially avail-
able in the required 0.20 percent concen-
tration (Harleco'). Alternatively, the dye
may be purified, a stock solution prepared
and then assayed according to the proce-
dure of 8carlngelll, et al. (4)
6.2.11 Pararosaniline Reagent. To a 250-
mi. volumetric fiask, add 20 mi. stock par-
arosaniline solution. Add an additional 0.2
mi. stock solution for each percent the stock
assays below 100 percent. Then add 25 mi.
3 M phosphoric acid and dilute to volume
with distilled water. This reagent is stable
for at least 9 months.
7. Procedure.
7.1 Sampling. Procedures are described
for short-term (30 minutes and 1 hour) and
for long-term (24 hours) sampl1ng. One can
select different - combinations of sampl1ng
rate and time to meet special needs. Sample
volumes should be adjusted, so that linearity
is malntained between absorbance and con-
centration over the dynamic range.
7.1.1 30-Minute and I-Hour Samplings.
Insert.. midget imp Inger into the sampling
system, Figure AI. Add 10 mi. TCM solution
to the Impinger. Collect sample at 1 liter/
minute for 30 minutes, or at 0.6 liter/minute
10r 1 hour, using either a rotameter, as
shown in Figure AI, or a critical orifice, as
shown in Figure Ala, to control lI.ow. Shield
the absorbing reagent 1rom direct sunlight
during and after sampling by covering the
impinger with aluminum 1011, -to prevent
deterioration. Determine the volume 01 air
sampled by multiplying the lI.ow rate by the
time in minutes and record the atmos-
pheric pressure and temperature. Remove
and stopper the impinger. If the sample
must be stored 10r more than a day before
analysts, keep it at 6' C. in a refrigerator
(see 4.2).
7.1.2 24-Hour Sampling. Place 60 mi.
TCM solution in a large absorber and col-
lect the sample at 0.2 liter/minute 10r 24
hours from midnight to midnight. Make sure
no entrainment 01 solution results with the
1mpinger. During collection and storage pro-
tect 1rom direct sunlight. Determine the
total air volume by multiplying the air lI.ow
rate by the time In minutes. The correction
of 24-hour measurements 10r temperature
and pressure is extremely dlmcult and is not
ordinarily done. However, the accuracy of
the measurement will be improved If mean-
1ngful corrections can be applied. If storage
1s necessary, re1rlgerate at 6' C. (see 4.2).
7.2 Analysis..
7.2.1 Sample Preparation. After collection,
11 a precipitate 1s observed in the sample,
remove it by centrifugation.
7.2.1.1 30-Minute and I-Hour Samples.
Transfer the sample quantitatively to a 26-
mi. volumetric lI.ask; use about 6 mi. dlst1lIed
water 10r rinsing. Delay analyses 10r 20 min-
utes to allow any ozone to decompose.
7.2.1.2 24-Hour Sample. Dl1ute the entire
sample to 60 mi. with absorbing solution.
Pipet 6 mi. of the sample into a 25-ml.
volumE:,tric lI.ask 10r chemical analyses. Bring
volume to 10 mi. with absorbing reagent.
Delay analyses for 20 minutes to allow any
ozone to decompose.
7.2.2 Determination. For each set 01 de-
terminations prepare a reagent blank by add-
ing 10 mi. unexposed TCM solution to a 25-
mL volumetric flask. Prepare a control solu-
tion by adding 2 mi. 01 working sulfite-TCM
solution and 8 mi. TCM solution to a 26-ml.
volumetric flask. To each flask containing el-
'Hartmen-Leddon, 60th and Woodland
A venue, Philadelphia, PA 19143.
RULES AND REGULATIONS
ther sample, control solution, or reagent
blank add 1 mI. 0.6 percent sulfamlc
acid and allow to react 10 minutes to de-
stroy the nitrite from oxides of nitrogen.
Accurately pipet in 2 ml. 0.2 percent
formaldehyde solution, then 6 mi. par-
arosaniline solution. Start a laboratory
timer that has been set for 30 minutes. Bring
aU flasks to volume with freshly bol1ed and
cooled dtst1lled water and mix thoroughly.
After 30 minutes and before 60 minutes, de-
termine the absorbances of the sample (de-
note as A) , reagent blank (denote as A.) and
the control solution at 648 nm. using 1-cm.
optical path length cells. Use dlst1lled water,
not the reagent blank, as the reference.
(NOTE I Thts ts important because of the color
sensitivity of the reagent blank to tempera-
ture changes which can be induced in the
cell compartment of a spectrophotometer.)
Do not allow the colored solution to stand
in the absorbance cells, because a film of dye
may be deposited. Clean cells with alcohol
after use. If the temperature of the determi-
nations does not differ by more than 2' C.
1rom the calibration temperature (8.2), the
reagent blank should be within 0.03 absorb-
ance unit of the y-Intercept 01 the calibra-
tion curve (8.2), If the reagent blank differs
by more than 0.03 absorbance unit from that
10und in the calibration curve, prepare a new
curve.
7.2.3 Absorbance Range. If the absorbance
of the sample solution ranges between 1.0
and 2.0, the sample can be dl1uted 1: 1 with
a portion of the reagent blank and read
within a few minutes. Solutions with higher
absorbance can 1;>e diluted up to sixfold with
the reagent blank in order to obtain onscale
readings within 10 percent of the true ab-
sorbance value.
8. Calibration and Efficiencies.
8.1 Flowmeters and' Hypodermic Needle.
Calibrate flowmeters and hypodermic nee-
dle (8) against a calibrated wet test meter.
8.2 Calibration Curves.
8.2.1 Procedure with Sulfite Solution. Ac-
curately pipet graduated amounts of the
working sulflte-TCM solution (6.2.9) (such
as 0, 0.6, I, 2, 3, and 4 mi.) into a series of
26-ml. volumetric flasks. Add sumcient TCM
solution to each flask to bring the volume to
approximately 10 ml. Then add the remaining
reagents as described in 7.2.2. For maximum
precision use a constant-temperature bath.
The temperature of calibration must be
maintained within :t I' C. and in the range
of 20' to 30' C. The temperature of calibra-
tion and the temperature of analysis must be
within 2 degrees. Plot the absorbance against
the total concentration in ",g. SO. for the
corresp0!ldlng solution. The total ~. SO. in
sol utlon equals the concentration of the
standard (Section 6.2.9) in ",g. SO,/ml. times
the mi. sulflte solution added- (",g. 80.=
",g./ml. 80,X mi. added). A linear relation-
ship should be obtained, and the y-intercept
should be within 0.03 absorbance unit of the
zero standard absorbance. For maximum pre-
cision determine the line of best fit using
regression analysis by the method of least
squares. Determine the slope of the line of
best flt, calculate its reciprocal and denote
as B,. B, ts the calibration factor. (See Sec-
tion 6.2.10.1 for specifications on the slope of
the calibration curve). This calibration fac-
tor can be used for calculating results pro-
vided there are no radical changes in
temperature or pH. At least one control
sample containing a known concentration of
So, for each series of determinations, is
recommended to insure the i'eliab1l1ty of this
factor.
8.2.2 Procedure with SO. Permeation
Tubes.
8.2.2.1 General Considerations. Atmos-
pheres containing accurately known amounts
of sulfur dioxide at levels of interest can be
prepared using permeation tubes. In the
systems for generating these atmospheres,
the permeation tube emits SO, gas at a
known, low, constant rate, provided the tem-
perature of the tube is held constant (:to.1'
C.) and provided the tube has been accu-
rately calibrated at the temperature of use.
The SO. gas permeating from the tube is
carried by a low flow of inert gas to a mix-
ing chamber where It ts accurately dl1uted
with SO,-free air to the level of interest and
the sample taken. These systems are shown
schematically in Figures A2 and A3 and have
been described in detal1 by O'Keeffe and
Ortman (9), Scaringel11, FrI\Y, and Saltzman
(10), and Scaringelll, O'Keeffe, Rosenberg,
and Bell (11).
8.2.2.2 Preparation 01 Standard A tmos-
pheres. Permeation tubes may be prepared
or purchased. Scaringelll, O'Keeffe, Rosen-
berg, and Bell (11) give detailed, explicit
directions for permeation tube calibration.
Tubes with a certified permeation rate are
available from the National Bureau of Stand-
ards. Tube permeation rates from 0.2 to 0.4
~./mlnute inert gas flows of about 60 mI./
minute and dilution air fiow rates from 1.1
to 16 liters/minutes conveniently give stand-
ard atmospheres containing desired levels
of SO. (26 to 390 ",g./m.'; 0.01 to 0.15 p.p.m.
SO,) . The concentration of SO, in any stand-
ard atmosphere can be calculated as follows:
P X 10'
C=-
Rd+RI
Where:
o =Concentration of SQ" ",g./m.' at ref-
erence conditions.
P = Tube permeation rate, ",g./mlnute.
Rd=Flow rate of dilution air, liter/minute
at reference conditions.
RI = Flow rate of inert gas, liter/minute at
reference conditions.
8.2.2.3 Sampling and Preparation of Cali-
bration Curve. Prepare a series (usually six)
of standard atmospheres containing SQ,
levels from 26 to 390 ",g. SO,/m.'. Sample each
atmosphere using similar apparatus and tak-
ing exactly the same air volume as will be
done in atmospheric sampling. Determine
absorbances as directed In 7.2. Plot the con-
centration of So. In ",g./m.' (x-axis ~ against
A-A, values (y-axis), draw the straight line
of best fit and determine the slope. Alter-
nativel:,r, regression analysis by the method
of least squares may be used to calculate the
slope. Calculate the reciprocal of tile slope
and denote as B..
8.3 Sampling Efficiency. Colleel1on effi-
ciency Is above 98 percent; emc1ency may
fall off, however, at concentrations below 25
",g,fm.'. (12,13)
9. Calculations.
9.1 Conversion 01 Volume. COllvert the
volume of air sampled to the volume at ref-
erence conditions of 25' C. and 760 mm. Hg.
(On 24-hour samples, this may not be
possible.) P 298
VR=VX-X-
760 t+273
VR=Volume of air at 26' C. and 760 mm.
Hg, liters.
V =Volume of air sampled, liters.
P =Barometric pressure, mm. Hg.
t =Temperature of air sample, 'C.
9.2 Sulfur Dioxide Concentration.
9.2.1 When sulfite solutions are used to
prepare calibration curves, compute the con-
centration of sulfur dioxide in the sample:
(A-A.) (1()3) (B.)
",g.SO,/m.'- YD
VR
A =8ample absorbance.
A,=Reagent blank absorbance.
l()3=Converslon of liters to cubic meters.
VR =The sample corrected to 25' C. and
760 mm. Hg, liters.
FEDERAL REGISTER, VOL. 36, NO. 84-FRIDAY, APRIL 30, 1971
A-2
-------
RULES AND REGULATIONS
B. = Cal1bratlon factor. ILg./absorbance
unit.
D =Dllutlon factor.
For 30-mlnute and I-hour samples,
D=I.
For 24-hour samples, D= 10.
9.2.2 When SO. gas standard atmospheres
are used to prepare calibration curves, com-
pute the sulfur dioxide In the sample. by the
following formula:
SO"ILg./m.' = (A-A.) XBg
A = Sample absorbance.
Ao=Reagent blank absorbance.
B. = (See 8.2.2.3) ,
9.2.3 Conversion 01 p.g./m.' to p.p.m.=It
desired, the concentration of sulfur dioxide
may be calculated as p.p.m. SO, at reference
conditions as follows:
p.p.m. BO,=p.g. BO,/m.' x 3.82 X 10""
10. Be/erences.
(1) West, P. W., and Gaeke, G. C., "Fixa-
tion of Sulfur Dioxide as Sulfltomer-
curate III and Subsequent Colori-
metric Determination", Anal. Chern.
28,1816 (1956).
(2) Ephralms, F., "Inorganic Chemistry,"
p. 562, Edited by P.C.L. Thorne and
E. R. Roberts, 5th Edition, Inter-
science. (1946).
(3) Lyles, G. R., Dowl1ng, F. B., and Blanch-
ard, V. J., "Quantitative Determina-
tion of Forma\dehyde In Parts Per
Hundred Million Concentration Lev-
el", J. Air Poll. Cont. Assoc. 15, 106
(1965) .
(4) Scaringelll, F. P., Saltzman, B. E., and
Frey, S. A., "Spectrophotometric De-
termination of Atmospheric Sulfur
Dioxide", Anal. Chern. 39, 1709 (1967).
(5) Pate, J. B., Ammons, B. E., Swanson,
--
::;)
TO
IMPINGER
\.
30ml
20ml
10 mJ
GLASS
WOOL
IMP INGER
TRAP
Fi9ure Ai. Sampling Iraln.
G. A., Lodge, J. P., Jr., "Nitrite In-
terference In Spectrophotometric De-
termination of Atmospheric Sulfur
DIoxide", Anal. Chem. 37, 942 (1965).
(6) Zurlo, N. and Grlffinl, A. M., "Measure-
ment of the SO, Content of Air In the
Presence of Oxides of Nitrogen and
Heavy Metals", Med. Lavero, 53, 330
(1962) .
(7) Scaringelll, F. P., Elfers, L.. Norris, D..
and Hochhelser, S., "Enhanced Sta-
bility of Sulfur Dioxide In Solution".
Anal. Chern. 42,1816 (1970).
(8) Lodge, J. P. Jr., Pate, J. B., Ammons,
B. E. and Swanson, G. A., "Use of
Hypodermic Needles as Critical Ori-
fices in Air Sampl1ng," J. Air Poll.
Cont. Assoc. 16,197 (1966).
(9) O'Keeffe, A. 'E.. and Ortman,. G. C.,
"Primary Standards for Trace Gas
Analysis", Anal. Chern. 38, 760 (1966).
(10) Scaringelll. F. P., Frey, S. A., and Saltz-
man, B. E.. "Evaluation of Teflon
Permeation Tubes for Use with Sulfur
Dioxide", Amer. Ind. Hygiene Assoc.
J. 28,260 (1967).
(11) Scaringelll, F. P., O'Keeffe, A. E., Rosen-
berg, E., and Bell, J. P., "Preparation
of Known Concentrations of Gases
and Vapors with Permeation Devices
Calibrated Gravimetrically", Anal.
Chern. 42,871 (1970).
(12) Urone, P., Evans, J. B., and Noyes, C. M.,
"Tracer Techniques In Sulfur DI-
oxide Colorimetric and Conductlo-
metric Methods", Anal Chern. 37, 1104
(1965) .
(13) Bostrom, C. E., "The Absorption of Sul-
fur Dioxide at Low Concentrations
(p.p.m.) Studied by an Isotopic
Tracer Method", Intern. J. Air Water
Poll. 9, 33 (1965).
HYPODERMIC
NEEDLE
-- RUBBER
SEPTUM
--
TOAJR
PUMP
MEMBRANE
FIL TER
Fi9ure Aia, Critical orifice flow control.
FEDERAL REGISTER. VOL, 36, NO. 84-FRIDAY, APRIL 30, 1971
A-3
-------
RULES AND REGULATIONS
TO HOOD
THERMOI.IETER
I'EllMEATIOH TUlia
IIUIIBL.E;R
FLOW IIETER
OR CRITICAl.
ORIFICE
DRIER
STIRRER
WATER IATIt
Flg\II1 Mo. APPIIaIW lor Alavlllltlric caUlntton 111<111,14 ..
CLE1AN 011' AIR
NEEDll;; VAlve
o
f'LOIIII!;;TER
OR
DRY TEST
II!;;TER
PERMEA TIDN TUBE
THERMOMETER
PURIFIED
AIR
OR
CYLINDER
tlITROGJ;;Jf
WAST!
DRIER
FIgure ",. FeQllullon lube IchelllOlle rot laboratory UI~.
FEDERAL REGISTER, YOLo 36, NO. 84-FRIDAY, APRIL 30, 1971
A-4
CYLINDER
AIR OR
NITRQGEN
1'1'" TER
pUMP
-------
APPENDIX B
STATISTICAL DESIGN AND ANALYSIS
-------
I.
II.
III.
IV.
TABLE OF CONTENTS
INTRODUCTION
. . . .
A.
B.
Purpose and Scope of the Experiment
Design of the Experiment
. . . . .
. .. . . . .. .
.. .. .. .
. . . .
PRELIMINARY DATA ANALYSIS. . .
A.
B.
C.
Presentation of Data. . . . . . .
Tests for Outlying Observations . . . .
Discussion of Results of Preliminary Data Analysis.
ANALYSIS OF VARIANCE
. .. . .. . ..
0- .. . .. .. .. .
.. . .. ..
.. . .. . .. . ..
A.
B.
C.
D.
Analysis of Variance of Concentrations Separately . . . .
Analysis of Variance for All Concentrations Analyzed Together
Linear Model Analysis. . . .
Comparison of Methods and Discussion of Results
APPLICATION OF THE RESULTS
. . .. .
A.
B.
C.
Precision of the Method
Lower Limit of Detection. .. ""
Accuracy and Bias. . . . . . . . . . . .
. .. . .. .. .. .. .. .
. . " .
LIST OF REFERENCES.
.. .. .. ..
B-i
.. . .. . " .
. . . .
. .. . .
.. . .. . . .
Page
8-1
8-1
8-1
8~3
84
84
8-6
8-7
8.7
8~9
8~11
8-14
8-16
8-16
8-19
8-22
8-22
-------
Figure
B-1
B-2
B-3
B-4
B-5
Table
B-1
B-II
B-III
B-IV
B-V
B-VI
B-VII
B-VIII
LIST OF ILLUSTRATIONS
Design of Sulfur Dioxide Method Experiment. L, Laboratories; D, Days;
C, Concentrations; R, Replicates. . . . . . . . . . . . . . . .
. . . . . .
Control Charts for Means, Slopes, and Standard Errors of Estimate for Linear Model
Analysis. Data in Transformed Scale. . . . . . . . . . . . . . . . .
Replication Error, Repeatability, and Reproducibility Versus Concentration for
Three Different Methods of Data Analysis. . . . . . . . . . . . . . .
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 (0.7 + O.OO1Xl) (41). . . . . . . . . . . . .
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 (0.7 + O.OO1J..LO) (41). . . . . . .
LIST OF TABLES
Deviation from Expected Values for Each Replicate for Each Concentration for Each
Day for Each Laboratory. Micrograms per Cubic Meter. ............
Analysis of Variance for Each Concentration. Data in Original Scale. Three
Factors: l, Laboratories; D, Days; R, Replicates. . . . . . . . . . . . .
Components of Variance for Each Concentration. Data in Original Scale. Three
Factors: l, Laboratories; D, Days; R, Replicates. . . . . . . . . . . . .
Analysis of Variance for All Concentrations Together. Data in Transformed Scale. Four
Factors: L, Laboratories; M, Materials or Concentrations; D, Days; R, Replicates. . . .
Components of Variance for All Concentrations Together. Data in Transformed Scale.
Four Factors: l, Laboratories; M, Materials or Concentrations; D, Days; R, Replicates.
Means, Slopes, and Standard Errors of Estimate for Linear Model Analysis. Data in
Transformed Scale. . . . . . . . . . . . . . . . . . . .. """
Analysis of Variance for linear Model. Data in Transformed Scale.
. . . . .
Components of Variance and Their Relative Importance for the Linear Model Analysis.
Components are Expressed as Standard Deviations in the Original Scale.. . . . . . .
B-ii
Page
B-2
B-12
B-IS
B-20
B-21
Page
B-S
B-8
B-8
B-1O
B-IO
B-12
B-B
B-14
-------
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
details of the program must be planned keeping the
prime objective in mind. This appendix describes the
design and analysis of the formal collaborative test
which followed the Method Familiarization Session.
The Method Familiarization Session has been
described in the main report.
A.
Purpose and Scope of the Experiment
The primary purpose was to establish the reli-
ability of the method in terms of systematic varia-
tion, precision, and accuracy. More emphasis was
placed on the inherent quality of the method when
properly used than upon the performance of the
laboratories-from the standpoint of the selection of
collaborators as well as from the standpoint of the
disposition of outlying results.
At the same time, 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, control samples, and blanks. As
a result, a substantial amount of data was obtained in
addition to the end result of the analytical procedure.
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, and days upon the pre-
cision of the method in addition to estimating the
replication error. The main experiment and all
B.l
secondary experiments were designed so that the
analysis of variance technique could be used.
Fourteen laboratories took part in the program.
An analyst. representing each laboratory attended the
Method Familiarization Session and subsequently
conducted the formal collaborative testing. These
individuals and their affiliations have been identified
elsewhere in the main report. These laboratories con-
stitute a random sample from a rather large popula-
tion of experienced laboratories.
Three different concentrations were analyzed
by each laboratory. The concentrations were
nominally 150, 275, and 820 J1g/m3. These concen-
trations were selected to approximate the low range,
the optimum range, and the high range for the
method. Due to variations among permeation tubes
and to variation in atmospheric pressure and tempera-
ture, it was not possible for each laboratory to
generate test atmospheres having the exact values
above; however, the expected concentration can be
determined accurately as a function of permeation
tube temperature, dilution air temperature and pres-
sure, and volumetric flow rate of the dilution air. The
permeation tube system has been described in the
main report. In most instances, it was the deviations
of the observed values from the expected values that
were subjected to statistical analysis.
Each of the three concentrations was analyzed
in triplicate on each of three separate days using
independently prepared reagents, standards, and cali-
bration curves. The reagents which were to be
prepared fresh each day are identified in the main
report. In the designation of the reagents to be
prepared fresh each day, stability was not the only
criterion since these operations represent a portion of
the variation between days.
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 incor-
porates this technique 9 -3)* In general, analysis of
variance 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 efficient statistical methods available in
analyzing the results. High efficiency in data utiliza-
tion becomes more important when the amount of
data is limited.
The form of the analysis depends upon the
statistical model under consideration. The experiment
was designed so that the data could be analyzed
according to three different models or techniques as
follows:
.
Analysis of variance with the data for
each concentration analyzed separately
Analysis of variance with the data for all
concentrations analyzed together, includ-
ing data transformation if required
.
.
Linear model analysis with data trans-
formation if required.
In addition to providing a comparison of the
techniques, this approach also provided the oppor-
tunity to use the technique for which results were
most convenient to apply, provided that all tech-
niques gave comparable results. It will be shown sub-
sequently that excellent agreement was obtained, and
that the second technique with data transformation
provided the most convenient and useful application
of the results. Each of the techniques will be
described in more 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 fourteen laboratories
analyzed each of three concentrations in triplicate on
each of three separate days resulting in a total of 378
individual determinations. The data are presented
appropriately in the next subsection. The data in this
form may readily be analyzed by each of the tech.
niques listed above in accordance with the respective
statistical model.
In collaborative testing, two general sources of
variability can be readily detected. First, the vari.
ability between laboratories (reproducibility) can be
I I I
l' L. L14
I
etc
I I
01
I 02 03
I I I I I I I I
C1 C2 C3 rt C2 rt-, C1 C2 rt-,
rh rh rh rh rh rh
R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3
FIGURE B-1. DESIGN OF SULFUR DIOXIDE METHOD EXPERIMENT.
L, LABORATORIES; D, DAYS; C, CONCENTRATIONS; R, REPLICATES.
*Superscript numbers in parentheses refer to the List of References at the end of this appendix.
B-2
-------
estimated. This is frequently the largest source of
variability and is not under the control of the investi-
gator. Second, the within-laboratory variability
(repeatability) 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 importance, may be mea-
sured if the proper design has been employed.
Alternatively, the separate sources may be con-
founded or lumped into a single variable by altering
the design. By employing the design above, separate
estimates can be made of the variability between days
and of the variability between replicates. These two
components, appropriately combined, constitute the
within-laboratory source of variability.
A useful purpose could have been served by
employing more than one analyst in each laboratory
or by including additional different concentrations.
Also, sensitivity could have been improved by increas-
ing the number of days or the number of replicates.
These innovations would have required considerably
more effort on the part of the volunteer collabora-
tors. A conservative estimate for the effect of analysts
can be made by assuming that a different analyst is
analogous to a different laboratory. It was believed
that sufficient sensitivity for the purpose was obtain-
able with the numbers of laboratories, days, and
replicates noted above.
Additional assumptions and rationale for each
of the techniques listed above will be stated later as
the technique is described and applied. If appropriate,
the statistical model will be stated in the respective
discussions.
Supplementary or secondary experiments were
incorporated to evaluate errors associated with vari-
ous steps within the method. To accomplish this, a
relatively large amount of intermediate data was
retrieved- These data consisted of (I) the individual
points for each and every calibration curve, (2) the
concentration and absorbance of all control samples
analyzed, and (3) the absorbances of all blanks. Care-
fully prepared instructions and data forms were used
to retrieve these data uniformly from every collabora-
tor. Each of these supplementary experiments was
designed so that the data could be analyzed by the
analysis of variance to determine whether variations
between days and between laboratories were signifi-
cant. The results of each of these supplementary
experiments have been discussed in the main report.
II. PRELIMINARY DATA ANALYSIS
In accordance with the experiment design
described above and with the collaborative test proce-
dure described in the main report, the full plan was
carried out satisfactorily and without any missing
data.
In a carefully planned program, dishonesty,
carelessness, or incompetence can readily be dctected
and the data eliminated. There were no data of this
category present in the results of this test. However,
extreme or atypical results must be dealt with. There
is no problem in detecting these results. Whether a
result is out-of-line or not may be decided by obvious
explanation (either by the investigator or the collabo-
rator), visual observation, or by statistical methods.
What disposition is to be made of the results of a
laboratory that are responsible for outlying points?
Three obvious alternatives are available; they are
(l) retain all data in the analysis, (2) delete the entire
data, or (3) make some logical substitution for the
atypical data so that the other data of the laboratory
can be utilized. No amount of discussion or statistical
testing can substitute for a straightforward facing of
the problem. Clearly, the use of the first alternative,
retention of all data, puts more emphasis upon
the performance of the laboratories rather than the
quality of the procedure. This would be in direct
opposition to the objectives stated previously.
Use of the second alternative, deletion of data,
is in accord with the objective; however, it carries
with it two distinct disadvantages. First, there is the
tendency to make the method appear more reliable
than perhaps it is. Second, good data must be sacri-
ficed to eliminate suspicious data. The proportion of
good data to bad data is usually high, making the
sacrifice a costly one, and at the same time reducing
the sensitivity of the experiment by reducing the cor-
B-3
-------
responding degrees of freedom. For example, an indi-
vidual laboratory in this collaborative test produced
27 individual results consisting of nine sets of tripli-
cate analyses. The statistical techniques require that
there be no missing data. Therefore, if one individual
result or one set of replicates were bad, a considerable
amount of good data would be lost if the laboratory
were omitted from the analysis.
The foregoing discussion makes the third alter-
native an attractive and logical compromise. Several
methods, both simple and complex, are available to
replace missing data. Only the more simple methods
appear to be justified in this case. The one selected
was to replace the outlying observation by its closest
neighbor. For example, if an individual replicate is an
outlier, it is replaced by the nearest value in its
respective set of three replicates. If the mean of a set
of three replicates is an outlier, the set of replicates is
replaced by the set of replicates from the same con-
centration whose mean is nearest the mean of the
outlier set. Replacements beyond these two cases will
rarely be required and are probably not justified. This
outlier replacement technique accomplishes two
objectives simultaneously. It salvages good data with-
out a high risk, and it avoids the tendency to make
the method appear more reliable than it might be.
Finally, what is to be done about the arithmetic
errors that sometimes appear? A check for these
errors must be made to avoid the significant ones.
This procedure, using computer technology, is rela-
tively inexpensive and does not require a great
amount of effort. At the same time, a set of error-free
data is generated which is consistent from laboratory
to laboratory in calculation sequence and round-off.
Since the emphasis is upon the quality of the method
and not upon the performance of the laboratories, it
seems justifiable to use these error.free data for all
subsequent analysis, and to evaluate the arithmetic
error problem from a qualitative standpoint. Cer-
tainly, if a procedure is so complex or cumbersome in
its calculations that it is overly vulnerable to errors,
that fact should be pointed out. However, it makes
no sense to express arithmetic erors quantitatively in
terms of means or variances or of components
thereof.
A.
Presentation of 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. There-
fore, the more voluminous raw data will be found in
Appendix C.
The volume of data can be considerably
reduced and the presentation simplified by tabulating
the deviations of the observed values from the ex.
pected values. That is, the expected result was sub-
tracted from the observed result and the algebraic
difference was tabulated. These data are presented in
Table B-1 and were derived from the data of
Tables C-I and C-II. Each section of Table B-1 repre.
sents a different concentration level and shows each
individual replicate for each laboratory for each day.
All errors have been corrected. It can be seen by
referring to Table C-II in Appendix C that the ranges
of the expected values are sufficiently narrow so that
comparison of deviations of observed values from
expected values within these ranges can be done with-
out risk of error.
Additional description of these data will be pre-
sented as appropriate in the discussion of the analysis
which follows.
B.
Tests for Outlying Observations
The data were first visually inspected for
unusually large departures from the expected values.
Only one such set of replicates was noted, and these
had been pointed out by the collaborator submitting
them. These data for Laboratory 926 on the second
day can be seen in Table B-I. The absolute values of
these observations were so near zero that some quite
unusual error was implied. Several explanations come
to mind; however, it is hardly worth the conjecture to
list them. Following the previously stated philosophy,
B4
-------
TABLE B.L DEVIATION FROM EXPECTED VALUES FOR EACH REPLICATE FOR EACH CONCENTRATION
FOR EACH DAY FOR EACH LABORATORY, MICROGRAMS PER CUBIC METER.
Laboratory Day 1 Day 2 Day 3
Code Number
Low Concentration
271 2 -8 -13 4 -2 -4 -9 -8 -7
274 7 7 11 2 7 12 3 9 19
305 -4 0 -6 -5 -2 -8 -2 -4 -10
345 19 40 30 31 43 48 -1 10 -13
500 22 -3 -3 -19 -19 -19 -8 4 -11
509 -54 -54 -56 -3 -12 -5 -35 -30 -35
526 -27 -26 -28 -24 -17 -18 -17 -29 -25
571 24 12 0 60 26 14 2 -3 -3
578 -8 -15 -15 -18 -26 -18 0 -4 -9
655 109 133 129 88 97 99 87 108 90
788 16 -14 -1 90 57 30 -19 -20 -23
920 4 5 -6 -20 -19 -21 0 -10 -10
926 24 19 24 -142 -137 -137 35 30 30
927 -5 -5 -5 -13 -5 -15 2 -8 -8
Intermediate Concentration
271 -16 -14 -15 -24 -21 -24 -20 -15 -19
274 22 29 29 14 20 28 45 45 45
305 -3 -3 -3 -8 -5 -7 -18 -10 -18
345 -13 4 -18 -26 21 32 -11 0 -6
500 10 7 14 -11 -2 -11 -3 0 42
509 -45 -45 -48 -26 -17 -17 -30 -43 -36
526 -38 -38 -35 -25 -30 -30 -25 -19 -16
571 24 14 12 -15 -7 5 7 -6 -10
578 10 -6 -7 -28 -25 -21 -10 -7 -7
655 87 76 87 53 44 63 48 55 54
788 91 45 38 36 22 29 12 -14 -20
920 -12 -7 -16 -20 -22 -22 -15 -18 -7
926 30 26 26 27 25 18 62 62 55
927 -10 -12 -10 -29 -19 -19 -12 -14 -14
High Concentration
271 -58 -67 -60 -40 -37 -43 -62 -69 -57
274 37 37 86 60 60 60 94 94 118
305 -44 -33 -44 -74 -64 -79 -73 -71 -64
345 -1 -23 -50 25 154 165 -56 -45 -45
500 0 -39 -27 -25 -37 -67 -70 -58 -70
509 -95 -93 -95 -34 -34 -88 -72 -74 -61
526 -103 -109 -103 -64 -51 -26 -58 -74 -52
571 72 35 23 -9 -24 -52 -17 -61 -39
578 -14 -17 -11 -144 -134 -132 -111 -118 -99
655 103 92 103 31 54 31 56 67 67
788 16 -30 -56 -40 -54 -67 -101 -101 -127
920 -34 -29 -39 -46 -49 -41 -29 -16 -36
926 91 91 111 74 70 84 164 164 170
927 -69 -69 -59 -65 -65 -65 -53 -43 -49
B-5
-------
these replicates were replaced by the set of replicates
for the first day for this concentration.
A quite thorough statistical examination for
outlying observations was then performed. It is
believed to be beyond the scope of this report to
describe this examination in detail; therefore, the
description will be superficial and the methods used
will be cited appropriately. Needless to say, computer
techniques were used to facilitate these analyses.
Two methods were used to test for outliers
among laboratory means, among day means within
laboratories, and among replicates. The respective
means or observations were examined by Dixon's
test(4) and also by a method attributed to David and
described by ASTM.(5) The second method was
accomplished by making the analysis of variance,
which will be described in the next subsection.
Although this might seem to be premature, it is fair
to say that these computer-assisted analyses are quick
and inexpensive and may be repeated, if necessary,
after the disposition of outliers or after later transfor-
mation of data. The output of the analysis of variance
computer program(6) was used as the input for a
special program(7) to test for outliers among the vari-
ous means. Testing was done at a high level of confi-
dence (99 percent), and any outliers detected by this
method were tested using Dixon's test. Borderline
cases were not rejected. Relative outliers between
days were ignored unless the magnitude was also sig-
nificant. It should be noted that these outlier tests
were applied to the data as they appear in Table B-1,
and, when a data transformation was later found to
be appropriate, the outlier tests were repeated on the
transformed data for verification.
The only outlying observations under these cri-
teria were the data for Laboratory 345 for the high
concentration on the second day (see Table B-1). The
disposition of these data will be described following
the description of the tests for homogeneity of vari-
ances below.
Bartlett's test(8) and Cochran's test(9) were
used to test for homogeneity of variances. The vari-
ances of the laboratory means for each of the three
concentrations were found to be nonhomogeneous by
both tests. This indicated the necessity to handle each
concentration separately or to find an appropriate
data transformation in order to stabilize the variance.
This was not unexpected, considering the difference
in magnitude of the deviations in Table B-1 which
appear to vary with concentration.
These tests of variances were pursued further to
find any laboratory with data substantially more scat-
tered than the main cluster. This examination showed
the data for Laboratory 345 for the high concentra-
tion for the second day to be inconsistent. The
variance of this set of replicates was extremely high
and in a class all by itself. The mean for this set was
shown to be an outlier above.
Since the remainder of the data for this labora-
tory did not contain any other atypical results, it was
logical to replace this set of replicates by the set of
replicates for the same concentration for the first day
(see Table B-1).
c.
Discussion of Results of Preliminary
Data Analysis
In the presentation of the results in this report,
all arithmetic errors, no matter how small or insignifi-
cant, have been corrected. No offense to the collabo-
rators is intended since this was simply a built-in part
of the design of the experiment. Collaborators may
note differences of one or two units in the least sig-
nificant digit of their reported values and the values
shown in Table C-I. Deviations beyond this magni-
tude reflect more significant arithmetic errors or
other errors in the calculation procedure.
A relatively small number of these types of
errors of varying degrees of magnitude was noted.
Only three of the fourteen laboratories submitting
results exhibited any errors of this type. Four
instances of inadvertent errors in arithmetic opera-
tions were noted and corrected. More important,
however, was the fact that two laboratories had diffi-
culty with the least squares technique which was a
part of the method. There are many separate mathe-
matical operations in this procedure and, conse-
B-6
-------
quently, many opportunities for errors, especially in
transcription of intermediate results. The method is
one containing complex calculational procedures and
is consequently vulnerable to arithmetic and proce-
dural errors. However, the majority of collaborators
have demonstrated the capability to handle this com-
plexity. There is no reason to believe that a careful
checking procedure would not eliminate this
problem.
The data produced as a result of the disposition
of the two outlying observations described above are
believed to be an excellent basis for the statistical
analyses to follow. The data are believed to be repre-
sentative and unbiased. The number of outliers is
small, especially in comparison with the first test
where nearly two-thirds of the laboratories produced
one or more atypical results.
In all cases of outlier analysis, the statistical
tests were interpreted with a good deal of judgment.
The quantitative results of a given test were viewed as
a guide and a part of the picture, not as an obligation
to delete or retain the observation. This combination
of objectivity and judgment is considered to be
extremely important and to be the backbone of all
inferences following.
III. ANALYSIS OF VARIANCE
I n this subsection, three analyses will be
described and the results discussed. The first two are
classic analysis of variance cases. The first handles
each concentration separately, while the second com-
bines all concentration data into a single analysis, and
includes the evaluation and application of the neces-
sary data transform to allow this treatment. The third
case, the linear model analysis, does not strictly con-
stitute a classic analysis of variance case but does
involve the technique. It is therefore logically
included here. Each of these cases will be discussed
under its respective heading below, and, finally, a
comparison of the results of each will be presented
along with conclusions derived from the most appli-
cable method. This multiple analysis is another
approach to insure the reliability of the final conclu-
sions.
A.
Analysis of Variance of Concentrations
Separately
This analysis is made in accordance with
recommended practices for conducting an inter-
laboratory study using one material.(1,3) Discussions
and recommendations have also been presented in
other sources.(10,11) An extremely valuable and
flexible computer program(6) facilitated the accom-
plishment of the mathematical treatment. At the
same time, a valuable but very specific computer
program(12) was developed to materially ease the
calculation of the components of variance.
The purpose of this analysis was to compare,
for each concentration, the magnitudes of three of
the four sources of variation which this study was
designed to examine. These are the relative variations
among laboratories, among days within laboratories,
and among replicates run together on the same day.
The mathematical model is as follows:
Yikm =A + Li + Dk(i) + em[k(i)]
(B-1)
where
1, 2, 3 .
tory
- p designates a labora-
k = 1, 2, 3
w designates a day
m = 1, 2, 3 n designates an indivi-
dual replication
The term Yikm represents an individual measurement,
A represents the overall average, Li represents the
effect of the ith laboratory, Dk(i) represents the
effect of the kth day nested in the ith laboratory, and
em [k(i)] represents the random deviation associat ~d
with an individual measurement.
In this study, there were p = 14 laboratories, w
= 3 days, and n = 3 replicates.
The analysis was applied to the deviations in
Table B-1 after the substitutions for the two outlier
cells. The results are shown in the analysis of variance
tables in Table B-II. All effects in each of the tables
are significant at the 95 percent level of significance.
B-7
-------
The components of variance and the repeat-
ability and reproducibility were calculated and are
shown in Table B-III. The percent of the total vari-
ance accounted for by each component is shown
along with the degrees of freedom and the 95 percent
confidence intervals for each. The confidence inter-
vals for the components were computed by a method
from Scheffe.(13) The degrees of freedom for the
repeatability and reproducibility were estimated
TABLE 8-IL ANALYSIS OF VARIANCE FOR EACH CONCENTRATION. DATA IN ORIGINAL SCALE. THREE
FACTORS: L, LABORATORIES; D, DAYS; R, REPLICATES.
Source of Variation Sum of Squares Degrees Mean Square Expected Mean Square
of Freedom
Low Concentration
L 124796.0000 13 9599.6923 OR + 30D + 90L
D(L) 22459.7778 28 802.1349 OR + 30D
R(LD) 6565.3333 84 78.1587 OR
Intermediate Concentration
L 89408.6349 13 6877.5873
D(L) 16944.2222 28 605.1508 Same
R(LD) 7528.0000 84 89.6190
High Concentration
L 455465.8810 13 35035.8370
D(L) 87629.1111 28 3129.6111 Same
R(LD) 18054.6667 84 214.9365
TABLE 8-111. COMPONENTS OF VARIANCE FOR EACH CONCENTRATION. DATA IN ORIGINAL SCALE. THREE
FACTORS: L, LABORATORIES; D, DAYS; R, REPLICATES.
Source of Variation Component Percent Degrees Standard 95 Percent Confidence
of Total of Freedom Deviation Interval
Low Concentration
L 977.5064 75.4 13 31.27 22 to 52
D(L) 241.3254 18.6 28 15.53 12 to 22
R(LD) 78.1587 6.0 84 8.84 8 to 10
Repeatability 319.4841 28 17.87
Reproducibility 1296.9905 13 36.01
Intermediate Concentration
L 696.9374 72.7 13 26.40 18 to 44
D(L) 171.8439 17.9 28 13.11 10 to 18
R(LD) 89.6190 9.4 84 9.47 8 to 11
Repeatability 261.4629 28 16.17
Reproducibility 958.4003 13 30.96
High Concentration
L 3545.1362 74.9 13 59.54 41 to 99
D(L) 971.5582 20.5 28 31.17 24 to 43
R(LD) 214.9365 4.6 84 14.66 13 to 17
Repeatability 1186.4947 28 34.45
Reproducibility 4731.6309 13 68.79
B-8
-------
according to ASTM recommended practice.(14)
These point estimates and their corresponding
confidence intervals show the effects at the highest
concentration to be significantly different from those
at the two lower concentrations, especially the
replication error and the variation between days.
Some very important conclusions can be drawn
at this point. First, it is now clear that the replication
error varies with the magnitude of the concentration.
This means that a data transformation is in order and
the basis for that transform has been established. The
transform will be evaluated and applied in the next
subsection.
Second, the relative contribution of each of the
factors to the total variance is now evident. As a
result, it can be seen that the component of variance
due to laboratOlies accounts for three-fourths of the
total variance-far larger than any other component.
The component due to days accounts for about one-
fifth of the total variance, and the component due to
the replication is small compared to either of the
other components. It accounts for roughly one-
twentieth of the total variance, which suggests that
replication is probably a waste of time and effort.
These point estimates will be compared graphi-
cally with the other methods later.
B.
Analysis of Variance for All Concentra-
tions Analyzed Together
The results of the analysis of variance of the
concentrations analyzed separately in the preceding
subsection have set the stage for the analysis in this
discussion. It was evident that it was not worthwhile
to make an analysis of variance with all concentra-
tions handled together without first making a data
transformation because of the lack of homogeneity of
variances between the different concentrations tested.
The use of a data transformation stabilizes the
variance and allows the analysis.
The work of Mandel(15, 16) illustrates a tech-
nique for determining an appropriate transform when
the variance (replication) varies with the magnitude
of the concentration. The relationship of the standard
deviation for replicates to concentration was obtained
from the analysis in the preceding subsection. The
line formed by these points can be expressed in terms
of its slope and intercept as
Standard deviation = 7 + 0.01 X concentration
Accordingly, the appropriate transform for each
observation is given by
z = K loge (A + By) - G
(B-2)
where z is the transformed variable, K and G are
arbitrary constants chosen for convenience, A = 7
from above, and B = 0.01 from above. The value of G
was chosen as zero and the value of K as 1000.
This transformation was applied to each of the
observations in Table C-I (with substitutions de-
scribed previously for outlying observations) and to
each of the expected values in Table C-II. A table of
differences analogous to Table B-1 was generated and
subsequently subjected to an analysis of variance.
This table has not been reproduced here.
The purpose of this analysis was the same as the
preceding analysis except that the laboratory effects,
day effects, and replication error could be expressed
as functions of the concentration. This has a distinct
advantage over the point estimates of the preceding
subsection.
Bartlett's test(8) and Cochran's test(9), in addi-
tion to the outlier tests( 4,5), were applied to the
transformed differences for verification and
assurance. These transformed data were analyzed
handling the concentrations separately according to
the technique of the preceding subsection to demon-
strate that the variances were indeed homogeneous.
The resulting assurances from this additional work
were well worth the small effort, and the relative
contributions of the different components for each
concentration were found to be nearly identical.
The mathematical model for this analysis is:
B-9
-------
Yikm = A + Li + Mj + Dk(i) + (LM)jj
+ (DM)k(i)j + em [k(i)j]
(B-3)
where
j = 1, 2, 3 . . . q designates a material (con-
centration).
All other subscripts have been defined previously.
The term Mj represents the main effect of mate-
rials, (LM)ij represents the laboratory-material in-
teraction, and (DM)k(i)j represents the day-mate-
rial interaction. All terms involving materials
(concentrations) are viewed as fixed effects while all
other effects, except the overall mean, are viewed as
random effects. All other terms have been previously
defined.
For this analysis, there were p = 14 labora-
tories, q = 3 materials (concentrations), w = 3 days
nested within a laboratory, and n = 3 replicates.
The resulting analysis of variance table is shown
in table B-IV and the corresponding components of
variance in Table B-V. All effects can be seen to be
significant from the 95 percent confidence intervals
in Table B-V. Remember that these estimates are now
based on transformed data. The various standard
deviations may be converted to the original scale by
the linear approximation.(15)
Uy
A +By
Uz = (0.7 + O.OOly)uz
KB
(B-4 )
where Uz is a standard deviation in the transformed
scale, Uy is the corresponding standard deviation in
the original scale, and y is the concentration. The
accuracy is sufficient for values of uz/K of less than
0.05. These relationships result in straight lines with
non-zero intercepts. They are simple and easy to use
and may be seen graphically for the replication error,
repeatability, and reproducibility by looking ahead to
Figure B-3 in a following subsection where they are
compared with the results from the point estimates of
the preceding analysis.
TABLE B-IV. ANALYSIS OF VARIANCE FOR ALL CONCENTRATJ9NS TOGETHER. DATA IN TRANSFORMED
SCALE. FOUR FACTORS: L, LABORATORIES;M, MATERIALS
ORCONCENTRATIONS;D, DAYS;R, REPLICATES.
Source of Variation Sum of Squares Degrees Mean Square Expected Mean Square
of Freedom
L 373851.5 296 13 28757.8100 uR + 9uD + 27uL
M 39722.1032 2 19861.0516 UR + 3uDM + 9uLM + 126uM
D(L) 57762.8631 28 2062.9594 UR + 9uD
LM 76098.7512 26 2926.8750 UR + 3uDM + 9uLM
DM(L) 28917.0515 56 516.3759 uR + 3uDM
R(LDM) 24063.7298 252 95.4910 UR
TABLE B-V. COMPONENTS OF VARIANCE FOR ALL CONCENTRATIONS TOGETHER. DATA IN TRANSFORMED
SCALE. FOUR FACTORS: L, LABORATORIES; M, MATERIALS OR
CONCENTRATIONS; D, DAYS; R, REPLICATES.
Source of Variation Component Percent Degrees Standard 95 Percent Confidence
of Total of Freedom Deviation Interval
L 988.6982 53.6 13 31.44 22 to 52
M 134.3982 7.3 2 11.59 2 to 100
D(L) 218.6076 11.8 28 14.79 12 to 20
LM 267.8332 14.5 26 16.37 12 to 24
DM(L) 140.2950 7.5 56 11.84 10 to 15
R(LDM) 95.4910 5.2 252 9.77 9 to 11
Repeatability 454.3936 84 21.32
Reproducibility 1710.9250 13 41.36
B-IO
-------
Referring to Table B-V, it can be seen that the
repeatability includes the day-material interaction
component in addition to the replication error and
the day component. The "reproducibility includes all
components included in the repeatability plus the
laboratory component and the laboratory-material
interaction component.
c.
Linear Model Analysis
The approach in this analysis is different from
that of the previous analysis. The assumption is made
that systematic differences exist between sets of
measurements made by the same observer at different
times or by different observers in different labora-
tories, and that these systematic differences are linear
functions of the magnitude of the measurements.
Hence, the technique is called "the linear
model."(1 , 15,16) The linear model leads to a simple
design, but requires a special method of statistical
analysis, geared to the practical objectives of a collab-
orative test.
The general design is: to each of p laboratories,
q materials have been sent for test, and each labora-
tory has analyzed each material n times. We still have
p = 14 laboratories running n = 3 replicates; however,
we now view each of the three concentrations on
each of the 3 days as a separate material and thus
have q = 9 materials. These 9 materials cover the
concentration range of interest for the method under
study. Now, the n determinations made by the ith
laboratory on the jth material constitute what will be
denoted as the "i,j cell." The n replicates of any par-
ticular cell are viewed as a random sample from a
theoretically infinite population of measurements
within that cell. The laboratories, however, are now
considered as a random sample from a larger popula-
tion of laboratories, but are considered as fixed vari-
ables. Therefore, the inferences involving the vari-
ability among laboratories are limited, at least theo-
retically, to those laboratories participating in the
test. The set of values which correspond to the q
materials is viewed as a fixed variable, but each mate-
rial is considered to be a random selection from a
population of materials with the same "value."
This model allows for nonconstant, nonrandom
differences between laboratories where the previous
method does not. 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.
The first step is to examine the relation
between the replication error and the magnitude of
the measurement. If the standard deviation varies
with the concentration, then an appropriate data
transformation must be made. This step is exactly the
same as previously, except that now we are dealing
only with the observations in Table C-I which have
been assembled into the i,j cells defined above. From
the assumption of linear relationships among the p
laboratories, it follows that the values obtained by
each laboratory are linearly related to the corre-
sponding average values of all laboratories.
Next, we may plot the transformed measured
values versus their respective means. 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
parameters are determined by a least squares regres-
sion analysis, and the results are shown in Table B- VI.
They are 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 readily
visible otherwise. Control limits, based upon the
de via tion from linearity, are shown for each
parameter in Figure B-2. These 95 percent control
limits indicate several points to be "out of control."
This indicates that there are other important sources
of error significantly larger than the replication error.
Examination of Figure B-2 reveals which
laboratories were responsible for the greatest devia-
tions from linearity, which laboratories showed the
greatest departure from unit slope, and which labora-
tories showed the greatest departures from the overall
mean. When viewing this figure, it is important to
B-ll
-------
TABLE B-VI. MEANS, SLOPES, AND STANDARD
ERRORS OF ESTIMATE FOR LINEAR MODEL
ANALYSIS. DATA IN TRANSFORMED SCALE.
Laboratory Mean Slope Standard Error
Code Number of Estimate
271 2359 0.9906 8.2
274 2409 1.0995 15.3
305 2361 0.9762 6.2
345 2380 0.9661 17.1
500 2369 0.9933 15.6
509 2339 1.0207 21.4
526 2344 1.0040 16.6
571 2384 1.0083 16.9
578 2351 0.9557 24.6
655 2453 0.9334 24.4
788 2379 0.9282 35.3
920 2363 1.0197 10.3
926 2426 1.1191 21.1
927 2358 0.9852 8.0
Mean 2377 1.0000 19.5*
*Pooled estimate.
~:: /
I :: ----------------------------------£------
- 2380 0-0-- '\
I /" 95" controillmib
2380 --------~c;;;:;.-o-~-----______L______---
0-
2340 0'--
...
1.35
I :~ -,---------------;-----------li-\---
DB" ----y=:::~~---~\~ ~~"::~~b-\-- ~
II ~ ,/\ A~/
~1" /
P
U) 10 /0
o-o........r;I'
"
D
609 526 678 921 271 305 920 500 788 345 571 274 926 655
l...8bomory Numblr
FIGURE B-2. CONTROL CHARTS FOR MEANS, SLOPES,
AND STANDARD ERRORS OF ESTIMATE FOR LINEAR
MODEL ANALYSIS. DATA IN TRANSFORMED SCALE.
watch for relationships between the parameters. The
linear model dictates that the correlation between the
means and the slopes be investigated, and this investi-
gation revealed practically no correlation between
these two parameters. It can be noticed that there are
two laboratories (578 and 788) which produced
results with a low slope IInd a high deviation from
linearity. These particular laboratories obtained
disproportionately lower results on the highest con-
centration in comparison with the two lower concen-
trations, thus accounting for this situation. No other
unique combinations or relationships are evident.
The general model for
results, classified according to
tories and materials, is:
the analysis of the
two criteria, labora-
y.. =A + L. +M. + (LM)..
'/ 1 / 1/
(B-5)
where
i = I, 2, 3 . - . p designates a laboratory
j = 1, 2, 3
. . q designates a material
The term Yij represents an individual measurement, A
represents the overall average, Li represents the effect
oflaboratory i, Mj represents the effect ofmaterialj,
and (LM)ij represents the interaction effect between
laboratory i and material j and includes the replica-
tion error.
The interaction term is partitioned further as
follows:
(LM)ij = (bi - b)(cj - c) + dij
(B-6)
where the first term on the right is the linear term in
which bi is the slope determined by the ith labora-
tory; b is the slope of the average response line, which
in this case is equal to one; Cj represents the true
value for the jth material; and c represents the true
mean value for all materials. The second term, dij, is
the deviation from linear term. The linear term indi-
cates the difference in slope of the line for a particu-
lar laboratory and the average slope for all labora-
tories, and the nonlinear term expresses the depar-
tures from linearity for this individual line.
Starting with the ordinary two-factor analysis
of variance, the deviation from linear component of
the interaction sum of squares was computed. The
B-12
-------
sum of squares for the linear component was
obtained by difference. Finally, a single degree of
freedom was extracted from the linear component of
interaction by multiplying the linear component sum
of squares by the square of the correlation coefficient
of the means versus the slopes. This is denoted the
concurrence term. The nonconcurrence term is com-
puted by difference. These terms are computed for
the sake of completeness, although it was apparent
that no appreciable correlation existed between the
means and the slopes. The final analysis is shown in
Table B-VII from which variance components can be
computed.
The components of variance were computed
using the technique of Mandel( 15) with the data from
Table B-VII. A computer program was prepared to
expedite these computations. The components are
defined as follows:
V( e) = the component of variance due to vari.
ability among replicates,
V(X) =
the component of variance character-
izing the differential response of
different laboratories to interfering
properties; it represents the irreducible
experimental error of the method,
-"
V(J.l) =
the component of variance due to that
part of the between-laboratory vari-
ability involving the variability of the
means of the response lines,
V(b) =
the component of variance due to that
part of the between-laboratory vari-
ability involving the portion of the var-
iability of the slopes of the response
lines which is unrelated to the means.
In the transformed scale, V(e) and V(X) are, of
course, constant and have the values 95.4 and 322.7,
respectively. V(J.l) and V(b), however, are dependent
upon the magnitudes of the measurement. The rela-
tive contributions to the total variance are indepen-
dent of which scale is used, and, since the trans-
formed scale values are difficult to visualize, it is
advantageous to reconvert to the original scale. This
can be done according to Equation (B-4), and the
results are shown in Table B-VIII for several values of
concentration. Also shown is the fraction of the total
variance accounted for by each component.
Since V(e), the replication component, is small
compared to V(A), it is again evident that replication
is probably a waste of time since V(X) constitutes a
lower limit. The total between-laboratory variability
TABLE B-VII. ANALYSIS OF VARIANCE FOR LINEAR MODEL.
DATA IN TRANSFORMED SCALE.
Source of Variation Sum of Squares Degrees Mean Square
of Freedom
Laboratories 122799.1556 13 9446.0889
Materials 7134311.6753 8 891788.9594
Laboratory X Material 51929.1766 104 499.3190
Linear 17192.1 13 1322.47
Concurrence 693.196 1 693.196
Nonconcurrence 16498.9 12 1374.91
Deviation from Linear 34737.1 91 381. 726
Replication Within Cells 24034.5137 252 95.3751
B-13
-------
TABLE B-VIII. COMPONENTS OF VARIANCE AND THEIR RELATIVE IMPORTANCE FOR THE LINEAR MODEL
ANALYSIS. COMPONENTS ARE EXPRESSED AS STANDARD DEVIATIONS IN THE ORIGINAL SCALE.
Source of Variation
Within-Laboratory Between-Laboratory Totalt
Concentration, Replication i\-Variation J.I-Variation o-Variation Standard
J.lg/m3 Standard Standard Percent* Standard Percent * Standard Percent * Deviation
Deviation Percent* Deviation Deviation Deviation
10 6.9 6 12.8 21 19.5 49 13.8 24 27.9
20 7.0 6 12.9 21 19.9 50 13.5 23 28.2
50 7.3 6 13.5 22 21.0 53 12.6 19 28.9
100 7.8 7 14.4 23 22.9 57 11.1 13 30.3
150 8.3 7 15.3 23 24.9 61 9.4 9 31.8
200 8.8 7 16.2 23 16.9 65 7.5 5 33.5
275 9.5 7 17.5 23 30.0 68 4.5 2 36.3
500 11.7 6 21.6 21 39.5 71 6.0 2 46.9
700 13.7 5 25.1 18 48.3 68 17.1 8 58.7
820 14.8 5 27.3 17 53.8 65 24.4 13 66.7
1000 16.6 4 30.5 15 ~2.1 61 36.1 20 79.8
*Percent of total variance.
tBased on a single determination per laboratory including all sources of variation.
is large compared to the total within-laboratory vari-
ability throughout the table. V(8) is generally small
compared to V(JL) throughout the intermediate part
of the range but becomes appreciable at both the high
and the low ends. This is most likely related to the
poor readability of absorbance values above approxi-
mately 0.8 absorbance unit on most spectrophotom-
eters. No speculation can be made regarding the lower
end since results below 150 IJ.g/m3 are extrapolated.
It is also possible that the calibration curves, absorb-
ance versus concentration, may deviate from linearity
at each end. This will be examined superficially in a
later section.
The repeatability and reproducibility must now
be defined and computed. The repeatability is
defined as the square root of the total within-
laboratory variance as
Repeatability = yV(e) + V(A)
(B-7)
The reproducibility is defined as the square root of
the total variance as
Reproducibility = yV(e) + V(A) + V(JL) + V(8) (B-8)
These parameters, in the original scale, are functions
of the magnitude of the measurement just as in the
preceding analysis. However, in this case, the relation-
ships are nonlinear and are not easily expressed in
terms of the original variables. For comparison with
the other estimates, see Figure B-3 in the following
subsection.
D.
Comparison of Methods and Discussion
of Results
In this subsection, the three methods described
above will be compared and certain inferences will be
made. However, it is not within the scope of this
report to make a detailed comparison in more com-
plex statistical terms. It is more appropriate to review
the results from a practical viewpoint.
The comparison is best made by referring to the
results in graphic form shown in Figure B-3. This
figure compares the replication error, the repeata-
bility, and the reproducibility for each method of
statistical analysis. First, the overall agreement be-
tween these methods is very good. The agreement for
the replication error is exact because the methods
have this much in common. The point estimates seem
to imply a minimum for repeatability and reproduc-
ibility in the midrange of concentration. The other
methods, because of their fundamental assumptions,
do not recognize any minimum. In this respect, the
results are inconclusive, and an experiment incorpora-
ting many more intermediate concentrations would
be required to verify such a condition. In considera-
tion of the optimum absorbance range of most
spectrophotometers, such a minimum could be
entirely possible.
B-14
-------
80
o Concentrations handled separately.
- Concentrations handled together
with data transformation.
70
Linear model with data
transformation.
60
50 Reproducibility
M
E
......
C)
::t
c'
0
'~
CtI
':; 40
Q)
Q
'C
...
CtI
'C
C
CtI
...
en
0
30
20
Repeatability
o
10
o
o
200
400
600
800
1000
Concentration,119/m3
FIGURE B-3. REPLICATION ERROR, REPEATABILITY, AND REPRODUCIBILITY VERSUS
CONCENTRATION FOR THREE DIFFERENT METHODS OF DATA ANALYSIS.
B-15
-------
The point estimates are therefore of limited use
since we must also make inferences between these
points. The other two methods of analysis provide for
objective estimates at other concentrations. The
second method, the analysis of variance with concen-
trations handled together, enjoys the advantage of a
simple expression for the standard deviations as a
function of concentration. The linear model expresses
the standard deviations as a function of concentration;
however, there are also additional parameters derived
from the collaborative test data and the function is
more complex. In view of the relatively large repeat-
ability and reproducibility, this complexity is not
considered to be justified.
The linear model has an advantage because of
its ability to describe and compare the various sources
of error more thoroughly. As mentioned previously,
the linear model is less sensitive to outlying observa-
tions than the other methods.
On the basis of the preceding discussion, we
arrive at the conclusion that the analysis of variance
handling all concentrations together with data trans-
formation offers the most convenient and practical
method of expressing the replication error, the
repeatability, and the reproducibility as a function of
concentration. All subsequent treatment of these
parameters will be made accordingly.
IV. APPLICATION OF THE RESULTS
We are now in a position to apply the results of
the previous section and answer some fundamental
questions-thus fulfilling the objectives of this
collaborative test. Unless otherwise stated below, a
95 percent level of significance is assumed. Let us also
reclarify that the results apply for 30-min sampling
and the use of the calibration procedure with sulfite
solution.
A.
Precision 01 the Method
We may use the expressions for the replication
error (aE), the within-laboratory (single-replicate,
multiple-day) variation (repeatability) (aD)' and the
B-16
between-laboratory (single-replicate, single-day,
single-analyst) variation (aL) from Figure B-3 which
are restated as follows:
aE = (0.7 + 0.00Iy)(10)
(B-9)
aD= (0.7 + 0.001y)(2l)
(B-lO)
aL = (0.7 + 0.001y)(41)
(B-1 1 )
where y is the concentration in p.g/m3 . All statements
regarding the precision of the method are derived
from these expressions. With these equations, the
precision for any desired case can be computed. Some
of the more useful cases are shown below.
In the application of the results to test class
means, we will resort to the studentized range.(17-20)
If an estimate of the standard deviation (a) is based
on v degrees of freedom and is independent of the
class means to be compared, and if these class means
are computed from N cases and selected from a group
of g means, then the 0.05 allowance (95 percent
confidence level) for any comparison is
I Xl- X2! max = QO.05(g,V) a/VJiT
(B-12)
where Xl is the highest mean and X2 is the lowest
class mean. Our interest will center around g = 2
because we will, in general, be interested in com-
paring two class means. The degrees of freedom v will
be taken from those corresponding to the indepen-
dent estimates of the standard deviation- The value of
N represents the number of observations that make
up the means. In computing checking limits for
duplicates, N is of course eqHal to one and the test is
identical to ASTM recommended practice. (21)
An obvious limitation is that the means must all
contain the same number of observations. When this
is not the case, the standard normal deviate is
appropriate and we shall use(22)
1- _I ~l
Xl -X2 = 1.96 a - +-
max Nl N2
(B-l3)
-------
where I Xl - X2 I is the absolute value of the dif-
ference in the two class means X I and X2, a is an
independent estimate, and NI and N2 are the num-
bers of observations in Xl and X2, respectively. The
results from this equation are the same as Equa-
tion (B-12) forN=NI =N2 and vis large. The results ,
are adequate if NI and N2 are relatively large (20 or
more).
To test whether the true value of a mean is
lower than a specified fixed value, the maximum
permissible difference is(23)
(X - ,uO)m ax = - 1.645 a/VN
(B-14 )
which is a one-sided test (at the 95 percent level of
confidence) where x is the mean, ,uo is the fixed
value, a is again an independent estimate, 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. Nevertheless, we would not
be thorough if we did not consider the measure of
acceptability of replicates. The expression from
Equations (B-9) and (B-12) for the checking limits for
duplicates is
Rmax = (2.77)(0.7 + 0.00Iy)(10)
(B-15)
where Rmax is the maximum permissible range
between duplicates. Two such replicates should be
considered suspect if they differ by more than Rmax'
agreement better than 20 percent cannot be expected
below 100,ug/m3
2.
Precision Between Days
In some instances, it will be necessary to
compare observations made by the same analyst on
different days. The following expression from Equa-
tions (B-lO) and (B-12) allows this comparison
(single-replicate ):
Rmax = (2.82)(0.7 + 0.001y)(21)
(B-16)
where Rmax is the maximum permissible range
between two observations. Two such values may not
be considered to belong to the same population if
they differ by more than Rm ax' Conversely, the two
values are not significantly different if they differ by
less than Rm ax .
It can now be noted that the method
cannot detect a difference of 10 percent between two
such values in the range of 0 to 1000 ,uglm3. A dif-
ference of 20 percent may be detected above
300 ,uglm3.
As an example of the futility of replica-
tion, the factor 21 in Equation (B-16) would be
reduced to 20 for duplicates, approximately the same
for triplicates, and to 19 for an infinite number of
replicates.
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 single-replicate observations. 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 dis-
tributed. Where they are normally distributed,
standard tests such as the t-test(24) may be applied.
It should be noted that agreement
between duplicates better than 5 percent cannot be A limiting case may be investigated if we
expected below 900 ,ug/m3. Agreement better than assume that two means Xl and X2 are normally dis-
10 percent cannot be expected below 300 ,ug/m3 , and tributed with at = a2 = aD, where aD is given by
B-17
-------
Equation (B-1 0). This is an unlikely, if not impos-
sible, situation which could only result from abso-
lutely constant concentrations at each of the
sampling stations. Under these assumptions, we may
apply Equations (B-1 0) and (B-13) and obtain
~1
Rmax=1.96(0.7+0.001xl)(21) -+- (B-17)
Nl N2
where Rmax is the maximum permissible range
between means Xl and X2 containing Nl and N2
observations, respectively. If the range exceeds Rm ax'
the means are significantly different and do not
belong to the same population.
Under the same limiting assumptions, we
may compare a mean x containing N observations
with some fixed value 110 and be able to state whether
the true value of X is less than Po. Equations (B-1 0)
and (B-14) may be applied to this case resulting in
Rmax = - 1.645(0.7 + 0.001110)(21)/$ (B-18)
where Rmax is the maximum permissible range
between X and 110. If X - 110 is less than Rm ax, then
the true value of x is less than 110 .
The variance of the values making up a
mean can be compared to the variance above by an
approximate F-test(25-27) of the variance of the
sample data. The data must be transformed according
to Equation (B-2). The denominator for the test may
be obtained from Table B-V. An F-ratio below the
critical value would indicate that all variation could
be accounted for by the random variation of the
analytical method. In other words, the set of data
could have resulted from the repeated analysis of a
sample whose true value was equal to the mean of the
sample distribution.
3.
Precision Between laboratories
Equations (B-11) and (B-12) allows this comparison
for a single-replicate single-analyst single-day:
Rmax = (3.06)(0.7 + 0.00Iy)(41)
(B-19)
where Rmax is the maximum permissible difference
between the observations of two different labora-
tories. Two such values may not be considered to
belong to the same population if they differ by more
than R m ax' Conversely, the two values are not signi-
ficantly different if they differ by less than Rm ax'
It can be seen that the method cannot
detect a difference of less than 20 percent between
single observations of two laboratories. At a level of
100 I1g/m3, a difference of less than 100 percent is
not detectable. It will, in general, be of limited useful-
ness to compare single observations of two labora-
tories.
Frequently, it will be necessary to com-
pare the means for each of two given sampling
stations. 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 single-determination. Their standard deviations will
not usually be equal, and one or both may not be
normally distributed. Where they are normally dis-
tributed, standard tests such as the t-test(24) may be
applied.
Similar to the preceding subsection, a
limiting case may be investigated if we assume that the
two means Xl and X2 containing Nl = N2 = N
observations are normally distributed with al = a2 =
aL, where aL is given by Equation (B-ll). Here again,
this is an unlikely, if not impossible, situation which
could only result from absolutely constant concentra-
tions at each sampling station. Nevertheless, a certain
amount of guidance can be derived. If we apply Equa-
tions (B-1 1) and (B-12) to this case, we obtain
Rm'lX = (3.06)(0.7 + 0.00Ixl)(41)/VAT
(B-20)
Probably the most frequent comparison
to be made will be that involving observations of two where Rmax is the maximum permissible range
different laboratories. The following expression from between the means Xl and X2' If the range exceeds
B-18 .
-------
Rmax, the means are significantly different and do
not belong to the same population.
It is interesting to pursue this line of
reasoning 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 N, we obtain:
2
N= [(3.06)(0.7; 0.00IY)(41)]
(B-21)
This expression now gives the minimum number of
observations (N) for any desired agreement (R)
between two means at any level of concentration (y).
These results are best illustrated in Figure B-4. This
figure shows the agreement versus the concentration
level for a family of sample sizes. This presentation is
most convenient because of its linearity. Super-
imposed on the curve are percentage agreement lines
for comparison purposes. For example, if we desired
agreement better than 5 percent at a concentration of
300 JJ.g/m3 , a minimum of 70 observations would be
required. This figure may not be used for agreement
of a mean with a fixed value.
Under the same assumptions as above,
with the exception that Nl may not equal N2 but
both are relatively large, Equations (B-ll) and (B-l3)
are used, yielding
~1
Rmax = 1.96(0.7+0.001xd(41) -+- (B-n)
Nl N2
where Rm ax is the maximum permissible range
between Xl and X2' If the range exceeds Rm ax' the
means are significantly different and do not belong to
the same population.
where Rmax is the maximum permissible range
between x and JJ.o. If x - JJ.o is less than Rm ax' then
the true value ofx is less than JJ.o.
We may rearrange Equation (B-23) and
solve for N obtaining
N=[ 1.645(0.7 + ~.001JJ.o)(41) T
(B-24)
This eq ua tion is exactly analogous to Equa-
tion (B-21). N is the minimum number of observa-
tions required to attain the agreement R under the
limiting assumptions. Figure B-5, which is analogous
to Figure B-4, best illustrates the resulting
relationships. For example, a minimum of 20 observa-
tions would be required to establish that the true
value of x is less than 300 JJ.glm3, while the actual
value is 285 JJ.glm3 (a 5 percent difference). Stated
differently, we may say that, given a set of 20 obser-
vations with a mean of 285 JJ.glm3, we may be
95 percent confident that the true mean is less than
300 JJ.glm3 .
Analogous to the preceding subsection,
the variance of the values making up a mean can be
compared to the variance above by the approximate
F-test. The denominator for the test is obtained from
Table B-V and the numerator is the variance of the
sample data, for the data transformed according to
Equation (B-2). Just as in the preceding subsection,
an F-ratio below the critical value would indicate that
all variation could be accounted for by the random
variation of the analytical method.
B.
Lower Limit of Detection
We have previously made two independent
estimates of the lower limit of detection. The first
was based on calibration curve data (see Sec-
tion III-C-1 of the main report) and is equal to
22 JJ.glm3. The second was based on control sample
data (see Section III-C-2 of the main report) and is
equal to 26 JJ.glm3 A third is possible, based on two
standard deviations (replication), which we shall
estimate from the data at the lowest concentration
Rmax = - 1.645(0.7 + 0.001JJ.o)(41)jv'N (B-23) tested to be 18 JJ.glm3 These are in very good
B-19
Under the same limiting assumptions, we
may compare a mean x containing N observations
with some fixed value JJ.o and be able to state whether
the true value of x is less than JJ.o. We again utilize
Equations (B-ll) and (B-14) for this type case
yielding
-------
220
/
/
/
/
/
/
/
/
~/
QS/
/
/
/
/
/
/
/
/
/
/
/
~~/
I);/'
/
/
/
/
/
/
80
/
/
/
/
/
/
/
/
/
~""~ /'"
/'
,/
,,/
\o:!/ /'
/'
/'
,/
N"" ,0
200
180
160
140
M
-€ 120
en
:::s.
I~
~ 100
1)(
60
40
,,/
/'
,/
,/ N == 30
".; -:.--
-- 0
-- N 10 ------
/./.......- --------
---
........ .....- ......... 2% -- -- -- -- -- --
~----------
~%_-
---
--
--
~
20
o
o
100
200
300.
400
500
x1,p.g/m3
600
700
800
900
1000
FIGURE 8-4. EXPECTED AGREEMENT BETWEEN 1WO MEANS VERSUS CONCENTRATION
FOR VARIOUS NUMBERS OF OBSERVATIONS (95 Percent Level of Significance).
EACH MEAN HAS N OBSERVATIONS WITH A STANDARD DEVIATION
EQUAL TO (0.7 + 0.00 Ix 1) (41).
B-20
-------
120
80
/
/
/
/
~/
R
/
/
/
/
/
/
/
/
/
/
<:sf> /
"'
/
/
/
/
/
/
100
M
E
......
0>
::t
o 60
::t
I
1)(
40
7
/
/
/
/
/
/
/
/
20
/
./'
./"
/
/
--
--
-
--
2% --
--
--
N- 30
N 100
o
o
100
200
300
400
500
JJ.o, 1l9/m3
600
700
800
900
1000
FIGURE B-5. EXPECTED AGREEMENT BETWEEN A MEAN AND A FIXED VALUE VERSUS
CONCENTRA nON FOR VARIOUS NUMBERS OF OBSERVATIONS (95 Percent Level of
Significance). THE MEAN HAS N OBSERVATIONS WITH A STANDARD DEVIA nON
EQUAL TO (0.7 + O.OOIIlO) (41).
B-21
-------
agreement, and it is not too important which one is
used; therefore, a value of 25 pg/m3 is proposed as a
practical figure. A single observation less than this
value is not distinguishable from zero. Whether the
mean of several observations, each a single determina-
tion, is significantly different from zero is dependent
upon the number of observations and their distribu-
tion, regardless of the magnitude of the mean.
Recorded results using this method should
carry no more than two significant digits. Originators
or recorders of data should assume the responsibility
of appending confidence limits (95 percent) to their
data.
C.
Accuracy and Bias
The overall average deviations from the
expected values for each concentration tested were
6.4, 2.2, and -23.9 pg/m3 for concentrations of 150,
275, and 820 pg/m3, respectively. These differences
are not significant, and therefore no systematic error,
bias, or inaccuracy was detectable.
LIST OF REFERENCES
1.
ASTM Manual for Conducting an Interlabora-
tory Study of a Test Method, ASTM STP No.
335, Am. Soc. Testing & Mats. (1963).
2.
Handbook of the AOAC, Second Edition,
October 1, 1966.
3.
1968 Book of ASTM Standards, Part 30,
Recommended Practice for Developing Preci-
sion Data on ASTM Methods for Analysis and
Testing of Industrial Chemicals, ASTM Designa-
tion: EI80-67, pp 459-480.
4.
1968 Book of ASTM Standards, op cit, Recom-
mended Practice for Dealing with Outlying
Observations, ASTM Designation: E 178-68, pp
437-439.
5.
Ibid, pp 444-447.
B.22
6.
Dixon, W. J., (Ed.), BMD Biomedical Computer
Programs, Second Edition, University of
California Press, Berkeley and Los Angeles, pp
586-600 (1968).
7.
Southwest Research Institute, Houston, Texas,
Computer Program OUTLY, for test for Out.
lying Observations, Unpublished (1971).
8.
Dixon, Wilfred J., and Massey, Frank J., Jr.,
Introduction to Statistical Analysis, McGraw-
Hill Book Company, Inc., New York, Chapter
10, pp 179-180 (1957).
9.
Ibid, p 180.
10.
Nelson, Benjamin N., "Survey and Application
of Interlaboratory Testing Techniques," Indus-
trial Quality Control, Vol. 23, pp 554.559 (May
1967).
11.
McArthur, D. S., Baldeschwieler, E. L., White,
W. H., and Anderson, J. S., "Evaluation of Test
Procedures," Analytical Chemistry, 26, pp
1012-1018 (1954).
12.
Southwest Research Institute, Houston, Texas,
Computer Program COMPO for Computing
Variance Components, Unpublished (1971).
13.
Scheffe, Henry, The Analysis of Variance, John
Wiley and Sons, Inc., New York, Chapter 7, pp
231-235 (1959).
14.
1968 Book of ASTM Standards, op cit, p 476.
15.
Mandel, J., "The Measuring Process,"
Technometrics, 1, pp 251-267 (1959).
16.
Mandel, J.,and Lashof, T. W., "The Interlabora-
tory Evaluation of Testing Methods," ASTM
Bulletin 239, pp 53-61 (1959).
17.
Duncan, Acheson J., Quality Control and
Industrial Statistics, Third Edition, Richard D.
Irwin, Inc., Homewood, Illinois, Chapter XXXI,
pp 632-636 (1965).
-------
18. Ibid, P 909.
19. Bennett, Carl A., and Franklin, Norman L.,
Statistical Analysis in Chemistry and the
Chemical Industry, John Wiley and Sons, Inc.,
New York, 1954, Chapter 4, pilL
20. Ibid, P 185-189.
21. 1968 Book of ASTM Standards, op cit,p476.
22. Dixon and Massey, op cit, P 120.
23. Ibid, pp 114-115.
24. Ibid, pp 123-124.
25. Ibid, pp 106-107.
26. Bennett and Franklin, op cit, pp 192-196.
27. Duncan, op cit, pp 511-517.
B-23
-------
APPENDIX C
TABULATION OF ORIGINAL DATA
-------
TABLE C-I. OBSERVED VALUES FOR EACH REPLICATE FOR EACH CONCENTRA nON FOR EACH DAY
FOR EACH LABORATORY, MICROGRAMS PER CUBIC METER.
Laboratory Day 1 Day 2 Day 3
Code Number
Low Concentration
271 145 135 130 147 141 139 134 135 136
274 161 161 165 155 160 165 156 162 172
305 144 148 142 143 146 140 147 145 139
345 169 190 180 181 193 198 149 160 137
500 176 151 151 135 135 135 146 158 143
509 92 92 90 143 134 141 III 116 III
526 114 114 112 115 121 120 122 110 114
571 164 152 140 202 168 156 143 137 137
578 138 131 131 127 119 127 145 141 136
655 253 277 273 233 244 244 232 253 235
788 171 141 154 245 212 185 135 134 131
920 150 151 140 127 128 126 147 137 137
926 173 168 173 7 12 12 184 180 180
927 144 144 144 135 145 135 150 140 '~
lntermediote Concentration
271 247 249 248 238 241 238 I 242 247 I 243
274 306 313 313 296 302 310 325 325 325
305 270 270 270 264 267 265 256 264 256 I
345 264 281 259 251 298 309 266 277 27\ I
500 294 291 298 272 281 272 280 283 I 325
I I
509 223 223 220 242 251 251 238 225 ( 232
526 220 220 225 229 226 224 231 238 240
571 282 272 270 247 253 265 268 255 249
578 278 262 261 238 241 245 256 259 259
655 352 341 352 322 313 332 3\4 32\ 320
788 375 329 322 322 308 315 296 270 264
920 258 263 254 250 248 248 255 252 263
926 303 299 299 301 299 292 338 338 331
927 264 262 264 246 256 256 261 26\ 261
-
High Concentration
271 731 722 729 744 747 741 723 I 716 728
274 884 884 933 903 903 903 931 931 955
305 772 783 772 738 748 733 749 751 758
345 826 804 777 852 981 992 771 782 782
500 848 809 821 821 809 779 776 788 776
509 707 709 707 764 764 710 730 728 741
526 668 668 668 696 709 734 706 690 712
571 843 806 794 760 751 717 757 713 729
578 786 783 789 651 661 663 684 677 696
655 895 884 895 836 859 836 851 862 862
788 865 819 793 814 800 787 747 747 721
920 770 775 765 761 758 766 778 791 771
926 908 908 928 901 903 917 987 987 987
927 749 749 759 757 757 757 762 772 772
C-l
-------
TABLE C-IL EXPECTED VALUES FOR EACH REPLICATE FOR EACH CONCENTRATION FOR EACH DAY
FOR EACH LABORATORY, MICROGRAMS PER CUBIC METER.
Laboratory Day 1 Day 2 Day 3
Code Number
Low Concentration
271 143 143 143 143 143 143 143 143 143
274 154 154 154 153 153 153 153 153 153
305 148 148 148 148 148 148 149 149 149
345 150 150 150 150 150 150 150 150 150
500 154 154 154 154 154 154 154 154 154
509 146 146 146 146 146 146 146 146 146
526 141 140 140 139 138 138 139 139 139
571 140 140 140 142 142 142 141 140 140
578 146 146 146 145 145 145 145 145 145
655 144 144 144 145 147 145 145 145 145
788 155 155 155 155 155 155 154 154 154
920 146 146 146 147 147 147 147 147 147
926 149 149 149 149 149 149 149 150 150
927 149 149 149 148 150 150 148 148 148
Intermediate Concentration
271 263 263 263 262 262 262 262 262 262
274 284 284 284 282 282 282 280 280 280
305 273 273 273 272 272 272 274 274 274
345 277 277 277 277 277 277 277 277 277
500 284 284 284 283 283 283 283 283 283
509 268 268 268 268 268 268 268 268 268
526 258 258 260 254 256 254 256 257 256
571 258 258 258 262 260 260 261 261 259
578 268 268 268 266 266 266 266 266 266
655 265 265 265 269 269 269 266 266 266
788 284 284 284 286 286 286 284 284 284
920 270 270 270 270 270 270 270 270 270
926 273 273 273 274 274 274 276 276 276
927 274 274 274 275 275 275 273 275 275
High Concentration
271 789 789 789 784 784 784 785 785 785
274 847 847 847 843 843 843 837 837 837
305 816 816 816 812 812 812 822 822 822
345 827 827 827 827 827 827 827 827 827
500 848 848 848 846 846 846 846 846 846
509 802 802 802 798 798 798 802 802 802
526 771 777 771 760 760 760 764 764 764
571 771 771 771 769 775 769 774 774 768
578 800 800 800 795 795 795 795 795 795
655 792 792 792 805 805 805 795 795 795
788 849 849 849 854 854 854 848 848 848
920 804 804 804 807 807 807 807 807 807
926 817 817 817 827 833 833 823 823 817
927 818 818 818 822 822 822 815 815 821
C~
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TABLE C-lII. CALIBRATION CURVE DATA FOR EACH DAY FOR EACH LABORATORY. SLOPE IN ABSORBANCE
PER MICROGRAM OF SULFUR DIOXIDE DETERMINED BY LEAST SQUARES.
OTHER PARAMETERS IN ABSORBANCE UNITS.
Laboratory Day Slope Intercept Intercept Standard Error
Code Number - Zero Standard of Estimate
I 0.0298 0.178 -0.002 0.0125
271 2 0.0288 0.182 0.019 0.0151
3 0.0293 0.159 0.002 0.0053
1 0.0327 0.169 0.005 0.0044
274 2 0.0335 0.172 0.004 0.0037
3 0.0305 0.185 0.008 0.0060
1 0.0293 0.181 0.001 0.0037
305 2 0.0300 0.170 -0.001 0.0034
3 0.0299 0.169 0.002 0.0035
1 0.0322 0.149 -0.001 0.0099
345 2 0.0298 0.160 0.000 0.0023
3 0.0303 0.163 0.006 0.0042
1 0.0282 0.141 0.009 0.0094
500 2 0.0282 0.134 0.009 0.0090
3 0.0279 0.117 0.002 0.0048
1 0.0300 0.175 -0.002 0.0021
509 2 0.0303 0.160 0.007 0.0083
3 0.0300 0.195 -0.001 0.0047
1 0.0312 0.149 -0.004 0.0028
526 2 0.0306 0.158 -0.006 0.0038
3 0.0302 0.150 -0.013 0.0094
1 0.0285 0.214 0.004 0.0121
571 2 0.0289 0.224 0.004 0.0048
3 0.0291 0.164 -0.001 0.0037
1 0.0271 0.142 -0.003 0.0057
578 2 0.0304 0.159 -0.001 0.0041
3 0.0305 0.161 0.001 0.0017
1 0.0299 0.188 0.006 0.0208
655 2 0.0302 0.184 0.002 0.0038
3 0.0303 0.188 0.007 0.0054
1 0.0316 0.148 0.006 0.0165
788 2 0.0311 0.165 0.010 0.0116
3 0.0326 0.140 -0.005 0.0062
1 0.0299 0.146 0.002 0.0071
920 2 0.0293 0.143 0.002 0.0018
3 0.0293 0.140 0.005 0.0038
1 0.0248 0.133 -0.007 0.0106
926 2 0.0254 0.141 0.002 0.0018
3 0.0249 0.146 0.002 0.0024
1 0.0319 0.174 -0.001 0.0062
927 2 0.0319 0.157 -0.008 0.0151
3 0.0318 0.158 0.003 0.0034
C-3
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TABLE C-IV. CONTROL SAMPLE DATA, MICROGRAMS OF
SULFUR DIOXIDE.
Laboratory Day Taken Found Difference
Code Number
1 15.14 16.19 1.05
271 2 15.14 15.85 0.71
3 15.14 15.59 0.45
1 15.64 15.89 0.25
274 2 14.66 14.34 -0.32
3 15.06 14.34 -0.72
1 14.04 14.50 0.46
305 2 13.90 14.10 0.20
3 13.88 14.13 0.25
1 14.18 14.45 0.27
345 2 15.46 14.96 -0.50
3 13.80 13.19 -0.61
1 15.56 15.80 0.24
500 2 15.60 16.59 0.99
3 15.92 16.66 0.74
1 15.44 15.29 -0.15
509 2 15.54 15.66 1.12
3 15.48 14.83 -0.65
1 15.30 15.27 -0.03
526 2 15.50 15.25 -0.25
3 13.60 12.53 -1.07
1 15.30 16.14 0.84
571 2 15.30 15.77 0.47
3 15.40 15.48 0.08
1 13.85 13.63 -0.22
655 2 14.16 13.83 -0.33
3 12.56 13.19 0.63
1 16.00 16.53 0.53
920 2 15.68 15.78 0.10
3 15.70 15.90 0.20
1 6.72 6.94 0.22
926 2 6.88 6.98 0.10
3 8.24 8.39 0.15
1 14.60 14.87 0.27
927 2 14.20 14.27 0.07
3 14.80 14.77 -0.03
C-4
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TABLE CoY. REAGENT BLANK DATA.
ABSORBANCE UNITS.
Laboratory Day 1 Day 2 Day 3
Code Number
271 0.198 0.164 0.158
274 0.168 0.168 0.165
305 0.185 0.170 0.167
345 0.153 0.147 0.158
500 0.138 0.131 0.116
509 0.164 0.170 0.220
526 0.153 0.163 0.160
571 0.210 0.210 0.180
578 0.145 0.160 0.160
655 0.182 0.182 0.181
788 0.145 0.125 0.180
920 0.144 0.141 0.133
926 0.140 0.139 0.144
927 0.175 0.165 0.160
C-5
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