On application of modified F – statistic: an example of sales distribution of pharmaceutical drugs

Abstract

This research work often found in Medicine, Agriculture and Social sciences. Most of the earlier works that have addressed the problem of testing equality of means assume homogeneity of variances across the groups being compared but in this work we want to focus in the area of medicine and make use heterogeneity of variances across the group means. Comparison of mean measurements coming from various sources (groups) often is hampered or made difficult by the associated variances not being identical. This is particularly common, for example, in pharmaceutical products where various generic products exist and products have variances that are group dependent. In this work, the use of harmonic mean of sample variances is demonstrated instead of Analysis of Variance (ANOVA) methodology, in order to remove the associated Behren’s – Fisher’s problem. This test statistic is more applicable in a situation when we have three or more samples to consider at a time, then F – test statistic is needed for testing the hypothesis that all the samples are drawn from the populations with the same means. The interest of this research work is to adopt a suitable test procedure to address heterogeneity of variance. The result shows that the modified F – test statistic is found to be appropriate for the data set obtained from the specific example considered in demonstrating the use of the test procedure.

Keywords: Ordered alternative, Modified F – test statistic, Variances heterogeneity, Harmonic mean of variances