TOST Equivalence Test :: SAS/STAT(R) 12.1 User's Guide

TOST Equivalence Test

The hypotheses for an equivalence test are

$\displaystyle H_0\colon$	$\displaystyle \mu < \theta _ L \quad \mbox{or}\quad \mu > \theta _ U$
$\displaystyle H_1\colon$	$\displaystyle \theta _ L \le \mu \le \theta _ U$

where $\theta _ L$ and $\theta _ U$ are the lower and upper bounds specified in the TOST option in the PROC TTEST statement, and $\mu$ is the analysis criterion (mean, mean ratio, or mean difference, depending on the analysis). Following the two one-sided tests (TOST) procedure of Schuirmann (1987), the equivalence test is conducted by performing two separate tests:

$\displaystyle H_{a0}\colon$	$\displaystyle \mu < \theta _ L$
$\displaystyle H_{a1}\colon$	$\displaystyle \mu \ge \theta _ L$

and

$\displaystyle H_{b0}\colon$	$\displaystyle \mu > \theta _ U$
$\displaystyle H_{b1}\colon$	$\displaystyle \mu \le \theta _ U$

The overall p-value is the larger of the two p-values of those tests.

Rejection of in favor of at significance level $\alpha$ occurs if and only if the $100(1-2\alpha )\%$ confidence interval for $\mu$ is contained completely within $\left( \theta _ L, \theta _ U \right)$ . So, the $100(1-2\alpha )\%$ confidence interval for $\mu$ is displayed in addition to the usual $100(1-\alpha )\%$ interval.

For further discussion of equivalence testing for the designs supported in the TTEST procedure, see Phillips (1990); Diletti, Hauschke, and Steinijans (1991); Hauschke et al. (1999).

The TTEST Procedure

TOST Equivalence Test