ASTM D2906-97
(Practice)Standard Practice for Statements on Precision and Bias for Textiles
Standard Practice for Statements on Precision and Bias for Textiles
SCOPE
1.1 This practice serves as a guide for using the information obtained as directed in Practice D2904 to prepare statements on precision and bias in ASTM methods prepared by Committee D-13. The manual on form and style for standards specifies that statements on precision and bias be included in test methods. Committee D-13 recommends at least a statement about single-operator precision in test methods. Whenever applicable, a statement on precision based on values from a statistical analysis of interlaboratory data is expected in tentative methods proposed for adoption as standard.
1.2 The preparation of statements on precision and bias requires a general knowledge of statistical principles including the use of components of variance estimated from an analysis of variance. Instructions covering such calculations are available in Practice D2904 or in any standard text (1, 2, 3, 4, and 5).
1.3 The instructions in this practice are specifically applicable to test methods in which test results are based ( ) on the measurement of variables, ( ) on the number of successes or failures in the specified number of observations, ( ) on the number of defects or incidents counted in a specified interval or in a specified amount of material, and ( ) on the presence or absence of an attribute in a test result (a go, no-go test). Instructions are also included for methods of test for which precision has not yet been estimated or for which precision and accuracy have been reported in another method of test. For observations based on the measurement of variables, the instructions of this practice specifically apply to test results that are the arithmetic average of individual observations. With qualified assistance, the same general principles can be applied to test results that are based on other functions of the data such as standard deviations.
1.4 This standard includes the following sections: Section No. Attributes, Statements Based on 15 Binomial Distributions, Calculations for 9 Binomial Distributions, Statements Based on 13 Categories of Data 7 Computer Preparation of Statements Based on Normal or Trans- 12 formed Data Normal Distributions and Transformed Data, Calculations for 8 Normal Distributions and Transformed Data, Statements Based on 11 Poisson Distributions, Calculations for 10 Poisson Distributions, Statements Based on 14 Precision and Bias Based on Other Methods 16 Precision Not Established, Statements When 17 Ratings, Statements Based on Special Cases of 18 Sources of Data 6 Statistical Data in Two Sections of Methods 5 Significance and Use 4
General Information
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Standards Content (Sample)
NOTICE: This standard has either been superseded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
Designation: D 2906 – 97
Standard Practice for
Statements on Precision and Bias for Textiles
This standard is issued under the fixed designation D 2906; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
Work was begun in August 1966 on recommendations for statements on precision and accuracy. The
first recommendations were issued as ASTMD-13 White Paper, Statements on Precision and Accuracy,
MARK I, December 1968, prepared by Subcommittee C-6 on Editorial Policy and Review. After a
decision that the recommendations should be a recommended practice under the responsibility of
Subcommittee D13.93, Sampling, Presentation and Interpretation of Data, the recommendations were
revised and published as Practice D 2906 – 70 T.
Information was added in Practice D 2906 – 73 on methods (1) for which precision has not been
established, (2) for which test results are not variables, and (3) for which statements are based on
another method. Practice D 2906 – 74 was expanded to include test methods in which test results are
based on the number of successes or failures in a specified number of observations or on the number
of defects or instances counted in a specified interval of time or in a specified amount of material. The
present text provides for a nontechnical summary at the beginning of recommended texts based on
normal distributions or on transformed data and for a more positive statement on accuracy when the
true value of a property can be defined only in terms of a test method.
In 1984, changes were introduced to replace the term “accuracy” with “bias” as directed in the May
1983 edition of Form and Style for ASTM Standards.
1. Scope the use of components of variance estimated from an analysis
of variance. Instructions covering such calculations are avail-
1.1 This practice serves as a guide for using the information
able in Practice D 2904 or in any standard text (1,2,3,4, and
obtained as directed in Practice D 2904 or obtained by other
5).
statistical techniques from other distributions, to prepare state-
1.3 The instructions in this practice are specifically appli-
ments on precision and bias in ASTM methods prepared by
cable to test methods in which test results are based ( 1)onthe
Committee D-13. The manual on form and style for standards
measurement of variables, (2) on the number of successes or
specifies that statements on precision and bias be included in
failures in the specified number of observations, (3)onthe
test methods. Committee D-13 recommends at least a state-
number of defects or incidents counted in a specified interval or
ment about single-operator precision in any new test method,
in a specified amount of material, and ( 4) on the presence or
or any test method not containing a precision statement that is
absence of an attribute in a test result (a go, no-go test).
put forward for 5-year approval, in both instances with a
Instructions are also included for methods of test for which
complete statement at the next reapproval. If a provisional test
precision has not yet been estimated or for which precision and
method is proposed, at least a statement on single-operator
accuracy have been reported in another method of test. For
precision is expected.
observations based on the measurement of variables, the
1.2 The preparation of statements on precision and bias
instructions of this practice specifically apply to test results that
requires a general knowledge of statistical principles including
are the arithmetic average of individual observations. With
qualified assistance, the same general principles can be applied
This practice is under the jurisdiction of ASTM Committee D-13 on Textiles
to test results that are based on other functions of the data such
and is the direct responsibility of Subcommittee D13.93 on Statistics.
Current edition approved Nov. 10, 1997. Published August 1998 . Originally as standard deviations.
published as D 2906 – 70 T. Last previous edition D 2906 – 91.
Form and Style for ASTM Standards, May 1983, available from American
Society for Testing and Materials, 100 Barr Harbor Drive, West Conshohocken, PA The boldface numbers in parentheses refer to the list of references at the end of
19428. this practice.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
NOTICE: This standard has either been superseded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
D 2906
1.4 This standard includes the following sections: obtained from a single method, for example, between operators
or between laboratories.
Section No.
3.1.3 characteristic, n—a property of items in a sample or
Attributes, Statements Based on 15
population which, when measured, counted, or otherwise
Binomial Distributions, Calculations for 9
Binomial Distributions, Statements Based on 13 observed, helps to distinguish between the items. (E 456)
Categories of Data 7
3.1.4 confidence level, n—the stated proportion of times the
Computer Preparation of Statements Based on Normal or Trans- 12
confidence interval is expected to include the population
formed Data
Normal Distributions and Transformed Data, Calculations for 8
parameter. (E 206)
Normal Distributions and Transformed Data, Statements Based on 11
3.1.4.1 Discussion—Statisticians generally accept that, in
Poisson Distributions, Calculations for 10
the absence of special considerations, 0.95 or 95 % is a realistic
Poisson Distributions, Statements Based on 14
Precision and Bias Based on Other Methods 16
confidence level. If the consequences of not including the
Precision Not Established, Statements When 17
unknown parameter in the confidence interval would be grave,
Ratings, Statements Based on Special Cases of 18
then a higher confidence level might be considered which
Sources of Data 6
Statistical Data in Two Sections of Methods 5
would lengthen the reported confidence interval. If the conse-
Significance and Use 4
quences of not including the unknown parameter in the
confidence interval are of less than usual concern, then a lower
2. Referenced Documents
confidence level might be considered which would shorten the
2.1 ASTM Standards:
reported confidence interval.
D 123 Terminology Relating to Textiles
3.1.5 critical difference, n—the observed difference be-
D 2904 Practice for Interlaboratory Testing of a Textile Test
tween two test results which should be considered significant at
Method that Produces Normally Distributed Data
the specified probability level.
D 2905 Practice for Statements on Number of Specimens
4,5 3.1.5.1 Discussion—The critical difference is not equal to
for Textiles
the expected variation in a large number of averages of
E 456 Terminology Relating to Quality and Statistics
observed values; it is limited to the expected difference
E 691 Practice for Conducting An Interlaboratory Study to
between only two such averages and is based on the standard
Determine the Precision of a Test Method
error for the difference between two averages and not on the
2.2 ASTM Adjuncts:
standard error of single averages.
TEX-PAC
3.1.6 laboratory sample, n—a portion of material taken to
NOTE 1—Tex-Pac is a group of PC programs on floppy disks, available
represent the lot sample, or the original material, and used in
through ASTM Headquarters, 100 Barr Harbor Drive, West Consho-
the laboratory as a source of test specimens.
hocken, PA 19428, USA. The calculations of critical differences and
3.1.7 lot sample, n—one or more shipping units taken at
confidence limits described in the various sections of this practice can be
random to represent an acceptance sampling lot and used as a
performed using some of the programs in this adjunct.
source of laboratory samples.
3. Terminology
3.1.8 parameter, n—in statistics, a variable that describes a
3.1 Definitions: characteristic of a population or mathematical model.
3.1.1 accuracy, n—of a test method, the degree of agree-
3.1.9 percentage point, n—a difference of 1 percent of a
ment between the true value of the property being tested (or
base quantity.
accepted standard value) and the average of many observations
3.1.9.1 Discussion—A phrase such as “a difference of X %”
made according to the test method, preferably by many
is ambiguous when referring to a difference in percentages. For
observers. See also bias and precision.
example, a change in the moisture regain of a material from
3.1.1.1 Discussion—Increased accuracy for a test method is
5 % to 7 % could be reported as an increase of 40 % of the
associated with decreased bias relative to an accepted reference
initial moisture regain or as an increase of two percentage
value. Although the total bias of a test method is equivalent to
points. The latter wording is recommended.
the accuracy of the test method, the present edition of Form
3.1.10 precision, n—the degree of agreement within a set of
and Style for ASTM Standards recommends using the term
observations or test results obtained as directed in a method.
“bias” since the accuracy of individual observed values is
3.1.10.1 Discussion—The term “precision”, delimited in
sometimes defined as involving both the precision and the bias
various ways, is used to describe different aspects of precision.
of the method.
This usage was chosen in preference to the use of “repeatabil-
3.1.2 bias, n—in statistics, a constant or systematic error in
ity” and “reproducibility” which have been assigned conflict-
test results.
ing meanings by various authors and standardizing bodies.
3.1.2.1 Discussion—Bias can exist between the true value
3.1.11 precision, n—under conditions of single-operator
and a test result obtained from one method, between test results
precision, the single-operator-laboratory-sample-apparatus-day
obtained from two methods, or between two test results
precision of a method; the precision of a set of statistically
independent observations all obtained as directed in the method
and obtained over the shortest practical time interval in one
Annual Book of ASTM Standards, Vol 07.01.
laboratory by a single operator using one apparatus and
Annual Book of ASTM Standards, Vol 07.02.
randomly drawn specimens from one sample of the material
Annual Book of ASTM Standards, Vol 14.02.
PC programs on floppy disks are available through ASTM. Request ADJD2906. being tested.
NOTICE: This standard has either been superseded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
D 2906
3.1.11.1 Discussion—Results obtained under conditions of 4.2 may be part of the statement.
single-operator precision represent the optimum precision that
NOTE 2—The final decision to use a specific method for acceptance
can be expected when using a method. Results obtained under
testing of commercial shipments must be made by the purchaser and the
conditions of within-laboratory and between-laboratory preci-
supplier and will depend on considerations other than the precision of the
sion represent the expected precision for successive test results
method, including the cost of sampling and testing and the value of the lot
of material being tested.
when a method is used respectively in one laboratory and in
more than one laboratory.
4.1.1 If serious disagreements between laboratories is rela-
3.1.12 precision, n—under conditions of within-laboratory
tively unlikely, consider the following statement (Note 3).
precision with multiple operators, the multi-operator, single-
NOTE 3—In these recommended texts, the numbers of sections, notes,
laboratory-sample, single-apparatus-day (within operator) pre-
footnotes, equations, and tables are for illustrative purposes and are not
cision of a method; the precision of a set of statistically
intended to conform to the numbers of other parts of this practice. In
independent test results all obtained in one laboratory using a
correspondence they can be best referenced by such phrases as: “the
single sample of material and with each test result obtained by
illustrative text in 4.1.1 numbered as 4.1.2.”
a different operator, with each operator using one apparatus to
4.1.2 Method D 0000 for the determination of (insert here
obtain the same number of observations by testing randomly
the name of the property) is considered satisfactory for
drawn specimens over the shortest practical time interval.
acceptance testing of commercial shipments of (insert here the
3.1.13 precision, n—under conditions of between-
name of the material) since (insert here the specific reason or
laboratory precision, the multi-laboratory, single-sample,
reasons, such as: (1) current estimates of between-laboratory
single-operator-apparatus-day (within-laboratory) precision of
precision are acceptable, (2) the method has been used exten-
a method; the precision of a set of statistically independent test
sively in the trade for acceptance testing, or ( 3) both of the
results all of which are obtained by testing the same sample of
preceding reasons.)
material and each of which is obtained in a different laboratory
4.1.3 If it is relatively likely that serious disagreements
by one operator using one apparatus to obtain the same number
between laboratories may occur but the method is the best
of observations by testing randomly drawn specimens over the
available, consider the following statement (Note 3).
shortest practical time interval.
4.1.4 Method D 0000 for the determination of (insert here
3.1.14 probability level, n—a general term that reflects the
the name of the property) may be used for the acceptance
stated proportion of times an event is likely to occur. (Compare
testing of commercial shipments of (insert here the name of the
to confidence level and significance level.)
material) but caution is advised since (insert here the specific
3.1.15 sample, n—(1) a portion of material which is taken
reason or reasons, such as: (1) information on between-
for testing or for record purposes. (See also sample lot; sample,
laboratory precision is lacking or incomplete or (2) between-
laboratory; and specimen.)(2) a group of specimens used, or
laboratory precision is known to be poor.) Comparative tests as
of observations made, which provide information that can be
directed in 4.2.1 may be desirable.
used for making statistical inferences about the population(s)
4.1.5 If a method is not recommended for acceptance testing
from which the specimens are drawn.
...
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