Beyond "non-significant" results: Why and how to test for practical equivalence.

Authors

Jakub Tomek, Aaron Caldwell, David A Eisner

Published in

Proceedings of the National Academy of Sciences of the United States of America. Volume 123. Issue 33. Pages e2611548123. Aug 18, 2026. Epub Aug 14, 2026.

Abstract

Reporting comparisons with P ≥ 0.05 as showing "no effect" or "no difference" remains one of the most widespread and problematic misinterpretations in the scientific literature. A statistically nonsignificant result shows only that the data do not provide strong evidence for a difference. This distinction matters because such findings can arise for two very different reasons: Either there is no meaningful difference, or a meaningful difference is present but cannot be detected reliably because of limited sample size or high variability. We highlight equivalence testing as a practical framework for distinguishing between these possibilities. Using the two one-sided tests (TOST) approach, investigators can formally test whether effects large enough to be scientifically, clinically, or practically meaningful can be ruled out. We explain the logic of TOST, show how it distinguishes practical equivalence from inconclusive evidence, and illustrate its use in paired and unpaired comparisons. To support broader adoption, we also introduce a freely available online calculator that enables researchers to perform common equivalence tests without coding.

PMID:
42599784
Bibliographic data and abstract were imported from PubMed on 15 Aug 2026.

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