| Summary: | 碩士 === 國立政治大學 === 應用數學系數學教學碩士在職專班 === 102 === The main purpose of this study is to compute the passing rate according to different capability values by using the Probability Generating Function Method presented in "A Statistical Analysis of Independent Items with Probability Structure" by C. C. Leu, 2008.
Therefore, we can find the difficulty index and the discrimination index of test problems based on the two-parameter logistic model in order to analyze the test quality. This method is more convenient and easier to use, because only the passing rate is needed to proceed.
We have randomly selected a sample of size 5000 on binary response data from the source file of the first 2009 Basic Competency Test for the junior high school students done by Research Center for Psychological and Educational Testing, National Taiwan Normal University; and computed the difficulty index and the discrimination index by using the classical non-parametric method, the classical parametric method, and two-parameter logistic model fitting method. Finally, we analyze the test quality and compare the results of three different methods.
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