Lably
Skip to content

Equivalence test

Tool used to draw statistical inferences from observed data

  • 5 min read
  • 3 chapters

Related on Lably

Through Statistical hypothesis test, Statistics and Type I and type II errors

LabStatisticsLabStatisticsLabStatisticsLabStatistics

Equivalence testing originates from the field of clinical trials. One application, known as a non-inferiority trial, is used to show that a new drug that is cheaper than available alternatives works as well as an existing drug. In essence, equivalence tests consist of calculating a confidence interval around an observed effect size and rejecting effects more extreme than the equivalence bound when the confidence interval does not overlap with the equivalence bound. In two-sided tests, both upper and lower equivalence bounds are specified. In non-inferiority trials, where the goal is to test the hypothesis that a new treatment is not worse than existing treatments, only a lower equivalence bound is specified.

Equivalence tests can be performed in addition to null-hypothesis significance tests. This might prevent common misinterpretations of p-values larger than the alpha level as support for the absence of a true effect. Furthermore, equivalence tests can identify effects that are statistically significant but practically insignificant, whenever effects are statistically different from zero, but also statistically smaller than any effect size deemed worthwhile (see the first figure). Equivalence tests were originally used in areas such as pharmaceutics, frequently in bioequivalence trials. However, these tests can be applied to any instance where the research question asks whether the means of two sets of scores are practically or theoretically equivalent. Equivalence tests have recently been introduced in evaluation of measurement devices, artificial intelligence, exercise physiology and sports science, political science, psychology, and economics. Several tests exist for equivalence analyses; however, more recently the two-one-sided t-tests (TOST) procedure has been garnering considerable attention. As outlined below, this approach is an adaptation of the widely known t-test.

TOST procedure

A very simple equivalence testing approach is the ‘two one-sided t-tests’ (TOST) procedure. In the TOST procedure an upper (ΔU) and lower (–ΔL) equivalence bound is specified based on the smallest effect size of interest (e.g., a positive or negative difference of d = 0.3). Two composite null hypotheses are tested: H01: Δ ≤ –ΔL and H02: Δ ≥ ΔU. When both these one-sided tests can be statistically rejected, we can conclude that –ΔL < Δ < ΔU, or that the observed effect falls within the equivalence bounds and is statistically smaller than any effect deemed worthwhile and considered practically equivalent. Alternatives to the TOST procedure have been developed as well. An app suitable for a variety of non-parametric as well as parametric equivalence tests is available, A recent modification to TOST makes the approach feasible in cases of repeated measures and assessing multiple variables.

Sign in to keep reading

2 more chapters are free with a Lably account.

More in Statistics

Mortality rateDeaths per 1,000 individuals per yearSystematic reviewComprehensive review of research literature using systematic methodsSensitivity and specificityStatistical measure of a binary classificationLongitudinal studyStudy with repeated observations over timePrevalenceNumber of disease cases in a given population at a specific timeStochasticRandomly determined process