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Date of Award
Education Evaluation and Research
Shlomo S. Sawilowsky
The adherence to classical parametric research methods continues, in part, because of the misconception of the robustness properties of these procedures to departures from parametric assumptions. It is demonstrated, however, that these procedures are decidedly nonrobust under variance in absence of treatment. Additionally, the performance of these procedures deteriorates under nonnormal distributions. Compared to parametric procedures, nonparametric and distribution-free research methods make minimal assumptions about underlying population data. They are robust to departures from parametric assumptions, and hold distinct power advantages under the most realistic conditions found in the applied research setting, specifically, the condition of concomitant heteroscedasticity and treatment effect under nonnormal distributions.
The selection of nonparametric methods for this investigation was based upon their ability to detect population differences under varying effect and variance conditions. The Wald-Wolfowitz Two-Sample Runs Test, the Rosenbaum Nonparametric Test of Dispersion and Location, and the Savage Test for Positive Random Variables were of interest in this examination. Six treatment effect sizes, five distributions, and four levels of variance are manipulated via Monte Carlo simulation to examine these methods and to compare their performance with that of their parametric counterparts.
Type I error rates for all tests under consideration are established, first under the Gaussian distribution, then for the remaining nonnormal distributions including the uniform, t, exponential, and Cauchy distributions. Next, the power properties of all tests are determined under the condition of treatment in absence of variance under all distributions. By holding the treatment to zero and allowing differing degrees of variation, the robustness properties of traditional parametric tests are examined. Finally, the comparative power of all tests is examined under the condition of heteroscedasticity and treatment effect.
The Wald-Wolfowitz test, Rosenbaum's test, and Savage's test all exhibit distinct power advantages under mild, moderate, and extreme degrees of variance. Under the condition of moderate variance, and for all treatment effects, it is determined that power superiority is highly distribution dependent. Conversely, under the condition of mild or extreme variance, power superiority is decisive.
Keywords: Nonparametric, Distribution-free, Wald-Wolfowitz, Rosenbaum, Savage, Wilcoxon, Mann-Whitney, Parametric, Student, t test, Welch-Satterthwaite.
Olson, Daryle Alan, "The Efficacy Of Select Nonparametric And Distribution-Free Research Methods: Examining The Case Of Concomitant Heteroscedasticity And Effect Of Treatment" (2013). Wayne State University Dissertations. 684.