The TTEST Procedure

TOST Equivalence Test

The hypotheses for an equivalence test are

\begin{align*} H_0\colon & \mu < \theta _ L \quad \mbox{or}\quad \mu > \theta _ U \\ H_1\colon & \theta _ L \le \mu \le \theta _ U \end{align*}

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:

\begin{align*} H_{a0}\colon & \mu < \theta _ L \\ H_{a1}\colon & \mu \ge \theta _ L \end{align*}


\begin{align*} H_{b0}\colon & \mu > \theta _ U \\ H_{b1}\colon & \mu \le \theta _ U \end{align*}

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).