Robust Procedure for the Fit of Oneway Analysis of Variance (ANOVA) models under uncorrelated errors

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November, 2016
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The possible dominance of basic assumption about underlying models on the analysis of data is of much concern to some statisticians (Anscombe (1967);Hogg (1974); B uning (1996)). The advocacy of distribution-free (nonparametric) tests for di erences in location problems between samples has been emphasized over the past seven decades (Hao and Houser, 2011). This study develops a robust tting procedure for one-way ANOVA models. Further investigation on Asymptotic Relative E ciency (ARE) of this procedure and parametric F-test under class of distributions was carried out. In line with these objectives, 10,000 simulations were carried out for a one-way ANOVA model with three levels for size 5, 10, 15, and 20. Intralevel correlation coe cient = 0 was considered in these simulations. The ndings revealed that the parametric F-test for Oneway ANOVA model performed better than the non-parametric Adaptive test proposed for symmetric and moderate tailed distributions and then in symmetric and light tailed distributions with ARE between 2% and 55%. However, the Adaptive test outperformed the F-test in symmetric and asymmetric with varying tail weights distributions with ARE between 5% and 70%. Although, the F-test displayed superiority in e ciency in symmetric medium and light tailed distributions, the Adaptive test was more effi cient in more broader class of continuous distribution.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the Degree of Master of Philosophy in Mathematical Statistics.