ASTM E2935-15
(Practice)Standard Practice for Conducting Equivalence Testing in Laboratory Applications
Standard Practice for Conducting Equivalence Testing in Laboratory Applications
SIGNIFICANCE AND USE
4.1 Laboratories conducting routine testing have a continuing need to evaluate test result bias, to evaluate changes for improving the test process performance, or to validate the transfer of a test method to a new location or apparatus. In all situations it must be demonstrated that any bias or innovation will have negligible effect on test results for a characteristic of a material. This standard provides statistical methods to confirm that the mean test results from a testing process are equivalent to those from a reference standard or another testing process, where equivalence is defined as agreement within prescribed limits, termed equivalence limits.
4.1.1 The intra-laboratory applications in this practice include, but are not limited to, the following:
(1) Evaluating the bias of a test method with respect to a certified reference material,
(2) Evaluating bias due to a minor change in a test method procedure,
(3) Qualifying new instruments, apparatus, or operators in a laboratory, and
(4) Qualifying new sources of reagents or other materials used in the test procedure.
4.1.2 This practice also supports evaluating systematic differences in a method transfer from a developing laboratory to a receiving laboratory.
4.2 This practice currently deals only with the equivalence of population means. In this standard, a population refers to a hypothetical set of test results arising from a stable testing process that measures a characteristic of a single material.
Note 1: The equivalence concept can also apply to population parameters other than means, such as precision, stated as variances, standard deviations, or relative standard deviations (coefficients of variation), linearity, sensitivity, specificity, etc.
4.3 The data analysis for equivalence testing of population means in this practice uses a statistical methodology termed the two one-sided tests (TOST) procedure which shall be described in detail in this standard (see X1.1). The TOST pr...
SCOPE
1.1 This practice provides statistical methodology for conducting equivalence testing on numerical data from two sources to determine if their true means differ by no more than predetermined limits.
1.2 Applications include (1) equivalence testing for bias against an accepted reference value, (2) determining equivalence of two test methods, test apparatus, instruments, reagent sources, or operators within a laboratory, and (3) equivalence of two laboratories in a method transfer.
1.3 The current guidance in this standard applies only to experiments conducted on a single material. Guidance is given for determining the amount of data required for an equivalence trial.
1.4 The statistical methodology for determining equivalence used is the two one-sided tests (TOST) procedure. The control of risks associated with the equivalence decision is discussed.
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E2935 − 15 An American National Standard
Standard Practice for
1
Conducting Equivalence Testing in Laboratory Applications
This standard is issued under the fixed designation E2935; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope E2586Practice for Calculating and Using Basic Statistics
1.1 This practice provides statistical methodology for con-
3. Terminology
ducting equivalence testing on numerical data from two
sources to determine if their true means differ by no more than
3.1 Definitions—See Terminology E456 for a more exten-
predetermined limits. sive listing of statistical terms.
3.1.1 accepted reference value, n—a value that serves as an
1.2 Applications include (1) equivalence testing for bias
agreed-upon reference for comparison, and which is derived
against an accepted reference value, (2) determining equiva-
as: (1) a theoretical or established value, based on scientific
lence of two test methods, test apparatus, instruments, reagent
principles, (2) an assigned or certified value, based on experi-
sources, or operators within a laboratory, and (3) equivalence
mental work of some national or international organization, or
of two laboratories in a method transfer.
(3) a consensus or certified value, based on collaborative
1.3 The current guidance in this standard applies only to
experimental work under the auspices of a scientific or
experiments conducted on a single material. Guidance is given
engineering group. E177
fordeterminingtheamountofdatarequiredforanequivalence
3.1.2 bias, n—the difference between the expectation of the
trial.
test results and an accepted reference value. E177
1.4 Thestatisticalmethodologyfordeterminingequivalence
3.1.3 confidence interval, n—an interval estimate [L, U]
used is the two one-sided tests (TOST) procedure. The control
with the statistics L and U as limits for the parameter θ and
of risks associated with the equivalence decision is discussed.
withconfidencelevel1–α,wherePr(L≤θ≤U)≥1–α. E2586
1.5 The values stated in SI units are to be regarded as
3.1.3.1 Discussion—Theconfidencelevel,1–α,reflectsthe
standard. No other units of measurement are included in this
proportion of cases that the confidence interval [L, U] would
standard.
containorcoverthetrueparametervalueinaseriesofrepeated
1.6 This standard does not purport to address all of the random samples under identical conditions. Once L and U are
safety concerns, if any, associated with its use. It is the given values, the resulting confidence interval either does or
responsibility of the user of this standard to establish appro- doesnotcontainit.Inthissense“confidence”appliesnottothe
priate safety and health practices and determine the applica- particular interval but only to the long run proportion of cases
bility of regulatory limitations prior to use. when repeating the procedure many times.
3.1.4 confidence level, n—thevalue,1–α,oftheprobability
2. Referenced Documents
associated with a confidence interval, often expressed as a
2
2.1 ASTM Standards: percentage. E2586
3.1.4.1 Discussion—α is generally a small number. Confi-
E177Practice for Use of the Terms Precision and Bias in
ASTM Test Methods dence level is often 95 % or 99 %.
E456Terminology Relating to Quality and Statistics
3.1.5 confidence limit, n—each of the limits, L and U, of a
E2282Guide for Defining the Test Result of a Test Method
confidence interval, or the limit of a one-sided confidence
interval. E2586
3.1.6 degrees of freedom, n—the number of independent
1
This test method is under the jurisdiction ofASTM Committee E11 on Quality
data points minus the number of parameters that have to be
and Statistics and is the direct responsibility of Subcommittee E11.20 on Test
estimated before calculating the variance. E2586
Method Evaluation and Quality Control.
Current edition approved Oct. 1, 2015. Published October 2015. Originally
3.1.7 equivalence, n—condition that two population param-
approved in 2013. Last previous edition approved in 2014 as E2935 – 14. DOI:
eters differ by no more than predetermined limits.
10.1520/E2935-15.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
3.1.8 intermediate precision conditions, n—conditions un-
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
der which test results are obtained with the same test method
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. usingtestunitsortestspecimenstakenatrandomfromasingle
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 194
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E2935 − 14 E2935 − 15 An American National Standard
Standard Practice for
1
Conducting Equivalence Testing in Laboratory Applications
This standard is issued under the fixed designation E2935; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This practice provides statistical methodology for conducting equivalence testing on numerical data from two sources to
determine if their true means are similar within differ by no more than predetermined limits.
1.2 Applications include (1) equivalence testing for bias against an accepted reference value, (2) determining equivalence of two
test methods, test apparatus, instruments, reagent sources, or operators within a laboratory, and (3) equivalence of two laboratories
in a method transfer.
1.3 The current guidance in this standard applies only to experiments conducted on a single material. Guidance is given for
determining the amount of data required for an equivalence trial.
1.4 The statistical methodology for determining equivalence used is the “Twotwo one-sided ttests-test” (TOST). (TOST)
procedure. The control of risks associated with the equivalence decision is discussed.
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2
2.1 ASTM Standards:
E177 Practice for Use of the Terms Precision and Bias in ASTM Test Methods
E456 Terminology Relating to Quality and Statistics
E2282 Guide for Defining the Test Result of a Test Method
E2586 Practice for Calculating and Using Basic Statistics
3. Terminology
3.1 Definitions—See Terminology E456 for a more extensive listing of statistical terms.
3.1.1 accepted reference value, n—a value that serves as an agreed-upon reference for comparison, and which is derived as: (1)
a theoretical or established value, based on scientific principles, (2) an assigned or certified value, based on experimental work of
some national or international organization, or (3) a consensus or certified value, based on collaborative experimental work under
the auspices of a scientific or engineering group. E177
3.1.2 bias, n—the difference between the expectation of the test results and an accepted reference value. E177
3.1.3 confidence interval, n—an interval estimate [L, U] with the statistics L and U as limits for the parameter θ and with
confidence level 1 – α, where Pr(L ≤ θ ≤ U) ≥ 1– α. E2586
1
This test method is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.20 on Test Method
Evaluation and Quality Control.
Current edition approved Oct. 1, 2014Oct. 1, 2015. Published August 2013October 2015. Originally approved in 2013. Last previous edition approved in 20132014 as
E2935 – 13.14. DOI: 10.1520/E2935-14.10.1520/E2935-15.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
3.1.3.1 Discussion—
The confidence level, 1 – α, reflects the proportion of cases that the confidence interval [L, U] would contain or cover the true
parameter value in a series of repeated random samples under identical conditions. Once L and U are given values, the resulting
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E2935 − 15
confidence interval either does or does not contain it. In this sense “confidence” applies not to the particular interval but only to
the long run proportion of cases when repeating the procedure many times.
3.1.4 confidence level, n—the value, 1 – α, of the probability associated with a confidence interval, often expressed as a
percentage. E2586
3.1.4.1 Discussion—
α is generally a small number. Confidence level is often 95 % or 99 %.
3.1.5 confidence limit, n—each of the limits, L an
...
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