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Full-Text Articles in Physical Sciences and Mathematics
Modeling Distributions Of Test Scores With Mixtures Of Beta Distributions, Jingyu Feng
Modeling Distributions Of Test Scores With Mixtures Of Beta Distributions, Jingyu Feng
Theses and Dissertations
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 …
Combining Predictors For Classification Using The Area Under The Roc Curve, Margaret S. Pepe, Tianxi Cai, Zheng Zhang, Gary M. Longton
Combining Predictors For Classification Using The Area Under The Roc Curve, Margaret S. Pepe, Tianxi Cai, Zheng Zhang, Gary M. Longton
UW Biostatistics Working Paper Series
No single biomarker for cancer is considered adequately sensitive and specific for cancer screening. It is expected that the results of multiple markers will need to be combined in order to yield adequately accurate classification. Typically the objective function that is optimized for combining markers is the likelihood function. In this paper we consider an alternative objective function -- the area under the empirical receiver operating characteristic curve (AUC). We note that it yields consistent estimates of parameters in a generalized linear model for the risk score but does not require specifying the link function. Like logistic regression it yields …