應用模糊統計於試題難易度評量

Abstract

試題難易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。因此本文將以模糊問卷調查進行試題難易度的探討。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易度評量。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易度指標，進而比較各試題之間難度的差異。本文的另一個重點，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，對各向度的難易度指標作加權，進而比較、分析。

Assessment for test difficulty have been the subject of many studies. The traditional method of a Likert scale questionnaire provides only a fixed scale choice, but it seems that we can’t fully express the real and complex thinking of respondents. Therefore, the thesis will apply fuzzy questionnaire to probe into test difficulty. Concepts such as Fuzzy mean, Fuzzy mode or Fuzzy median are applied in studies of assessment for test difficulty. The thesis will be based on these conceptions to define a new distance, and obtain the difficulty index of test through some conversion. Moreover, it will compare the differences of difficulty among test items. Another focus of this paper is to determine the difficulty of each item according to various dimensions of difficulty factors. Afterwards, the difficulty index of each dimension will be weighted, compared, and analyzed with the concept of fuzzy relative weight.