Modified Wilcoxon Signed-Rank Test

DOI: 10.4236/ojs.2012.22019   PDF   HTML     6,486 Downloads   12,324 Views   Citations

Abstract

This paper briefly reviews the Wilcoxon signed rank sum test and proposes a modification. Unlike the Wilcoxon method, the proposed approach does not require that the populations being studied be continuous. Also unlike the Wilcoxon signed rank test the proposed method, does not require the absence of zero differences or tied absolute values of differences. Rather the proposed method structurally makes provisions for these possibilities. The proposed test statistic also enables the estimation of the probabilities of positive, zero or tied and negative differences within the data. This was illustrated with an example and the proposed method was generally more efficient and hence more powerful than the Wilcoxon test statistic with the power increasing as the number of tied observations or zero differences increases.

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I. Anaene Oyeka and G. Ebuh, "Modified Wilcoxon Signed-Rank Test," Open Journal of Statistics, Vol. 2 No. 2, 2012, pp. 172-176. doi: 10.4236/ojs.2012.22019.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] R. De-W. Derryberry, S. B. Schou and W. J. Conover, “Teaching Rank-Based Tests by Emphasizing Structural Similarities to Corresponding Parametric Tests,” Journal of Statistics Education, Vol. 18, No. 1, 2010, pp. 1-19. www.amstat.org/publications/jse/v18n1/derryberry.pdf
[2] D. Gibbon, “Non Parametric Statistics,” McGraw Hill, New York, 1971. onlinelibrary.wiley.com/doi/10.1111/j.2044-8317.
[3] R. Shier, “Statistics,” The Wilcoxon Signed Rank Sum Test, Mathematics Learning Support Centre, 2004, pp. 1- 3. mlsc.lboro.ac.uk/resources/statistics/signtest.pdf
[4] I. C. A. Oyeka, “An Introduction to Applied Statistical Methods,” 8th Edition, Nobern Avocation Publishing Company, Enugu, 2009, pp. 496-533.
[5] B. H. Robbins, “Non Parametric Tests,” Scholars Series, 2010, pp.1-30. biostat.mc.vanderbilt.edu/wiki/pub/Main/.../NonParametrics. pdf

  
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