Designs Robust against Violation of Normality Assumption in the Standard F-test

A. Biswas, P. Das and N. K. Mandal

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 14, 2898-2910

Abstract: In this article, designs are found for which the F-test of analysis of variance is insensitive to violation of normality assumption. Atiqullah (1962) proved that the F-test for treatments adjusting for blocks in the intra-block analysis of a balanced incomplete block design is robust against non-normality in the observations. Here an attempt has been made to identify other designs robust in this sense. In particular, it is observed that for testing relevant hypothesis, a partially balanced incomplete block design in block design setup, under certain conditions, is robust. Robustness of a balanced treatment incomplete block design and a partially balanced treatment incomplete block design (Biswas, 2012), in treatment-control design setup, is also studied. Moreover, a new measure of robustness is introduced for further study. The performance of the F-test in presence of non-normality in the observations for a quadratically balanced design is also examined.

Date: 2015
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DOI: 10.1080/03610926.2013.799697

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