OJS  Vol.2 No.2 , April 2012
Modified Wilcoxon Signed-Rank Test
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.

Cite this paper
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.
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

 
 
Top