On the Admissibility and Consistency of Tests for Homogeneity of Variances

Abstract

Consider the one-way fixed and balanced analysis of variance model under the assumptions of independence and normality. The problem is to test for homogeneity of variances. A necessary and sufficient condition for admissibility of a test among the class of scale invariant tests is given. Hartley's test and Cochran's test are not in the class and therefore are inadmissible. Various scale invariant tests are examined for parameter consistency. Parameter consistency in this case means the following: Consider a sequence of values of the maximal invariant parameter in the alternative space. If the Kullback-Leibler distance from this sequence to the null point tends to infinity then the power of the test tends to 1. Several well known test are shown to be parameter consistent (PC) for all significance levels. Some well known tests however may not be PC or may be PC only for certain significance levels. Extensions of PC results to nonnormal cases are indicated.