On the admissibility and consistency of tests for homogeneity of variances
The authors consider the hypothesis testing problem for the homogeneity of variances in the one-way fixed and balanced analysis of variance model under the assumptions of independence and normality. They obtain a necessary and sufficient condition for admissibility of a test among the class of scale invariant tests. In particular they show that some classical tests such as Hartley's test and Cochran's test are not admissible. A certain limiting property (parameter consistency) of scale invariant tests is defined and it is shown that several well-known tests are parameter consistent for all significance levels. They also show that some well-known tests may not be parameter consistent or may be parameter consistent only for certain significance levels. Extensions to non-normal cases are also indicated.
one-way fixed and balanced analysis of variance model
scientific article; zbMATH DE number 4131437