When n replicates are available from a factorial experiment, several methods exist for testing the validity of the assumption of equal variances within the "cells" or treatment combinations of the experiment. A new test is proposed for variances of random samples believed to be from normal populations. This new test combines both the familiar graphical analysis of means for treatment effects (ANOME) and the analysis of the logarithms of the within-group variances to produce a graphical display of the test for variance homogeneity. To determine robustness of the proposed test against departures from the underlying normality assumption, this new test is also evaluated for non-normal populations. Another analysis-of-means-type test was developed by Wludyka and Nelson which utilizes Dirichlet distributions and specially constructed tables. The new test, proposed herein, has an advantage in that it relies solely on critical values developed for the analysis of- means procedure. As an added simplification, only those critical values corresponding to infinite degrees of freedom are required. A In ANOME analysis of Nelson's data (used to demonstrate the In ANOVA procedure) yielded the same conclusion. Also, simulation results indicate that when the underlying assumption of normality is not feasible, the In ANOME procedure demonstrated equivalent or superior Type-I error-rate stability and power among tests which rely on that assumption. However, when the underlying assumption of normality is tenable, Bartlett's test performs the best of all homogeneity-of-variance tests studied in maintaining stable Type-I errors and power.
Library of Congress Subject Headings
Analysis of variance; Experimental design; Mathematical statistics
Department, Program, or Center
The John D. Hromi Center for Quality and Applied Statistics (KGCOE)
Volino, Casey, "Analysis of heterogeneity of variance using anome on ln S^2" (1998). Thesis. Rochester Institute of Technology. Accessed from
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