# Equivalence Test

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:  12 | > μD

Ha:  12 | <= μD

This can also be written as:

H0:   μ12  > μD  or  μ12  < -μD

Ha:    - μD <= μ12 <= μD

[- μD,  μD] is the interval of equivalence or indifference

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

1. Upper one-sided test

H01:  μ12  > μD

Ha1:  μ12  <= μD

2. Lower one-sided test

H02:  μ12  < -μD

Ha2:  μ12  >= - μD

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,  μD ], you can reject the null hypothesis and conclude that the data suggest that the means are equivalent.