Some New Results on Grubbs' Estimators.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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Consider a two-way classification with n rows and r columns and the usual model of analysis of variance except that the error components of the model may have heterogeneous variances by columns. When r3, the joint distributions of the Sj and the Qj are given for the first time in closed form. Two tests proposed by Russell and Bradley are examined when r3, one for variance homogeneity and the second for one possible disparate variance. A very simple distribution is found for the test statistic of the first test and its non-null distribution is derived also. The distribution of the second test statistic was known to be the central variance-ratio distribution in the null case and now its ration to a parameter of noncentrality is shown to have that same distribution in the non-null case. Extensive simulation studies show that the distribution of the test statistic may be approximated very well by a chi-square distribution.
- Statistics and Probability