Accession Number : ADA133922

Title :   Some New Results on Grubbs' Estimators.

Descriptive Note : Technical rept.,


Personal Author(s) : Brindley,Dennis A ; Bradley,Ralph A

PDF Url : ADA133922

Report Date : Jun 1983

Pagination or Media Count : 24

Abstract : 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 r=3, 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 r=3, 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.

Descriptors :   *Statistical tests, *Statistical distributions, *Estimates, *Analysis of variance, Distribution theory, Chi square test, Nulls(Amplitude), Simulation, Homogeneity, Variations

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE