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**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 procedure will be adapted to the type of objective and experiment design selected.

4.3.1 Historically, this procedure originated in the pharmaceutical industry for use in bioequivalence trials (1, 2),3 denoted as the Two One-Sided Tests Procedure, and has since been adopted for other applications, particularly in testing and measurement applications (3, 4).

4.3.2 The conventional Student’s t test used for detecting differences is not recommended for equivalence testing as it does not properly control the consumer’s and producer’s risks for this application (see X1.3).

4.4 Risk Management—Guidance is provided for determining the amount of data required to control the risks of making the wrong decision in accepting or rejecting equivalence (see X1.2).

4.4.1 The consumer’s risk is the probability of accepting equivalence when the actual bias or difference in means is equal to the equivalence limit. This probability is controlled to a low level so that accepting equivalence gives a high degree of assurance that differences in question are less than the equivalence limit.

4.4.2 The producer’s risk is the risk of falsely rejecting equivalence. If improvements are rejected this can lead to opportunity losses to the company and its laboratories (the producers) or cause additional unnecessary effort in improving the testing process.

**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 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.*

**2. Referenced Documents** *(purchase separately)* The documents listed below are referenced within the subject standard but are not provided as part of the standard.

**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

**ICS Code**

ICS Number Code 03.120.30 (Application of statistical methods)

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**DOI:** 10.1520/E2935-15

ASTM International is a member of CrossRef.

**Citation Format**

ASTM E2935-15, Standard Practice for Conducting Equivalence Testing in Laboratory Applications, ASTM International, West Conshohocken, PA, 2015, www.astm.org

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