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

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  • A. Biswas
  • P. Das
  • N. K. Mandal

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.

Suggested Citation

  • A. Biswas & P. Das & N. K. Mandal, 2015. "Designs Robust against Violation of Normality Assumption in the Standard F-test," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(14), pages 2898-2910, July.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:14:p:2898-2910
    DOI: 10.1080/03610926.2013.799697
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