ASTM E2935-13
(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 bias 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 t-test” (TOST) procedure which shall be described in detail in this standard (see X1.1). The TOST procedure will be adapted to the...
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 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 t-test” (TOST). 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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Standards Content (Sample)
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Designation: E2935 − 13 AnAmerican National Standard
Standard Practice for
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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 3. Terminology
1.1 This practice provides statistical methodology for con- 3.1 Definitions—See Terminology E456 for a more exten-
ducting equivalence testing on numerical data from two sive listing of statistical terms.
sources to determine if their true means are similar within
3.1.1 accepted reference value, n—a value that serves as an
predetermined limits.
agreed-upon reference for comparison, and which is derived
as: (1) a theoretical or established value, based on scientific
1.2 Applications include (1) equivalence testing for bias
principles, (2) an assigned or certified value, based on experi-
against an accepted reference value, (2) determining equiva-
mental work of some national or international organization, or
lence of two test methods, test apparatus, instruments, reagent
(3) a consensus or certified value, based on collaborative
sources, or operators within a laboratory, and (3) equivalence
experimental work under the auspices of a scientific or
of two laboratories in a method transfer.
engineering group. E177
1.3 The current guidance in this standard applies only to
3.1.2 bias, n—the difference between the expectation of the
experiments conducted on a single material. Guidance is given
test results and an accepted reference value. E177
for determining the amount of data required for an equivalence
trial.
3.1.3 confidence interval, n—an interval estimate [L, U]
with the statistics L and U as limits for the parameter θ and
1.4 Thestatisticalmethodologyfordeterminingequivalence
withconfidencelevel1–α,wherePr(L≤θ≤U)≥1–α. E2586
used is the “Two one-sided t-test” (TOST).The control of risks
3.1.3.1 Discussion—The confidence level, 1 –α, reflects the
associated with the equivalence decision is discussed.
proportion of cases that the confidence interval [L, U] would
1.5 The values stated in SI units are to be regarded as
containorcoverthetrueparametervalueinaseriesofrepeated
standard. No other units of measurement are included in this
random samples under identical conditions. Once L and U are
standard.
given values, the resulting confidence interval either does or
1.6 This standard does not purport to address all of the
doesnotcontainit.Inthissense“confidence”appliesnottothe
safety concerns, if any, associated with its use. It is the
particular interval but only to the long run proportion of cases
responsibility of the user of this standard to establish appro-
when repeating the procedure many times.
priate safety and health practices and determine the applica-
3.1.4 confidence level, n—thevalue,1–α,oftheprobability
bility of regulatory limitations prior to use.
associated with a confidence interval, often expressed as a
percentage. E2586
2. Referenced Documents
2 3.1.4.1 Discussion—α is generally a small number. Confi-
2.1 ASTM Standards:
dence level is often 95 % or 99 %.
E177 Practice for Use of the Terms Precision and Bias in
ASTM Test Methods
3.1.5 confidence limit, n—each of the limits, L and U, of a
E456 Terminology Relating to Quality and Statistics confidence interval, or the limit of a one-sided confidence
E2282 Guide for Defining the Test Result of a Test Method interval. E2586
E2586 Practice for Calculating and Using Basic Statistics
3.1.6 degrees of freedom, n—the number of independent
data points minus the number of parameters that have to be
estimated before calculating the variance. E2586
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This test method is under the jurisdiction ofASTM Committee E11 on Quality
and Statistics and is the direct responsibility of Subcommittee E11.20 on Test
3.1.7 equivalence, n—similarity between two population
Method Evaluation and Quality Control.
parameters within predetermined limits.
Current edition approved Aug. 1, 2013. Published August 2013. DOI: 10.1520/
E2935-13.
3.1.8 intermediate precision conditions, n—conditions un-
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For referenced ASTM standards, visit the ASTM website, www.astm.org, or
der which test results are obtained with the same test method
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
usingtestunitsortestspecimenstakenatrandomfromasingle
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. quantity of material that is as nearly homogeneous as possible,
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