Equivalence Tests: A Practical Primer for t Tests, Correlations, and Meta-Analyses

Soc Psychol Personal Sci. 2017 May;8(4):355-362. doi: 10.1177/1948550617697177. Epub 2017 May 5.


Scientists should be able to provide support for the absence of a meaningful effect. Currently, researchers often incorrectly conclude an effect is absent based a nonsignificant result. A widely recommended approach within a frequentist framework is to test for equivalence. In equivalence tests, such as the two one-sided tests (TOST) procedure discussed in this article, an upper and lower equivalence bound is specified based on the smallest effect size of interest. The TOST procedure can be used to statistically reject the presence of effects large enough to be considered worthwhile. This practical primer with accompanying spreadsheet and R package enables psychologists to easily perform equivalence tests (and power analyses) by setting equivalence bounds based on standardized effect sizes and provides recommendations to prespecify equivalence bounds. Extending your statistical tool kit with equivalence tests is an easy way to improve your statistical and theoretical inferences.

Keywords: equivalence testing; null hypothesis significance testing; power analysis; research methods.