Robustness And Power Of The Kornbrot Rank Difference, Signed Ranks, And Dependent Samples T-Test

<p> <strong>ABSTRACT</strong> </p> <p> <strong>ROBUSTNESS AND POWER OF THE KORNBROT RANK DIFFERENCE, SIGNED RANKS, AND DEPENDENT SAMPLES T-TEST</strong> </p> <p>by</p> <p> <strong>NORMAN N. HAIDOUS</strong> </p> <p>December 2012</p> <p> <strong>Advisor:</strong>Dr. Shlomo S. Sawilowsky</p> <p> <strong>Major:</strong>Evaluation and Research - Statistics</p> <p> <strong>Degree:</strong>Doctor of Philosophy</p> <p> 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). </p> <p> 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.</p> <p> 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.</p>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Education Evaluation and Research

Year dc:date.available

2012

Author dc:creator

• Haidous, Norman

Contributors dc:contributor

• Shlomo Sawilowsky

• non parametric statistics
• Rank Difference Test
• t-test
• Wilcoxon Signed-Ranks
• Statistics and Probability

Repository record dc:identifier

https://digitalcommons.wayne.edu/oa_dissertations/596

OAI identifier oai:identifier

oai:digitalcommons.wayne.edu:oa_dissertations-1595