Equivalence testing is used when a researcher wants to show that the means between two groups are practically equivalent. Pharmaceutical companies, for example, might use it to determine whether a new, cheaper drug is as effective as the more expensive industry standard. This can be tested in the frequentist paradigm via Schuirmann's two one-sided test.

In equivalence testing, the null and alternative hypotheses are given as follows:

H0:

Ha:

This can also be written as:

H0:

Ha:

[- μD,

We can then break up these hypotheses into two separate one sided hypothesis tests as follows:

1. Upper one-sided test

H01:

Ha1:

2. Lower one-sided test

H02:

Ha2:

The p-value for the test of
equivalence is taken as the maximum p-value
for both one-sided tests. An alternative procedure is to compute a 90%
confidence interval for the mean difference (assuming equal variances),
and if this confidence interval is contained within [- μD,