Three-Sided Testing to Establish Practical Significance: A Tutorial

Peder Isager and Jack Fitzgerald
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Peder Isager: Oslo New University College

No 24-077/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: 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.

Keywords: Three-sided testing; equivalence testing; interval testing; hypothesis testing; R; Stata; NHST; effect size (search for similar items in EconPapers)
JEL-codes: C12 C18 C87 (search for similar items in EconPapers)
Date: 2024-12-20
New Economics Papers: this item is included in nep-ecm
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