Iterative Chi-Square Test for Equivalence of Multiple Treatment Groups

• Activity Number: 198
• Type: Topic Contributed
• Date/Time: Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section*
• Author(s): Tie-Hua Ng*+
• Affiliation(s): Food and Drug Administration
• Keywords: Equivalence testing ; Active control ; Nuisance parameter

Abstract

A measure of closeness among three or more means from normal populations was proposed by Ng (2000). The F-statistic was proposed to test the null hypothesis that this measure of closeness is greater or equal to some prespecified d (>0), against the alternative hypothesis that this measure of closeness is smaller than d. The null distribution of the F-statistic at the boundary depends on d and the assumed common variance (V) with equal sample sizes. Thus, the critical value depends on V, which must be estimated, resulting in an inflation of the type I error rate. Ng (2001) proposed an iterative approach to resolve this problem. Briefly, multiplying the chi-square statistic by V results in a test statistic T1. The distribution of T1 depends on V. To start the iterative process, determine the critical value for T1 as a function of V, define a test statistic by subtracting the estimated critical value from T1, and then calculate its critical value as a function of V. This iterative process stops when the critical value becomes reasonably flat. This paper provides tabulations for implementing the proposed test. A numerical example is used to illustrate the use of the tabulations.