Open Access Dissertation
Date of Award
Education Evaluation and Research
Shlomo S. Sawilowsky
The author examined how, in the context of experimental design, one might become aware of the Behrens-Fisher problem (heteroscedasticity) in order to apply an approximate solution, such as the Yuen's statistic (1974). It was expected that both the Mood-Westenberg dispersion test (1948) and the Siegel-Tukey test (1960) would remain robust with respect to Type I and Type II error properties (and associated power levels) for detecting variance changes when their assumptions of equal means was slightly violated (i.e., the Behrens-Fisher problem). With the use of Monte Carlo Simulations, the author reviewed 34,606 permutations composed of interactions between various sample sizes, alpha levels, distributions/data sets, variance changes and means shifts. While the Mood-Westenberg (1948) and Siegel-Tukey (1960) tests both remained robust under certain conditions with respect to Type I and II error properties, the Siegel-Tukey test (1960) was by far the most robust of the two statistics, able to handle a more diverse set of conditions and would therefore be the statistic of choice in identifying the Behrens-Fisher problem.
Lowenstein, Linda Candy, "Robustness And Power Comparison Of The Mood-Westenberg And Siegel-Tukey Tests" (2015). Wayne State University Dissertations. 1151.