試題反應理論架構下之試題分析

Abstract

本文運用呂金川(2008)〝機率架構下獨立型試題之統計分析〞一文中的機率生成函數法，在各能力值(即學生答對總題數)下，計算特定試題的答對率，藉以產生配適試題反應理論中二參數邏輯式模型之數據資料，進而求出特定試題之難度與鑑別度值，據以評定特定試題之品質。本文所提方法的便利性是，在僅知各試題答對率的資訊下便可進行。\n\n我們也以古典測驗理論之無母數方法、母數方法以及本文中所提出試題反應理論之二參數邏輯式模型配適法，對國立台灣師範大學心理與教育測驗研究發展中心所提供5000筆98年第一次國中基本學力測驗數學科原始反應檔的資料，執行試題難度與鑑別度之計算，並對試題品質做分析，同時也比較各種方法所獲至結果的異同。

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.\nTherefore, 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.\nWe 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.