模糊統計在試題難度上的應用

Applying of Fuzzy Statistics in Item Difficulty

試題難度評量一直是許多人研究的課題。但傳統方法的五點量表問卷只提供固定尺度的選擇，似乎無法完整地表達受測者真實且複雜的思考。因此本研究將以模糊統計的角度進行試題難度的探討。過去許多研究應用模糊平均數、模糊眾數或模糊中位數等概念於試題難度評量。而本文將以此為基礎，定義一種新的距離，再透過一些轉換取得試題的難度指標，進而比較各試題之間難度的差異。本研究的另一個重點，是各個不同難度因子的向度來決定各試題的難度。再以模糊相對權重的概念，對各向度的難度指標作加權，進而比較、分析。在此研究中，模糊難度的數值，和IRT 的難度b 值與試題通過率P 值之相關達到一定水準。代表此方法所得出的結果，已有相當程度的驗證。

The traditional method of using the Likert scale in questionnaires provides researchers with information of fixed scale choices, which does not allow participants fully express their candid and complex thinking. The current paper applies fuzzy statistics to examine item difficulty of questionnaires. Concepts such as fuzzy mean, fuzzy mode or fuzzy median are applied. Based on the conceptions of fuzzy statistics, we try to define a new distance, which was transformed to obtain an item difficulty index that allows the comparisons between test items. Another focus of this paper is to determine the difficulty level of test items by examining various dimensions of difficulty factors. The weights of the dimensions of the item difficulty were compared and analyzed with the concept of fuzzy relative weight. The fuzzy difficulty index derived from this study shows promising features that is highly correlated with traditional difficulty indices.