Unbiasedness of Tests for Homogeneity of Variances.
STANFORD UNIV CALIF DEPT OF STATISTICS
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Consider the classical homogeneity of variances model. That is, suppose one has a one way layout, with independent random samples of equal sizes in each column. Assume the samples are from normal populations with unknown means and unknown variances. One wishes to test the hypothesis that all the variances are equal. R. V. Laue 1965 defined a two parameter family of statistics to test the homogeneity hypothesis. The family is defined as a function of the ratio of mean value functions of the sample variances. Included in the family are many of the well known tests for homogeneity. In this paper the authors investigate which of the tests is unbiased. Although the authors are unable to resolve the question for every test in the family, they can demostrate the unbiased character for several subfamilies, which include some of the better known tests. Author
- Statistics and Probability