政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/94848

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/94848

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/94848

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/94848

Title:	機率架構下獨立型試題之統計分析 A Statistical Analysis of Independent Items with Probability Structure
Authors:	呂金川
Contributors:	宋傳欽呂金川
Keywords:	獨立型試題難度值鑑別度值
Date:	2008
Issue Date:	2016-05-09 11:58:23 (UTC+8)
Abstract:	賦予獨立型試題一適當機率架構，在古典測驗理論的概念下，探討試題難度與鑑別度之計算公式，並以九十六學年度第二次國中基本學力測驗數學科試題為例說明;同時將獲得結果與傳統計算方式之結果相互比較，嘗試發掘兩者間的差異及其形成原因。關鍵詞 : 獨立型試題、難度值、鑑別度值 Modeling independent items with a probability structure , we investigate the computational formula of difficulty index and that of discrimination index. Data taken from the Mathematics Test Items of the Second Basic Competence Test for Junior High School Students in 2007 are used for empirical verification and the result is compared with that obtained by the traditional method. Discrepancies between these two methods are also discussed in this study. keyword: independent items, difficulty index, discrimination index 謝辭 i 英文摘要 ii 中文摘要 iii 1 緒論 1 1.1 前言 1 1.2 研究動機 2 1.3 研究內容及架構 2 2文獻探討 3 2.1測驗理論發展 3 2.2古典試題分析理論 5 2.3傳統模式範例 9 2.4選擇題試題 11 3 試題難度與鑑別度之探討 12 3.1機率架構之基本假設 12 3.2答對題數的機率分配 13 3.3難度與鑑別度計算公式之推導 17 3.4未知參數之估計 20 3.5操作程序 21 4 實例分析 22 4.1範例操作 22 4.2基測數學科試題分析 25 5 兩模式之比較 27 5.1差異性探討 27 5.2差異性成因 32. 6 總結 38. 7 附錄 39. 7.1附錄一、答對題數機率分配之推導 39. 7.2附錄二、不含某特定題之答對題數的機率分配的推導 41. 7.3附錄三、TESTER For Windows 程式 2.0 版軟體執行檔 43 7.4附錄四、Mathematica5軟體執行檔整理 53
Reference:	【1】余民寧（1991），試題反應理論的介紹-測驗理論的發展趨勢(一)，研習資訊雙月刊，8卷6期，13-18頁。【2】余民寧（2002），教育測驗與評量-成就測驗與教學評量（第二版），心理出版社，台北市。【3】林光賢、劉明郎（2006），機率導論，華泰文化書局，台北市。【4】洪維恩（2006），Mathematica5數學運算大師，旗標出版股份有限公司，台北市。【5】陳英豪、吳裕益（1190），測驗與評量，復文圖書出版社，台北市。【6】黃義雄（2005），機率與統計，五南圖書出版社，台北市。【7】楊明宗（2005），應用統計學，華泰文化書局，台北市。【8】顏月珠（2001），應用數理統計學，三民書局，台北市。【9】Arnold S. F. (1990), Mathematical Statistics, Prentice-Hall International Inc, New Jersey. 【10】Rohatgi V. K. (1976), An Introduction to Probability Theory and Mathematical Statistics, Wiley, New York.
Description:	碩士國立政治大學應用數學系 94972007
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0094972007
Data Type:	thesis
Appears in Collections:	[Department of Mathematical Sciences] Theses

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