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Home  >  Volume 33

Development of Testing Ordered Mean Against a Control Under Heterogeneous Variance by Abidoye A.O, Jolayemi E.T, Sanni O.O.M and Oyejola B. A (Pages 125-128)
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Comparison of more than two population means based on independent random samples is common in research 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. However, when the variances are unequal, the pooled sample variance overestimates the appropriate variance and the test statistic become conservative. This is the well known Behrens – Fisher problem.  There is therefore the need to seek for an alternative sample mean variance better than the pooled variance.  The harmonic mean of variances was found to be better and therefore it being proposed as an alternative to the pooled sample variance when there is heterogeneity of variances. The interest of this research work is to develop a suitable test procedure based on the harmonic mean of variance to address heterogeneity of variance. We are proposing an hypothesis testing technique for testing ordered alternatives under heterogeneous variance for testing g ordered mean when one of this mean is being considered  a control (standard) with the objective of a  proposal of a test statistic for testing equality of means against directional alternative in the presence of heterogeneity of variance. In this study, the use of harmonic mean of sample variance is demonstrated with a practical application.  The result shows that the proposed t – test statistic is found to be appropriate for the data set obtained from the specific example considered in demonstrating this  test procedure.

                Keywords: Ordered alternative, t – test statistic, variances heterogeneity, harmonic mean of variances, a control