| Summary: | 碩士 === 國立彰化師範大學 === 數學系所 === 93 === Number-correct raw scores of the Basic Competence Test for Junior High School Students (BC test) are transformed into scale scores to stabilize measurement error variability. This study examined four density estimation methods applied to the raw-to-scale score transformations of BC test. Four-parameter beta compound binomial model, extended beta-binomial model, item response model and kernel smoothing were utilized to 50 replications of random samples of 5,000 from 2002, 2003 and 2004 examinees' populations. The performance of each estimation technique was carefully investigated by criteria including bias, variance, and mean square error. It is concluded that the four-parameter beta compound binomial model produced the most accurate estimates. Suggestions for further research are also provided.
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