Equivalence test

A very simple equivalence testing approach is the ‘two one-sided t-tests’ (TOST) procedure. In the TOST procedure an upper (ΔU) and lower (–ΔL) equivalence bound is specified based on the smallest effect size of interest (e.g., a positive or negative difference of d = 0.3). Two composite null hypotheses are tested: H01: Δ ≤ –ΔL and H02: Δ ≥ ΔU. When both these one-sided tests can be statistically rejected, we can conclude that –ΔL U, or that the observed effect falls within the equivalence bounds and is statistically smaller than any effect deemed worthwhile and considered practically equivalent. A recent modification to TOST makes the approach feasible in cases of repeated measures and assessing multiple variables. == Comparison between t-test and equivalence test ==

The equivalence test can be induced from the t-test. == See also ==

The papers below are good introductions to equivalence testing. • • • • • • • • An applied introduction to equivalence testing appears in Section 4.2 of Vincent Arel-Bundock’s open-access book Model to Meaning. == References ==