A new method is given for testing if there is a difference between two population proportions. The size of the test is exact in the sense that it is the maximum probability of rejecting a true null hypothesis. A method is given for determining a greatest lower bound on the power of the test over a region in which the difference in the two population proportions is at least a given value between zero and one. A specified greatest lower bound for the power by the researcher is used to determine the minimum total sample size needed. A comparison is made with a commonly used approximation method. We demonstrate that the actual size of the test for the approximation method is greater than the specified size while our new method has a size of no more the specified size. Further, the recommended method for determining the minimum total sample size for the approximation method is, in general, greater than what is needed by our new test. Some examples are given.
","abstract_html":"<p>A new method is given for testing if there is a difference between two population proportions. The size of the test is exact in the sense that it is the maximum probability of rejecting a true null hypothesis. A method is given for determining a greatest lower bound on the power of the test over a region in which the difference in the two population proportions is at least a given value between zero and one. A specified greatest lower bound for the power by the researcher is used to determine the minimum total sample size needed. A comparison is made with a commonly used approximation method. We demonstrate that the actual size of the test for the approximation method is greater than the specified size while our new method has a size of no more the specified size. Further, the recommended method for determining the minimum total sample size for the approximation method is, in general, greater than what is needed by our new test. Some examples are given.</p>","abstract_has_math":false,"creators":["Zhang, Yiran"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (restricted to Georgia Southern)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Andrew V. Sills","Broderick O. Oluyede"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:28:00Z","subjects":["ETD","Population Proportions","Size","Power","Comparisons","Statistical Methodology","Statistics and Probability"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1140","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Andrew V. Sills","Broderick O. Oluyede"]},{"key":"dc:creator","label":"Author","values":["Zhang, Yiran"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-07-03T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (restricted to Georgia Southern)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Population Proportions","Size","Power","Comparisons","Statistical Methodology","Statistics and Probability"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1140"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A new method is given for testing if there is a difference between two population proportions. The size of the test is exact in the sense that it is the maximum probability of rejecting a true null hypothesis. A method is given for determining a greatest lower bound on the power of the test over a region in which the difference in the two population proportions is at least a given value between zero and one. A specified greatest lower bound for the power by the researcher is used to determine the minimum total sample size needed. A comparison is made with a commonly used approximation method. We demonstrate that the actual size of the test for the approximation method is greater than the specified size while our new method has a size of no more the specified size. Further, the recommended method for determining the minimum total sample size for the approximation method is, in general, greater than what is needed by our new test. Some examples are given.
"]},{"key":"dc:title","label":"Title","values":["Test of Significance about Two Population Proportions"]}]}],"canonical_facts":{"dc:contributor":["Andrew V. Sills","Broderick O. Oluyede"],"dc:creator":["Zhang, Yiran"],"dc:date.available":["2019-07-03T07:00:00Z"],"dc:description.abstract":["A new method is given for testing if there is a difference between two population proportions. The size of the test is exact in the sense that it is the maximum probability of rejecting a true null hypothesis. A method is given for determining a greatest lower bound on the power of the test over a region in which the difference in the two population proportions is at least a given value between zero and one. A specified greatest lower bound for the power by the researcher is used to determine the minimum total sample size needed. A comparison is made with a commonly used approximation method. We demonstrate that the actual size of the test for the approximation method is greater than the specified size while our new method has a size of no more the specified size. Further, the recommended method for determining the minimum total sample size for the approximation method is, in general, greater than what is needed by our new test. Some examples are given.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1140"],"dc:subject":["ETD","Population Proportions","Size","Power","Comparisons","Statistical Methodology","Statistics and Probability"],"dc:title":["Test of Significance about Two Population Proportions"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (restricted to Georgia Southern)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:28:00Z"}