Abstract

A prerequisite for the Analysis of Variance (ANOVA) in many academic and practical studies is that the variances of the observed groups are  identical, and this is usually called the test of homogeneity of variance (HOV). In literature, the comparison of different HOV tests with respect to  their statistical strengths and flaws has been well documented. Regarding their flaws, the comparison of these HOV tests in the framework of factorial ANOVA has not been clearly documented. This research focused on exploring various forms of residuals and introduced a correction factor to boost the performance of Levene's test in single factor and  factorial ANOVA. The  zij in the modified Levene’s test was obtained based on various forms of residuals yij's. Again, three different forms of correction factors , and (k/2)  were also considered in the modification of the test. Using 1000 simulations for every possibility and form of the residual, the coherence of every variant was examined under multiple conditions, including various combinations of factor levels, repetitions, mean variations, and variance deviations to false positives and false negatives.  According to the research, merging the application of the absolute residuals of  yij with the correction factor  (k/2)    was the most effective for the test result, and it held for all situations with factorial and single factor ANOVA. However, using the square of residuals of  yij was superior to the residuals' performance. The statistical likelihood of the test reliably decreases as the number of covariates and the intensity of factors rise, regardless of the number of reproductions, for all types of residuals that have been studied. Again, it was observed that,  with the absolute residuals of yij  and correction factor  (k/2) ,  the efficiency of Levene’s test can be improved, and the problem of the conservative of the test can be dealt with.

Statistics