A New Non-parametric Test Procedure for the Median of an Asymmetrical Population
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 6, November 2016, Pages: 376-386
Received: Oct. 11, 2016; Accepted: Oct. 25, 2016; Published: Nov. 17, 2016
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Author
Mohammad Ibrahim Ahmmad Soliman Gaafar, Department of Statistics, Faculty of Commerce, Alexandria University, Alexandria, Egypt
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Abstract
This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed models, simulation results show that the proposed test procedure is superior to all competitor tests under consideration in terms of preserving the empirical size of the test at its nominal level and also having higher empirical powers.
Keywords
Power Transformations, Non-parametric Procedures, The Normal Scores Test, The Wilcoxon Signed Ranks Test, The Sign Test, The Shapiro-Wilk Test
To cite this article
Mohammad Ibrahim Ahmmad Soliman Gaafar, A New Non-parametric Test Procedure for the Median of an Asymmetrical Population, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 6, 2016, pp. 376-386. doi: 10.11648/j.ajtas.20160506.17
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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