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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Lowenstein, Linda Candy"],"institution":null,"degree_name":"Ph.D.","degree_level":"Open Access Dissertation","degree_discipline":"Education Evaluation and Research","degree_department":null,"school":null,"contributors":["Shlomo S. Sawilowsky"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-01T08:00:00Z","date_published":"2015-01-01T08:00:00Z","updated_at":"2026-07-24T06:00:03Z","subjects":["Behrens-Fisher","Mood-Westenberg","Robustness and Power","Siegel-Tukey","Variance change","Yuen's Statistic","Educational Assessment, Evaluation, and Research"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wayne.edu/oa_dissertations/1151","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Shlomo S. Sawilowsky"]},{"key":"dc:creator","label":"Author","values":["Lowenstein, Linda Candy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-01-01T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Education Evaluation and Research"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Behrens-Fisher","Mood-Westenberg","Robustness and Power","Siegel-Tukey","Variance change","Yuen's Statistic","Educational Assessment, Evaluation, and Research"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wayne.edu/oa_dissertations/1151"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Robustness And Power Comparison Of The Mood-Westenberg And Siegel-Tukey Tests"]}]}],"canonical_facts":{"dc:contributor":["Shlomo S. Sawilowsky"],"dc:creator":["Lowenstein, Linda Candy"],"dc:date.available":["2014-01-01T08:00:00Z"],"dc:description.abstract":["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.
"],"dc:identifier":["https://digitalcommons.wayne.edu/oa_dissertations/1151"],"dc:subject":["Behrens-Fisher","Mood-Westenberg","Robustness and Power","Siegel-Tukey","Variance change","Yuen's Statistic","Educational Assessment, Evaluation, and Research"],"dc:title":["Robustness And Power Comparison Of The Mood-Westenberg And Siegel-Tukey Tests"],"thesis:degree_discipline":["Education Evaluation and Research"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T06:00:03Z"}