PROC TTEST: TOST Equivalence Test :: SAS/STAT(R) 9.22 User's Guide

The TTEST Procedure

TOST Equivalence Test

The hypotheses for an equivalence test are

	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$

where $\text{[math]}$ and $\text{[math]}$ are the lower and upper bounds specified in the TOST option in the PROC TTEST statement, and $\text{[math]}$ 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:

	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$

and

	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$

The overall $\text{[math]}$ -value is the larger of the two $\text{[math]}$ -values of those tests.

Rejection of $\text{[math]}$ in favor of $\text{[math]}$ at significance level $\text{[math]}$ occurs if and only if the $\text{[math]}$ confidence interval for $\text{[math]}$ is contained completely within $\text{[math]}$ . So, the $\text{[math]}$ confidence interval for $\text{[math]}$ is displayed in addition to the usual $\text{[math]}$ interval.

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

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