Global InformationEquivalence test information
Equivalence tests are a variety of hypothesis tests used to draw statistical inferences from observed data. In these tests, the null hypothesis is defined as an effect large enough to be deemed interesting, specified by an equivalence bound. The alternative hypothesis is any effect that is less extreme than said equivalence bound. The observed data are statistically compared against the equivalence bounds. If the statistical test indicates the observed data is surprising, assuming that true effects are at least as extreme as the equivalence bounds, a Neyman-Pearson approach to statistical inferences can be used to reject effect sizes larger than the equivalence bounds with a pre-specified Type 1 error rate.
Equivalence testing originates from the field of clinical trials.[1] 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.[2][3][4][5] 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).[6] 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. As such, equivalence analyses have seen increased usage in almost all medical research fields. Additionally, the field of psychology has been adopting the use of equivalence testing, particularly in clinical trials. This is not to say, however, that equivalence analyses should be limited to clinical trials, and the application of these tests can occur in a range of research areas. In this regard, equivalence tests have recently been introduced in evaluation of measurement devices,[7][8] artificial intelligence[9] as well as exercise physiology and sports science.[10] 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.
- ^ Snapinn, Steven M. (2000). "Noninferiority trials". Current Controlled Trials in Cardiovascular Medicine. 1 (1): 19–21. doi:10.1186/CVM-1-1-019. PMC 59590. PMID 11714400.
- ^ Rogers, James L.; Howard, Kenneth I.; Vessey, John T. (1993). "Using significance tests to evaluate equivalence between two experimental groups". Psychological Bulletin. 113 (3): 553–565. doi:10.1037/0033-2909.113.3.553. PMID 8316613.
- ^ Statistics applied to clinical trials (4th ed.). Springer. 2009. ISBN 978-1402095221.
- ^ Piaggio, Gilda; Elbourne, Diana R.; Altman, Douglas G.; Pocock, Stuart J.; Evans, Stephen J. W.; CONSORT Group, for the (8 March 2006). "Reporting of Noninferiority and Equivalence Randomized Trials" (PDF). JAMA. 295 (10): 1152–60. doi:10.1001/jama.295.10.1152. PMID 16522836.
- ^ Piantadosi, Steven (28 August 2017). Clinical trials : a methodologic perspective (Third ed.). John Wiley & Sons. p. 8.6.2. ISBN 978-1-118-95920-6.
- ^ Lakens, Daniël (2017-05-05). "Equivalence Tests". Social Psychological and Personality Science. 8 (4): 355–362. doi:10.1177/1948550617697177. PMC 5502906. PMID 28736600.
- ^ Cite error: The named reference
siebert2019was invoked but never defined (see the help page). - ^ Schnellbach, Teresa (2022). Hydraulic Data Analysis Using Python. doi:10.26083/tuprints-00022026.
- ^ Jahn, Nico; Siebert, Michael (2022). "Engineering the Neural Automatic Passenger Counter". Engineering Applications of Artificial Intelligence. 114. arXiv:2203.01156. doi:10.1016/j.engappai.2022.105148.
- ^ Mazzolari, Raffaele; Porcelli, Simone; Bishop, David J.; Lakens, Daniël (March 2022). "Myths and methodologies: The use of equivalence and non‐inferiority tests for interventional studies in exercise physiology and sport science". Experimental Physiology. 107 (3): 201–212. doi:10.1113/EP090171. ISSN 0958-0670. PMID 35041233. S2CID 246051376.