Historically, it has been accepted practice for critical values for the Winsorized t test for independent samples to be based on adjusted degrees of freedom depending on the number of total non-Winsorized (approximate) values. Recently, a new such table of Winsorized critical values has been developed via approximate randomization by Monte Carlo simulation.
Based on eight common data distributions estimated from Psychology and Education along with the normal and five Mathematical distributions, these two tables of values were compared with respect to robustness to types I and II errors through Monte Carlo simulations for one and 10% Winsorized values per end.
20% Winsorized results were generally non-robust for approximate critical values and mixed for Monte Carlo-derived critical values. With one Winsorized value per end, for small samples, type I error results generally support the use of the newly-developed table of Monte Carlo-derived critical values over the approximate critical values. For larger samples (one Winsorized value per end), approximate critical values become increasingly robust (in most cases, stringently-so for samples of 90 or more) to type I error while maintaining an advantage over Monte Carlo-derived critical values with respect to type II error.
","abstract_html":"<p>Historically, it has been accepted practice for critical values for the Winsorized t test for independent samples to be based on adjusted degrees of freedom depending on the number of total non-Winsorized (approximate) values. Recently, a new such table of Winsorized critical values has been developed via approximate randomization by Monte Carlo simulation.</p> <p>Based on eight common data distributions estimated from Psychology and Education along with the normal and five Mathematical distributions, these two tables of values were compared with respect to robustness to types I and II errors through Monte Carlo simulations for one and 10% Winsorized values per end.</p> <p>20% Winsorized results were generally non-robust for approximate critical values and mixed for Monte Carlo-derived critical values. With one Winsorized value per end, for small samples, type I error results generally support the use of the newly-developed table of Monte Carlo-derived critical values over the approximate critical values. For larger samples (one Winsorized value per end), approximate critical values become increasingly robust (in most cases, stringently-so for samples of 90 or more) to type I error while maintaining an advantage over Monte Carlo-derived critical values with respect to type II error.</p>","abstract_has_math":false,"creators":["Lance, Michael"],"institution":null,"degree_name":"Ph.D.","degree_level":"Open Access Dissertation","degree_discipline":"Education Evaluation and Research","degree_department":null,"school":null,"contributors":["Shlomo Sawilowsky"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T05:58:42Z","subjects":["robustness","t-test","type I error","type II error","winsorize","Educational Assessment, Evaluation, and Research","Psychology","Statistics and Probability"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wayne.edu/oa_dissertations/173","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Shlomo Sawilowsky"]},{"key":"dc:creator","label":"Author","values":["Lance, Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2011-01-04T08:00:00Z"]},{"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":["robustness","t-test","type I error","type II error","winsorize","Educational Assessment, Evaluation, and Research","Psychology","Statistics and Probability"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wayne.edu/oa_dissertations/173"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Historically, it has been accepted practice for critical values for the Winsorized t test for independent samples to be based on adjusted degrees of freedom depending on the number of total non-Winsorized (approximate) values. Recently, a new such table of Winsorized critical values has been developed via approximate randomization by Monte Carlo simulation.
Based on eight common data distributions estimated from Psychology and Education along with the normal and five Mathematical distributions, these two tables of values were compared with respect to robustness to types I and II errors through Monte Carlo simulations for one and 10% Winsorized values per end.
20% Winsorized results were generally non-robust for approximate critical values and mixed for Monte Carlo-derived critical values. With one Winsorized value per end, for small samples, type I error results generally support the use of the newly-developed table of Monte Carlo-derived critical values over the approximate critical values. For larger samples (one Winsorized value per end), approximate critical values become increasingly robust (in most cases, stringently-so for samples of 90 or more) to type I error while maintaining an advantage over Monte Carlo-derived critical values with respect to type II error.
"]},{"key":"dc:title","label":"Title","values":["Approximate Vs. Monte Carlo Critical Values For The Winsorized T-Test"]}]}],"canonical_facts":{"dc:contributor":["Shlomo Sawilowsky"],"dc:creator":["Lance, Michael"],"dc:date.available":["2011-01-04T08:00:00Z"],"dc:description.abstract":["Historically, it has been accepted practice for critical values for the Winsorized t test for independent samples to be based on adjusted degrees of freedom depending on the number of total non-Winsorized (approximate) values. Recently, a new such table of Winsorized critical values has been developed via approximate randomization by Monte Carlo simulation.
Based on eight common data distributions estimated from Psychology and Education along with the normal and five Mathematical distributions, these two tables of values were compared with respect to robustness to types I and II errors through Monte Carlo simulations for one and 10% Winsorized values per end.
20% Winsorized results were generally non-robust for approximate critical values and mixed for Monte Carlo-derived critical values. With one Winsorized value per end, for small samples, type I error results generally support the use of the newly-developed table of Monte Carlo-derived critical values over the approximate critical values. For larger samples (one Winsorized value per end), approximate critical values become increasingly robust (in most cases, stringently-so for samples of 90 or more) to type I error while maintaining an advantage over Monte Carlo-derived critical values with respect to type II error.
"],"dc:identifier":["https://digitalcommons.wayne.edu/oa_dissertations/173"],"dc:subject":["robustness","t-test","type I error","type II error","winsorize","Educational Assessment, Evaluation, and Research","Psychology","Statistics and Probability"],"dc:title":["Approximate Vs. Monte Carlo Critical Values For The Winsorized T-Test"],"thesis:degree_discipline":["Education Evaluation and Research"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T05:58:42Z"}