试题结构理论.doc

教學評量理論與實務講義(郭伯臣，July 1, 2004)試題結構理論Ordering Theory要獲得試題關聯結構圖最重要的便是需了解試題間的順序性，而目前Airasian & Bart的順序理論及竹谷 誠的試題關聯結構分析法是最常用來定義試題間順序性的二種方法。 for 其中表第s個學生答對試題i，表第s個學生答錯試題i表試題j答對人數的機率。表試題k答對人數的機率。表試題j答錯人數的機率。表試題k答錯人數的機率。表試題j與試題k均答對的機率。表試題j答錯且試題k答對的機率。表試題j答對且試題k答錯的機率。表試題j與試題k均答錯的機率。試題j試題k對1錯0合計對1錯0合計1依前節所舉的順序性的意義，可以知道若從試題j到試題k會產生完全的順序性時，不但表示試題j比試題k容易而且當發生時，意味著(0,1)不會發生。如在實際的資料中，欲產生從試題j到試題k的順序性，則希望(0,1)的形式發生少一點，亦即且為定數時，則有順序性的存在(Airasian & Bart, 1973; Bart & Krus, 1973)。此一順序性係數有一缺點，便是不能完全反映兩兩試題間的相關係數(Tatsuoka & Tatsuoka, 1981;竹谷 試, 1991;許天維,民84)。以下是設定在=0.04時所產生不合宜的三個實例：例1:試題k試題j對錯合計對0.450.050.50錯0.050.450.50合計0.500.501.00此例中，、皆0.04，所以兩個方向均無次序性，但仔細計算其相關係數，其結果高達0.80，這樣高的相關係數沒有次序性頗令人起疑。在此情況，如用竹谷 誠改良式的順序性公式，則有行試題j到擁題k與行試題k到試題j的順序性。例2:試題k試題j對錯合計對0.500.150.65錯0.050.300.35合計0.550.451.00此例中，、皆0.04，所以兩個方向均無次序性，但仔細計算其相關係數，其結果高達0.60，這樣高的相關係數沒有次序性頗令人起疑。在此情況，如用竹谷 誠改良式的順序性公式，則有行試題j到擁題k與行試題k到試題j的順序性。例3:試題k試題j對錯合計對0.030.470.50錯0.030.470.50合計0.060.941.00此例中，有試題j到試題k的次序性。但計算其相關係數，其結果為0，這樣的相關係數有次序性亦令人起疑。如用竹谷 誠改良式順序性公式，則得到沒有順序性的結果，應較為合理。If , then item j could be linked forwards to item k.概念結構圖試卷第1至21題解題所需概念題號分數連加型式通分進位約分1真+真2真+真3真+真4真+真5帶+真6假+真7假+帶8真+真9帶+真10帶+帶11真+真12真+真13真+真14帶+假15整+假+帶16帶+帶+帶17真+真+真18真+真+真19真+真+真20真+真+真21帶+真+帶貳、IRSP1及OTP1一、理論基礎IRSP1及OTP1是分別由竹谷 誠(1991)的試題關聯結構分析法(item relational structure analysis;簡稱IRS)及Airasian & Bart(1973)的順序理論(ordering theory;簡稱OT)，理論部分請參閱郭伯臣（民84）無參數試題反應理論與試題順序結構分析法之多點計分整合模式一文，而此二程式皆為郭伯臣及田聖才所開發，在本文中僅介紹IRSP1中IRS此一部分的功能及OTP1中OT此一部分的功能，有關IRS的理論及使用情況請參閱劉湘川、許天維、郭伯臣、胡豐榮（民83）。二、輸入資料檔格式IRSP1及OTP1目前只能處理二元計分的資料，進行分析時，需先製造二個檔，一個檔案其檔名必須為： *.dat，另一個檔案其檔名必須為：*.lse，其中表示研究者可自行命名的部分，但不得超過八個字，*.dat的檔案中分成二大部分，一為受試者基本資料，最多一行，另一部分為受試者各題的得分，各得分間須有空格或斷行來加以區隔：*.lse的檔案中通常只有二行，第一行為受試者人數，第二行為試題數。以下將以mmm.dat及mmm.lse為例進行做用說明。mmm.dat (30題，581位受試者) 其格式如下：2 1 001 1 第一位受試者基本資料描述（整行）各題的得分情形（題間有空格）1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 12 1 002 21 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 02 1 003 21 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 . .mmm.lse (30題，581位受試者) 其格式如下：581 受試者人數（第一行）30 試題數（第二行）三、使用方式當資料檔(*.dat)及格式檔(*.lse)建立完成時，可利用下列步驟來使程式進行分析：1.將可執行IRSP1及包含欲分析的資料檔和格式檔之磁片放入A磁碟機。2.鍵入A:cdirsp3.鍵入A:irspirsp1 ，此時則會出現下面的畫面：4.在command:之處鍵入irs5.按Enter後，則會出現下列畫面6.在依指示鍵入資料檔檔名(frac.dat)及格式檔檔名(frac.lse)7.鍵入Enter後，就會顯現出此一群體的試題關聯結構圖，而命令區則會出現此一資料檔的人數及試題數。8.接著在command:之處鍵入move Enter 後按左右方向鍵即可將圖形移動，移動至理想的位置後，再按一次Enter即可將圖形固定。9.同理在command:之處鍵入item Enter 後，電腦會問題號為何？鍵入題號後再按Enter後，即可由左右方向鍵將試題水平移動，移動至理想的位置後，再按一次Enter即可將圖形固定。10.固定後如欲繼續移動另一試題，則只要在輸入題號及Enter即可再移動。11.在command:之處鍵入delete Enter 後，電腦會問題號為何？鍵入題號後再按Enter後，即可將此一試題在螢幕上消除。亦可用add此一指令將消失的試題重新呈現。12.如欲繼續消除另一試題，則只要在輸入題號及Enter即可。而下圖是僅保留真分數加法有關的試題。13.可再利用item此一指令將試題移動至較易觀察的位置，如下圖所示。14.接著可用print此一指令將此圖印出，並用save此一指令將相關的結果檔加以儲存。15.亦可利用limit指令來改變閥值，減少或增加箭頭數。16.再利用delete及item二指令即可得到下圖，很明顯較閥值為0.5（內定值）時少了四個箭頭。17.最後當忘記目前的狀態時，可用status此一指令來察看。至於OTP1的使用則將irs的指令改為ot即可，詳細指令請見附錄。四、輸出檔案（ *.rec ）之內容（一）RJK.REC此一結果檔內容為試題j至k的關聯係數矩陣+1.000 +1.000 +1.000 +1.000 +1.000 +1.000 +1.000 +1.000 +1.000 +1.000 +1.000 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