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| Title: | 非固定權重因子之試題難易度模糊統計評估
Fuzzy statistical evaluation with non-fixed weighted factors in the item difficult parameter |
| Authors: | 許家源 |
| Contributors: | 吳柏林
許家源 |
| Keywords: | 難易度預估
模糊統計
數學試題
無母體數檢定
Difficult forecast
Fuzzy Statistics
Mathematics question
Nonparametric Tests |
| Date: | 2010 |
| Issue Date: | 2013-09-04 15:17:52 (UTC+8) |
| 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。
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.
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. |
| Reference: | [1] 吳柏林(2005)，模糊統計導論：方法與應用，臺北：五南。
[2] 吳柏林(2002)，現代統計學，臺北：全程。
[3] 吳柏林、曾能芳(1998)，模糊回歸參數估計及在景氣對策信號之分析應用，中國統計學報，36(4)，399-420。
[4] 吳柏林、楊文山(1997)，模糊統計在社會調查分析的應用，社會科學計量方法發展與應用，楊文山主編：中央研究院中山人文社會科學研究所，289-316。
[5] 李白飛、林福來、林光賢(1994)。大學入學考試數學科試題分析與命題研究(三)。大學入學考試中心。
[6] 黃仁德、吳柏林(1995)，臺灣短期貨幣需求函數穩定性的檢定，模糊時間數列方法之應用，臺灣經濟學會年會論文集，169-190。
[7] Dubois, D. and Prade, H. (1991), Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions, Fuzzy Sets and Systems, 40, 143-202.
[8] Lowen, R. (1990), A fuzzy language interpolation theorem. Fuzzy Sets and Systems, 34, 33-38.
[9] Ruspini, E. (1991), Approximate Reasoning: past, present, future. Information Sciences, 57, 297-317.
[10] Tseng, T. and Klein, C. (1992), A new Algorithm for fuzzy multicriteria decision making. International Journal of Approximate Reasoning, 6, 45-66.
[11] Zadeh, L. A. (1965), Fuzzy Sets. Information and Control, 8, 338-353.
[12] Zimmermann, H. J. (1991), Fuzzy Sets Theory and Its Applications. Boston: Kluwer Academic. |
| Description: | 碩士
國立政治大學
應用數學系數學教學碩士在職專班
96972015
99 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0969720151 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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| 015101.pdf | | 931Kb | Adobe PDF2 | 425 | View/Open |
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