TEST OF HOMOGENEITY BASED ON GEOMETRIC MEAN OF VARIANCES

Abstract

Prior to comparison of means, there is k-population variances   need to be tested.   The usual contention is that .  The propose methodology utilizes the Geometric Mean among sample variances to estimate the pooled variance,  that plays a vital role in the final computation in the z-statistic. When the null hypothesis is false, this statistical innovation deserves to be considered as potential methodology.The illustration of this methodology using empirical data sets  analyzed through the use of the  Bartlett’s test exhibited the same decisions when analyzed by this propose methodology.  This means that the innovation brought about by this method captures similar utility at a minimum computational procedure. For simulated data sets with homogenous variances, the propose methodology is prone to detect heterogeneity due to artificial differences brought by large proportion of variance to its mean. For simulated data sets under the mixed distribution, the propose methodology is more sensitive to detect heterogeneity of variances.  Theproposemethodology has demonstrated a significantly higher power to detect differences of variances compared to the conventional Bartlett’s test based on paired t-test.  This methodology can be considered as an alternative statistical tool when there is no certainty to assume the homogeneity of variances prior to analysis of variances in comparing group means.