On the Development of an Exponentiated F Test for One-way ANOVA in the Presence of Outlier(s)

摘要

The classical Fisher-Snedecor test which compares several population means depends on the underlined assumptions which include; independent of populations, constant variance and absence of outlier among others .Arguably the source of violation of some of these assumptions is the outlier which lead to unequal variances. Outlier leads to inequality in the variances of the populations which consequently leads to the failure of the classical-F to take correct decision in terms of the null hypothesis. A series of robust tests have been carried out to ameliorate these lapses with some degrees of inaccuracies and limitations in terms of inflating the type 1 error and the power of different combination of parameters at various sample sizes while still uses the conventional F-table. This study focuses on developing robust F-test called exponentiated F test with the introduction of one shape parameter to the conventional F-distribution capable of taking decisions on ANOVA that are robust to the existence of outlier. The performance of the robust F test was compared with the existing F-tests in the literature using the power of test. Real life and simulated data were used to illustrate the applicability and efficiency of the proposed distribution over the existing ones. Experimental data with balanced and unbalanced design were used with populations sizes k=3 and k=5 were simulated with 10000 replications and varying degrees of outliers were ejected randomly. The results obtained indicate that the Proposed Exponentiated-F test is uniformly most powerful than the conventional-F tests for analysis of variance in the presence of outlier and is therefore recommended for use by researchers.