{"id":{"repo_id":"byu","oai_identifier":"oai:scholarsarchive.byu.edu:etd-1690"},"canonical_url":"https://search.dev.ndltd.org/etd/byu/oai:scholarsarchive.byu.edu:etd-1690","repository":{"repo_id":"byu","name":"Brigham Young University","base_url":"https://scholarsarchive.byu.edu/do/oai/"},"display":{"title":"Modeling Distributions of Test Scores with Mixtures of Beta Distributions","abstract":"Test score distributions are used to make important instructional decisions about students. The test scores usually do not follow a normal distribution. In some cases, the scores appear to follow a bimodal distribution that can be modeled with a mixture of beta distributions. This bimodality may be due different levels of students' ability. The purpose of this study was to develop and apply statistical techniques for fitting beta mixtures and detecting bimodality in test score distributions. Maximum likelihood and Bayesian methods were used to estimate the five parameters of the beta mixture distribution for scores in four quizzes in a cell biology class at Brigham Young University. The mixing proportion was examined to draw conclusions about bimodality. We were successful in fitting the beta mixture to the data, but the methods were only partially successful in detecting bimodality.","abstract_html":"Test score distributions are used to make important instructional decisions about students. The test scores usually do not follow a normal distribution. In some cases, the scores appear to follow a bimodal distribution that can be modeled with a mixture of beta distributions. This bimodality may be due different levels of students' ability. The purpose of this study was to develop and apply statistical techniques for fitting beta mixtures and detecting bimodality in test score distributions. Maximum likelihood and Bayesian methods were used to estimate the five parameters of the beta mixture distribution for scores in four quizzes in a cell biology class at Brigham Young University. The mixing proportion was examined to draw conclusions about bimodality. We were successful in fitting the beta mixture to the data, but the methods were only partially successful in detecting bimodality.","abstract_has_math":false,"creators":["Feng, Jingyu"],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:28:12Z","subjects":["mixture distribution","Beta mixture distribution","Bayesian","likelihood","Statistics and Probability"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/691","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Feng, Jingyu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2005-11-08T08:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Selected Project"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["mixture distribution","Beta mixture distribution","Bayesian","likelihood","Statistics and Probability"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/691","https://scholarsarchive.byu.edu/context/etd/article/1690/viewcontent/ETD_CISOPTR_511.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physical and Mathematical Sciences; Statistics"]},{"key":"dc:description.abstract","label":"Abstract","values":["Test score distributions are used to make important instructional decisions about students. The test scores usually do not follow a normal distribution. In some cases, the scores appear to follow a bimodal distribution that can be modeled with a mixture of beta distributions. This bimodality may be due different levels of students' ability. The purpose of this study was to develop and apply statistical techniques for fitting beta mixtures and detecting bimodality in test score distributions. Maximum likelihood and Bayesian methods were used to estimate the five parameters of the beta mixture distribution for scores in four quizzes in a cell biology class at Brigham Young University. The mixing proportion was examined to draw conclusions about bimodality. We were successful in fitting the beta mixture to the data, but the methods were only partially successful in detecting bimodality."]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["Modeling Distributions of Test Scores with Mixtures of Beta Distributions"]}]}],"canonical_facts":{"dc:creator":["Feng, Jingyu"],"dc:date":["2005-11-08T08:00:00Z"],"dc:description":["Physical and Mathematical Sciences; Statistics"],"dc:description.abstract":["Test score distributions are used to make important instructional decisions about students. The test scores usually do not follow a normal distribution. In some cases, the scores appear to follow a bimodal distribution that can be modeled with a mixture of beta distributions. This bimodality may be due different levels of students' ability. The purpose of this study was to develop and apply statistical techniques for fitting beta mixtures and detecting bimodality in test score distributions. Maximum likelihood and Bayesian methods were used to estimate the five parameters of the beta mixture distribution for scores in four quizzes in a cell biology class at Brigham Young University. The mixing proportion was examined to draw conclusions about bimodality. We were successful in fitting the beta mixture to the data, but the methods were only partially successful in detecting bimodality."],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/691","https://scholarsarchive.byu.edu/context/etd/article/1690/viewcontent/ETD_CISOPTR_511.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["mixture distribution","Beta mixture distribution","Bayesian","likelihood","Statistics and Probability"],"dc:title":["Modeling Distributions of Test Scores with Mixtures of Beta Distributions"],"dc:type":["Selected Project"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:28:12Z"}