The TTEST Procedure

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  $


$\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 $H_0$ in favor of $H_1$ 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).