On the use of analysis of variance under unequal group variances

Abstract

In this study, we imposed Analysis of variances test (ANOVA) which use when we have more than two treatments or different levels of a single factors that we wish to compare then we assume homogeneity of variances across the groups being compared although most of the earlier works that have addressed the problem of testing equality of mean variance overestimates the appropriate variance and the test statistic becomes conservative. This is the well-known Behrens – Fisher problem.  Then we are interested in comparing several treatments means in this work, we made use the analysis of variance under unequal variances when the groups variances differ. It will be very inappropriate to use the pooled sample variance (S²_P) as a single value for the variances, instead the sample harmonic mean of variances (S²_H) is proposed as an alternative to the pooled sample variance when there is heterogeneity of variances. The distribution theoretically and confirmed using simulation studies and this proposed harmonic mean of variance was, examined in this work and found useful for unequal variances. Data set from Kwara State Ministry of Health on the incidence of diabetes diseases for male patients was used to illustrate the relevance of our proposed test statistic.