非固定權重因子之試題難易度模糊統計評估

Abstract

在試題難易度分析上，傳統方式常以答對率或得分率的高低來認定試題的難易度。但答對率或得分率高低並不能真正表達應試者在答題時的難易感受程度。過去研究指出影響數學科試題難易度的主要因素有三：評量的數學內容、解題時的思考策略及解題所需的步驟數。\n本論文針對影響數學科試題難易度的三個主要因素進行分析統計。以模糊統計的角度，提出非固定權重因子之二維模糊數。應用模糊數絕對距離的概念以摒除族群中異端值，最後針對不同族群進行難易指標分析與檢定。

On the basis of difficulty analysis, the hit rate or the scoring rate are considered as the index of the difficulty of the questions traditionally. However, these rates can not represent how test takers feel when taking tests. According to the previous papers on this subject, they note three factors to affect the difficulty analysis on math questions the content of the evaluation, the strategies of question solving, and the required steps to solve a question.\n This research is focused on the three major factors which influence the difficulty of math examinations. With the angle of fuzzy statistics, a two-dimension fuzzy number will be presented with non-fixed weighted factors. By applying the absolute distance concept of fuzzy number, the extreme values are excluded. Consequently, the indices of difficulty from different groups can be tested and analyzed.