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

August 18, 2026| Source: Proceedings of the National Academy of Sciences of the United States of America

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.

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Extensive glacier loss in the coterminous United States.

Glaciers populate the mountain ranges of the western conterminous United States and despite their importance to alpine hydrology, their area and volume change have never been comprehensively evaluated. Our study shows that since the mid-twentieth century about one-quarter of the glaciers have disappeared and the overall area and volume are reduced by one-third. The pattern of glacier shrinkage suggests most glaciers in the conterminous United States are largely maintained by local topographic in

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Physical/TechOctober 20, 2026

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Physical/TechOctober 20, 2026

Antiferromagnetism and tightly bound Cooper pairs induced by kinetic frustration.

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Physical/TechOctober 20, 2026

Coordinated transformations of the labyrinth and occiput during the dinosaur-bird transition.

Evolutionary shape changes of the vertebrate semicircular canals (SCCs) are often ascribed to evolutionary transitions in locomotion, including the origin of flight during the dinosaur-bird transition. However, the potential for transformations of braincase architecture to influence SCC shape independent of sensory-functional adaptation has generally been overlooked. We evaluate the influence of both factors using a large dataset of 146 living and recently extinct crown birds, including taxa rep