Open Access Dissertation
Date of Award
Education Evaluation and Research
ROBUSTNESS AND POWER OF THE KORNBROT RANK DIFFERENCE, SIGNED RANKS, AND DEPENDENT SAMPLES T-TEST
NORMAN N. HAIDOUS
Advisor:Dr. Shlomo S. Sawilowsky
Major:Evaluation and Research - Statistics
Degree:Doctor of Philosophy
The purpose of the study was to compare the power and accuracy of the Wilcoxon Signed-Ranks test in comparison to the rank difference test when the assumption of normality is not met, the data are ordinal, and the sample size is small. The study also investigated Kornbrot's (1990) claim that the rank difference test should be used over the Wilcoxon Signed-Ranks tests "in all paired comparison designs where the data are not both of internal scale type and of known distribution time" (p. 258).
The study design allowed for the comparison of the comparative power and robustness of the Wilcoxon-Signed Ranks-Test, rank difference test, and the t-test. Utilizing five distributions (Normal, chi-square, df = 1, chi-square, df = 2, chi-square, df = 8, and t distribution, df = 3) and three sample sizes (10, 10), (15, 15), and (20, 20). All distributions and their data sets were created by using a pseudo-random number generator, via Monte Carlo simulation, using Fortran 77.
The results showed the t-test had power advantages over the Wilcoxon Signed-Ranks test and the rank differences, but with explanation. There was no evidence within the results to confirm that the rank difference test had substantial power advantages over Wilcoxon Signed-Ranks test.
Haidous, Norman, "Robustness And Power Of The Kornbrot Rank Difference, Signed Ranks, And Dependent Samples T-Test" (2012). Wayne State University Dissertations. 596.