Testing and Selecting for Equivalence with Respect to a Control

Abstract

The problem of equivalence assessment of several treatments with a control is considered. The first approach uses a hypothesis testing formulation in which the alternative states global equivalence. With respect to a family of distributions with location parameter, a test based on a two-sided many-one statistic is proposed. Least favorable parameter configuration results are presented as being necessary to evaluate critical values and to determine sample sizes implied by certain power requirements when planning experiments. The second approach concerns a stepwise selection procedure. The goal is to select a subset of treatments containing all those actually equivalent to the control in the absence of global equivalence. The normal case is dealt with in detail for randomized block designs as well as for one-way layouts. Concerning the test problem, optimal allocations of total sample sizes are determined to guarantee specified power requirements for the one-way layout.

Key Words:

• Closed subset selection procedure
• Least favorable configuration
• Multiple hypotheses testing
• One-way layout
• Randomized block design
• Sample size determination