STAT-16: Statistical Techniques for Equivalence Testing

This is part of a series of articles covering the procedures in the book Statistical Procedures for the Medical Device Industry.


This procedure provides statistical techniques for demonstrating equivalence of a new product or process to an existing product or process. This is an alternate approach to demonstrating the product or process meets established requirements per the following procedures:.


    1. Confidence Limits for the Difference between Two Averages
    2. Equivalence Test for Two Averages
    3. Confidence Limits for the Difference between Two Averages—Paired Data
    4. Equivalence Test for Two Averages—Paired Data
    5. Confidence Limits for the Ratio of Two Standard Deviations
    6. Equivalence Test for Two Standard Deviations


  • Equivalence does not mean identical.  It means the difference is less than some predetermined difference Δ.

  • Demonstrating equivalence requires defining a difference Δ that is considered significant and then demonstrating with high confidence the difference is less than Δ.  Equivalence tests are based on confidence intervals.  The validated spreadsheet STAT-12 to 16 – Confidence Intervals and Equivalence Tests.xlsx  accompanying the book can be used for performing equivalence tests.  For example, suppose a difference of 2 or more is considered a significant difference.  As shown below, the 95 confidence interval for the difference is between -2 and 2 so one can claim equivalence.


  • Procedures for calculating sample size are provided.  However, a passing equivalence test is valid regardless of the sample size used.  For smaller sample sizes the confidence intervals will be wider, making it harder to pass.  The risk of too small a sample size is falsely failing the equivalence test.  The procedure for calculating sample size is too ensure a reasonable chance of passing equivalent groups.
  • Equivalence tests cannot be chained together.  B is equivalent to A and C is equivalent to B does not mean C is equivalent to A.  The difference could be 2 times Δ.  One must prove directly that C is equivalent to A.  An alternate approach is to use A to establish specification limits and then show B and C meet the specification limits.  Setting specification limits is described in STAT-11, Statistical Techniques for Setting Specifications.
  • A t-test by itself is not a valid approach for demonstrating equivalence.  If it is believed that equivalence testing requires fewer samples than demonstrating the specification limits are meet, equivalence testing is being done wrong.  Equivalence testing is generally used when there are not specification limits.

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