DIF分析在小樣本情境中的效果—以視障生和普通生在國中基測數學科之DIF為例

Abstract

本研究目的在於探討焦點組一百人的情況下偵測DIF的偵測效果，希望能了解增加參照組人數、調整能力分組組數等策略是否能提升偵測效果。本研究共分為三個部分，研究一和研究二為模擬研究，研究三為利用實證資料進行DIF分析。研究一的主要目的在於了解能力分組組數對於檢測效果的影響，依變項為DIF的正確偵測率和第一類型錯誤率。研究二的主要目的在於了解使用不同偵測DIF方法時調整樣本人數比例對於偵測效果的影響，依變項與研究一同。研究三參考研究一和研究二的結果對於九十四年和九十五年第一次國中基測數學科普通生和視障生的實際作答反應進行DIF分析。研究一結果顯示，在焦點組一百人且能力有差異的情況下，能力分組組數以兩組的結果最能夠兼顧正確偵測率和第一類型錯誤率，此組數即被研究二所採用。研究二結果顯示，在焦點組一百人的情況下，樣本人數比例和能力差異是影響偵測效果的主要因素；在焦點組五百人的情況下，方法和試題DIF比率是影響偵測效果的主要因素；若控制在能力有差異的情況下，對於焦點組人數較少（如一百人時）時採用MH-2搭配樣本人數100/1000（焦點組/參照組）的組合具有較佳效能，可以達到正確偵測率0.703、第一類型錯誤率0.073的結果。研究三結果顯示，九十四年和九十五年第一次國中基測數學科當中各有兩題、一題產生DIF，並對於可能原因進一步予以解釋。

The purpose of the research is to explore the efficiency of DIF detection when the sample size of focal group is small.. There are three parts in the research; Study 1 and Study 2 are simulation studies and Study 3 is an empirical study. The aim of Study 1 is to examine the efficiency of DIF detection of different score group width. The dependent variables are power and Type 1 error. The aim of Study 2 is to examine the efficiency of DIF detection in different methods and sample size ratio of reference and focal group. The dependent variables are the same as Study 1. Study 3 is an empirical study for detecting the DIF item between visual impaired and general students of the basic competence test for junior high school students（BCTEST）. The result of Study 1 suggest with two score group is better when focal group size is 100 and the ability distribution is unequal. The result of Study 2 suggest that the sample size ratio of reference and focal group and the difference of ability distribution affect the efficiency of DIF the most when focal group is 100. The method and DIF item percentage affect the efficiency of DIF the most when focal group is 500. When ability distribution is controlled unequal, MH-2 combined with 100/1000 can reach the DIF detecting power of 0.703 and type 1 error of 0.073. The result of Study 3 suggests there are two DIF items in 2005 BCTEST and one DIF item in 2006 BCTEST, and discussion about the reason of DIF is also provided in Study 3.