Equivalence testing for linear regression

TL;DR

This paper presents equivalence testing methods for linear regression to confirm the absence of meaningful associations, including tests for regression coefficients and semipartial correlations, with comparisons to Bayesian approaches.

Contribution

It introduces new equivalence testing procedures for linear regression coefficients and semipartial correlations, expanding the statistical tools for assessing null effects.

Findings

Proposed equivalence tests for regression coefficients and semipartial correlations.

Compared frequentist and Bayesian equivalence testing methods.

Applied tests to real-world examples in the literature.

Abstract

We introduce equivalence testing procedures for linear regression analyses. Such tests can be very useful for confirming the lack of a meaningful association between a continuous outcome and a continuous or binary predictor. Specifically, we propose an equivalence test for unstandardized regression coefficients and an equivalence test for semipartial correlation coefficients. We review how to define valid hypotheses, how to calculate p-values, and how these tests compare to an alternative Bayesian approach with applications to examples in the literature.