Coping with variance heterogeneity

Abstract

An approximate solution to the problem of testing equality of means of normal populations, when the variances may differ, is developed. The proposed solution utilizes the F-test with a random critical function. A series expansion based on results of Gideon and Gurland (1976) yields the true level of significance of the test. For a small number of populations in the test the technique is viable, but for a larger number a simulation study is made to compare the behavior of this test with that of some other well-known tests. The proposed test appears to provide better control of the true significance level, especially for small sample sizes. Futhermore, since it utilizes the ordinary F-statistic, it is simpler and more easily computed than some others.