A maximum test using the parametric dependent samples t-test and the non-parametric Wilcoxon sign rank test was created using a FORTRAN program and various subroutines of the International Mathematical and Statistical Libraries (IMSL, 1980). Two tailed critical values were derived from a mixed normal distribution. Critical values obtained were at the 0.05, 0.025, 0.01 and 0.005 alpha levels via sample sizes (n) 8 through 30, 45, 60, 90 and 120. Critical values were compared to values obtained through the application of the Bonferroni correction method. It was concluded that the Bonferroni is an unnecessary method. Findings of the study are tremendously important for the field inferential statistics. The maximum test is known to restrain Type I error to nominal alpha. The maximum test as created in this study not only rids the problems encountered when choosing one test of significance over another but it also allows a researcher to obtain and interpret results without the concern for Type I error inflation.
","abstract_html":"<p>A maximum test using the parametric dependent samples t-test and the non-parametric Wilcoxon sign rank test was created using a FORTRAN program and various subroutines of the International Mathematical and Statistical Libraries (IMSL, 1980). Two tailed critical values were derived from a mixed normal distribution. Critical values obtained were at the 0.05, 0.025, 0.01 and 0.005 alpha levels via sample sizes (n) 8 through 30, 45, 60, 90 and 120. Critical values were compared to values obtained through the application of the Bonferroni correction method. It was concluded that the Bonferroni is an unnecessary method. Findings of the study are tremendously important for the field inferential statistics. The maximum test is known to restrain Type I error to nominal alpha. The maximum test as created in this study not only rids the problems encountered when choosing one test of significance over another but it also allows a researcher to obtain and interpret results without the concern for Type I error inflation.</p>","abstract_has_math":false,"creators":["Maggio, Saverpierre"],"institution":null,"degree_name":"Ph.D.","degree_level":"Open Access Dissertation","degree_discipline":"Education Evaluation and Research","degree_department":null,"school":null,"contributors":["Dr. Sholmo S. Sawilowsky"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-01-01T08:00:00Z","date_published":"2012-01-01T08:00:00Z","updated_at":"2026-07-24T05:59:11Z","subjects":["applied statistics, Bonferroni, dependent t-test, Maximum test, mixed normal distribution, Wilcoxon sign rank test","Educational Assessment, Evaluation, and Research","Quantitative Psychology","Statistics and Probability"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wayne.edu/oa_dissertations/574","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. Sholmo S. Sawilowsky"]},{"key":"dc:creator","label":"Author","values":["Maggio, Saverpierre"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2012-01-01T08:00:00Z"]},{"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":["applied statistics, Bonferroni, dependent t-test, Maximum test, mixed normal distribution, Wilcoxon sign rank test","Educational Assessment, Evaluation, and Research","Quantitative Psychology","Statistics and Probability"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wayne.edu/oa_dissertations/574"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A maximum test using the parametric dependent samples t-test and the non-parametric Wilcoxon sign rank test was created using a FORTRAN program and various subroutines of the International Mathematical and Statistical Libraries (IMSL, 1980). Two tailed critical values were derived from a mixed normal distribution. Critical values obtained were at the 0.05, 0.025, 0.01 and 0.005 alpha levels via sample sizes (n) 8 through 30, 45, 60, 90 and 120. Critical values were compared to values obtained through the application of the Bonferroni correction method. It was concluded that the Bonferroni is an unnecessary method. Findings of the study are tremendously important for the field inferential statistics. The maximum test is known to restrain Type I error to nominal alpha. The maximum test as created in this study not only rids the problems encountered when choosing one test of significance over another but it also allows a researcher to obtain and interpret results without the concern for Type I error inflation.
"]},{"key":"dc:title","label":"Title","values":["The dependent samples t and wilcoxon sign rank maximum test"]}]}],"canonical_facts":{"dc:contributor":["Dr. Sholmo S. Sawilowsky"],"dc:creator":["Maggio, Saverpierre"],"dc:date.available":["2012-01-01T08:00:00Z"],"dc:description.abstract":["A maximum test using the parametric dependent samples t-test and the non-parametric Wilcoxon sign rank test was created using a FORTRAN program and various subroutines of the International Mathematical and Statistical Libraries (IMSL, 1980). Two tailed critical values were derived from a mixed normal distribution. Critical values obtained were at the 0.05, 0.025, 0.01 and 0.005 alpha levels via sample sizes (n) 8 through 30, 45, 60, 90 and 120. Critical values were compared to values obtained through the application of the Bonferroni correction method. It was concluded that the Bonferroni is an unnecessary method. Findings of the study are tremendously important for the field inferential statistics. The maximum test is known to restrain Type I error to nominal alpha. The maximum test as created in this study not only rids the problems encountered when choosing one test of significance over another but it also allows a researcher to obtain and interpret results without the concern for Type I error inflation.
"],"dc:identifier":["https://digitalcommons.wayne.edu/oa_dissertations/574"],"dc:subject":["applied statistics, Bonferroni, dependent t-test, Maximum test, mixed normal distribution, Wilcoxon sign rank test","Educational Assessment, Evaluation, and Research","Quantitative Psychology","Statistics and Probability"],"dc:title":["The dependent samples t and wilcoxon sign rank maximum test"],"thesis:degree_discipline":["Education Evaluation and Research"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T05:59:11Z"}