The beta distribution is used in numerous real-world applications, including areas such as manufacturing (quality control) and analyzing patient outcomes in health care. It also plays a key role in statistical theory, including multivariate analysis of variance (MANOVA) and Bayesian statistics. It is a flexible distribution that can account for many different characteristics of real data. To our surprise, there has been very little work or discussion on performing statistical hypothesis testing for the mean when it is reasonable to assume that the population is beta distributed. Many analysts conduct traditional analyses using a t-test or nonparametric approach, try transformations, or use standard maximum likelihood-based approaches. We showed via simulations that these tools cannot appropriately control type I error rates for various situations. Additionally, this research has set out to construct a uniformly most powerful test using saddle point approximations. These approximations tend to have better accuracy than traditional likelihood-based methods, even when sample sizes are quite low. We provide the necessary methodology development to perform the test. Further simulation studies on power of test are conducted to compare our new method to traditional approaches and illustrate the superiority of our test in many situations. We also provided recommendations on the best way to use this new approach.
","abstract_html":"<p>The beta distribution is used in numerous real-world applications, including areas such as manufacturing (quality control) and analyzing patient outcomes in health care. It also plays a key role in statistical theory, including multivariate analysis of variance (MANOVA) and Bayesian statistics. It is a flexible distribution that can account for many different characteristics of real data. To our surprise, there has been very little work or discussion on performing statistical hypothesis testing for the mean when it is reasonable to assume that the population is beta distributed. Many analysts conduct traditional analyses using a t-test or nonparametric approach, try transformations, or use standard maximum likelihood-based approaches. We showed via simulations that these tools cannot appropriately control type I error rates for various situations. Additionally, this research has set out to construct a uniformly most powerful test using saddle point approximations. These approximations tend to have better accuracy than traditional likelihood-based methods, even when sample sizes are quite low. We provide the necessary methodology development to perform the test. Further simulation studies on power of test are conducted to compare our new method to traditional approaches and illustrate the superiority of our test in many situations. We also provided recommendations on the best way to use this new approach.</p>","abstract_has_math":false,"creators":["Kyei, Richard Ntiamoah"],"institution":null,"degree_name":"Master of Science - Statistics","degree_level":"Thesis","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":["Jacob Turner, Ph.D.","Robert Henderson, Ph.D.","Jonathan Mitchell, Ph.D."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-08-01T07:00:00Z","date_published":"2024-08-01T07:00:00Z","updated_at":"2026-07-24T04:30:45Z","subjects":["Statistical inference","Mean of beta distribution","Saddlepoint Approximation","Inference on the mean of beta distribution","Uniformly most powerful test","UMP test","Applied Statistics","Mathematics","Other Physical Sciences and Mathematics","Other Statistics and Probability","Statistical Methodology","Statistical Theory","Statistics and Probability"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.sfasu.edu/etds/565","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jacob Turner, Ph.D.","Robert Henderson, Ph.D.","Jonathan Mitchell, Ph.D."]},{"key":"dc:creator","label":"Author","values":["Kyei, Richard Ntiamoah"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2024-08-07T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science - Statistics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Statistical inference","Mean of beta distribution","Saddlepoint Approximation","Inference on the mean of beta distribution","Uniformly most powerful test","UMP test","Applied Statistics","Mathematics","Other Physical Sciences and Mathematics","Other Statistics and Probability","Statistical Methodology","Statistical Theory","Statistics and Probability"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.sfasu.edu/etds/565"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The beta distribution is used in numerous real-world applications, including areas such as manufacturing (quality control) and analyzing patient outcomes in health care. It also plays a key role in statistical theory, including multivariate analysis of variance (MANOVA) and Bayesian statistics. It is a flexible distribution that can account for many different characteristics of real data. To our surprise, there has been very little work or discussion on performing statistical hypothesis testing for the mean when it is reasonable to assume that the population is beta distributed. Many analysts conduct traditional analyses using a t-test or nonparametric approach, try transformations, or use standard maximum likelihood-based approaches. We showed via simulations that these tools cannot appropriately control type I error rates for various situations. Additionally, this research has set out to construct a uniformly most powerful test using saddle point approximations. These approximations tend to have better accuracy than traditional likelihood-based methods, even when sample sizes are quite low. We provide the necessary methodology development to perform the test. Further simulation studies on power of test are conducted to compare our new method to traditional approaches and illustrate the superiority of our test in many situations. We also provided recommendations on the best way to use this new approach.
"]},{"key":"dc:title","label":"Title","values":["A UNIFORMLY MOST POWERFUL TEST FOR THE MEAN OF A BETA DISTRIBUTION"]}]}],"canonical_facts":{"dc:contributor":["Jacob Turner, Ph.D.","Robert Henderson, Ph.D.","Jonathan Mitchell, Ph.D."],"dc:creator":["Kyei, Richard Ntiamoah"],"dc:date.available":["2024-08-07T07:00:00Z"],"dc:description.abstract":["The beta distribution is used in numerous real-world applications, including areas such as manufacturing (quality control) and analyzing patient outcomes in health care. It also plays a key role in statistical theory, including multivariate analysis of variance (MANOVA) and Bayesian statistics. It is a flexible distribution that can account for many different characteristics of real data. To our surprise, there has been very little work or discussion on performing statistical hypothesis testing for the mean when it is reasonable to assume that the population is beta distributed. Many analysts conduct traditional analyses using a t-test or nonparametric approach, try transformations, or use standard maximum likelihood-based approaches. We showed via simulations that these tools cannot appropriately control type I error rates for various situations. Additionally, this research has set out to construct a uniformly most powerful test using saddle point approximations. These approximations tend to have better accuracy than traditional likelihood-based methods, even when sample sizes are quite low. We provide the necessary methodology development to perform the test. Further simulation studies on power of test are conducted to compare our new method to traditional approaches and illustrate the superiority of our test in many situations. We also provided recommendations on the best way to use this new approach.
"],"dc:identifier":["https://scholarworks.sfasu.edu/etds/565"],"dc:subject":["Statistical inference","Mean of beta distribution","Saddlepoint Approximation","Inference on the mean of beta distribution","Uniformly most powerful test","UMP test","Applied Statistics","Mathematics","Other Physical Sciences and Mathematics","Other Statistics and Probability","Statistical Methodology","Statistical Theory","Statistics and Probability"],"dc:title":["A UNIFORMLY MOST POWERFUL TEST FOR THE MEAN OF A BETA DISTRIBUTION"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science - Statistics"]},"updated_at":"2026-07-24T04:30:45Z"}