American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
Open Access
Journal Browser
Go
American Journal of Applied Mathematics and Statistics. 2013, 1(5), 99-102
DOI: 10.12691/ajams-1-5-4
Open AccessArticle

Robustness and Power of the Kornbrot Rank Difference, Signed Ranks, and Dependent Samples T-test

Norman N. Haidous1, and Shlomo S. Sawilowsky1

1Department of Evaluation and Research, Wayne State University, Detroit, USA

Pub. Date: October 22, 2013

Cite this paper:
Norman N. Haidous and Shlomo S. Sawilowsky. Robustness and Power of the Kornbrot Rank Difference, Signed Ranks, and Dependent Samples T-test. American Journal of Applied Mathematics and Statistics. 2013; 1(5):99-102. doi: 10.12691/ajams-1-5-4

Abstract

The purpose of the study was to compare the power and accuracy of the Kornbrot rank difference test to classical parametric and nonparametric alternatives when the assumption of normality is not met, the data are ordinal, and the sample size is small. Although the procedure is robust, there was no evidence the rank difference test had power advantages over Wilcoxon Signed-Ranks test.

Keywords:
nonparametric statistics power rank tests Monte Carlo simulations

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.) New York: McGraw-Hill.
 
[2]  Blair, R. C., & Higgins, J. J. (1985). Comparison of the power of the Paired Samples t test to that of Wilcoxon’s Signed-Ranks test under various population shapes. Psychological Bulletin, 97 (1), 119-128.
 
[3]  Sawilowsky, S.S. (1990). Nonparametric test of interaction in experimental design. Review of Educational Research, 60(1), 91-126.
 
[4]  Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.) New York: McGraw-Hill.
 
[5]  Sawilowsky, S. & Blair, R. C. (1992). A more realistic look at the robustness and Type II error properties of the t-test to departures from population normality. Psychological Bulletin, 111(2), 352-360.
 
[6]  Hodges, J. L., & Lehman, E. L. (1956). The efficiency of some nonparametric competitors of the t-test. Annals of Mathematical Statistics, 27(2), 324-335.
 
[7]  Sawilowsky, S. & Fahoome, G. (2003). Statistics Through Monte Carlo Simulation with Fortran. Oak Park: JMASM.
 
[8]  Kornbrot, D. E. (1990). The rank difference test: A new and meaningful alternative to the Wilcoxon signed ranks test for ordinal data. British Journal of Mathematical and Statistical Psychology, 43, 241-264.
 
[9]  Bradley, J. V. (1978). Robustness? British Journal of Mathematical & Statistical Psychology, 31, 144-152.
 
[10]  Headrick, T. C., & Sawilowsky, S. S. (2000). Weighted simplex procedures for determining boundary points and constants for the univariate and multivariate power methods. Journal of Educational and Behavioral Statistics, 25, 417-436.
 
[11]  Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521-532.
 
[12]  Smith, J. (2009). Intermediate r values for use in the Fleishman power method. Journal of Modern Applied Statistical Methods, 8(2), 610-612.
 
[13]  Sawilowsky, S. (2009). New effect size rules of thumb. Theoretical and Behavioral Foundations, 8,2, 597-599.
 
[14]  Gibbons, J., & Chakraborti, S. (1991). Comparisons of the Mann-Whitney, Student’s t, and Alternate t Tests for means of normal distribution. The Journal of Experimental Education 59(3), 258-267.