以相關係數探討題組型試題之鑑別度

Abstract

題組題是依據所提供之新情境和資料作答的試題類型，它能測量到學生的理解、應用、分析或評鑑能力，一般來說，同一題組內各子題有某種程度的關聯性。由於題組題是近幾年國民中學基本學力測驗常見的試題類型，且目前各種鑑別度定義僅針對單一試題作鑑別度分析，若將其應用在分析題組型試題鑑別度時，除了無法計算題組本身的鑑別度之外，甚至會忽略題組內各子題之間的關聯性。此外，目前題組鑑別度的相關研究並不多，故本論文以複相關係數的觀點探討其鑑別度，提供新的研究方向。本文先分析獨立型試題鑑別度，並將其研究結果拓展至題組型試題。對於獨立型試題，本文驗證了以點二系列相關為定義的鑑別度是以相關係數為定義的鑑別度之特例。對於題組型試題，在蒐集測驗結果資料後，本文運用迴歸分析的技巧計算「題組本身」鑑別度，同時，為了探求在排除同一題組內前面各子題影響力後的子題鑑別度對於該題組鑑別度的貢獻程度，故本文提出「淨得分」與「淨鑑別度」的新概念，並發現題組鑑別度與各子題淨鑑別度之間有密切的關聯性；再者，本文亦提供了檢定各子題淨鑑別度是否顯著的統計方法。最後，以99年第一次國中基測英語科試題為例，利用本文研究結果計算其獨立型試題鑑別度以及題組試題之題組鑑別度、各子題鑑別度與各子題淨鑑別度，並與其它有關試題鑑別度的研究作比較與分析。

For testlet, it is answered by the provided new situation and information, can measure the student’s understanding, application, analysis and judging ability. Generally speaking, a relation exists in each item within testlet. In the recent years, testlet is an usual type in the Basic Competence Test for Junior High School. Moreover, current all definitions of discrimination index are only focusing on the single item. When these definitions are applied to analyze the discrimination index of testlet directly, not only the discrimination index of testlet can not be calculated but the relation between items within testlet will be neglected. Furthermore, due to the lack of the discrimination index study on testlet, this thesis investigates the discrimination index of testlet by regression analysis with the view point of multiple correlation coefficient and provides a new direction for the following study. This thesis is investigating the discrimination index of independent items, and this result is applied to testlet. For individual items, this study proves that point-biserial correlation is a special case of correlation coefficient. For testlet, after data collection, this study calculates the discrimination index of testlet itself by regression analysis. In the meantime, for investigating the contribution of the discrimination index of testlet of item within testlet which is getting rid of the influence of the previous items in the same testlet, this study proposes a new concept of “net score” and “net discrimination”. First, this study finds the close relation between the discrimination index of testlet and item within testlet. Second, this study states how to find the “net” discrimination index of item within testlet is remarkable or not by statistics. Finally, this study takes the English test items of the First Basic Competence Test for Junior High School Students in 2010 as example to calculate their discrimination index of individual item, testlet, item with testlet, and the net discrimination index of item within testlet, separately, by the deduced formula. A comparison and analysis between this and related study also have been taken into process in this study.