Interpret Equivalence Against Prespecified Bounds

Define what would count as similar enough

An equivalence analysis asks whether the effect lies within a scientifically justified interval of differences considered sufficiently small. It does not ask whether the effect equals zero exactly. Choose the bounds, scale and direction before reviewing the comparative result, using substantive evidence rather than the observed confidence interval.

The statsmodels two-one-sided-tests documentation describes an equivalence test for independent samples with lower and upper bounds. The computational test cannot justify the bounds; that remains part of the study’s scientific design.

Align the confidence level and test

For the standard two one-sided tests approach with each test at alpha 0.05, equivalence corresponds to a two-sided 90% confidence interval lying wholly inside the prespecified bounds, under the matching model and assumptions. Do not substitute a different interval level without recognizing that the decision rule changes.

Check the effect scale. Bounds of −2 and 2 units describe an absolute difference, while ratio-scale bounds may require a transformed analysis. Preserve which group is subtracted from which, and whether the bounds are symmetric for a scientifically meaningful reason.

Compare hypothetical intervals

Suppose the equivalence region is from −2 to 2 units. A compatible 90% interval of [−0.8, 1.4] lies entirely inside it and supports equivalence under the specified procedure. An interval of [−3, 1] includes zero but crosses the lower equivalence bound, so it does not establish equivalence.

An interval of [0.2, 1.5] can exclude zero and still lie inside the equivalence region. Thus a small difference can be statistically distinguishable from zero while remaining within the prespecified acceptable range. This is not a contradiction: the two analyses answer different questions.

Report uncertainty without switching claims

State the justification for the bounds, analysis population, interval method and both one-sided test results where appropriate. Investigate missing outcomes, nonadherence and model assumptions because a biased estimate toward no difference can make equivalence appear easier to demonstrate.

If the interval is not contained within the bounds, describe the result as inconclusive for equivalence rather than proof of a meaningful difference. Do not widen the bounds after seeing the data. A useful report lets readers assess both the numerical evidence and whether the chosen definition of sufficiently similar is credible for the intended decision.

Source verification: 6 November 2026. Examples are hypothetical.