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Peer-Reviewed Publication
Proc Natl Acad Sci U S A2026;123(33):e2611548123.August 18, 2026Journal Article

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

Jakub Tomek1, Aaron Caldwell2, David A Eisner3
1Department of Anatomy, Physiology, and Genetics, University of Oxford, Oxford OX1 3PT, United Kingdom.
2Department of Biostatistics, Fay W. Boozman College of Public Health, University of Arkansas for Medical Sciences Northwest, Springdale, AR 72205.
3Division of Cardiovascular Sciences, University of Manchester, Manchester M13 9NT, United Kingdom.
PubMed DOI

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 me…

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