Three-sided testing to establish practical significance: A tutorial

Researchers may want to know whether an observed statistical relationship is either meaningfully negative, meaningfully positive, or small enough to be considered practically equivalent to zero. Such a question can not be addressed with standard null hypothesis significance testing, nor with standard equivalence testing. Three-sided testing (TST) is a procedure to address such questions, by simultaneously testing whether an estimated relationship is significantly below, within, or above predetermined smallest effect sizes of interest. TST is a natural extension of the standard two one-sided tests (TOST) procedure for equivalence testing. TST offers a more comprehensive decision framework than TOST with no penalty to error rates or statistical power. In this paper, we give a non-technical introduction to TST, provide commands for conducting TST in R, Jamovi, and Stata, and provide a Shiny app for easy implementation. Whenever a meaningful smallest effect size of interest can be specified, TST should be combined with null hypothesis significance testing as a standard frequentist testing procedure.