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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.

Orientador: Prof. Dr. Daniel Miranda Machado / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional - PROFMAT, Santo André, 2017. / Um dos objetivos desse trabalho é explicar a Teoria de Resposta ao Item, conhecida como TRI, enfatizando o modelo logístico de três parâmetros e descrevendo suas principais características. Outro objetivo é mostrar como o professor pode utilizar ferramentas estatísticas, em uma planilha eletrônica, para: verificar a qualidade das questões que compõe sua prova; analisar se existe uma correlação entre dois instrumentos de avaliação; utilizar a média escolar de um aluno para inferir sobre o seu desempenho no vestibular; entre outras possibilidades. Com a finalidade de explicar a TRI e seu método de estimação de parâmetros por Máxima Verossimilhança, são apresentados previamente os modelos Matemáticos, Probabilísticos e Estatísticos, pilares dessa teoria. Além disso, é descrito como os programas de avaliações educacionais em larga escala de diversos países utilizam a TRI para monitorar o desempenho de seus sistemas educacionais. Em seguida, são expostas algumas ferramentas Estatísticas, em específico, o coeficiente de correlação, o método de mínimos quadrados e o ponto bisserial que podem colaborar nos processos de avaliações educacionais que fazem parte da rotina escolar. São ilustrados também exemplos de planilhas eletrônicas com a descrição passo a passo de sua construção e dos comandos utilizados. Desse modo, espera-se contribuir para compreensão da TRI e, consequentemente, dos indicativos educacionais produzidos pelos programas de avaliações em larga escala, bem como, para atuação e reflexão da prática docente em seus métodos de avaliação educacional. / One of the goals of this work is to explain Item Response Theory, known as IRT, emphasizing the Three-Parameter Logistic model and describing its main characteristics. Another objective is to demonstrate how educators can use statistical tools within a spreadsheet to: verify the quality and reliability of test questions; examine whether there is a correlation between two assessment tools; use the school average of a student to predict his or her performance in entrance examinations; among other possibilities. To explain IRT and its method of parameter estimation by maximum likelihood, this work presents the mathematical, probabilistic and statistical models that are the pillars of the theory. It also describes how the large-scale educational assessment programs of various countries use IRT to monitor the performance of their education systems. Then, this work presents a selection of statistical tools, specifically, the correlation coefficient, the least squares method and the point biserial correlation, which could contribute to the process of routine educational assessments. Also provided are illustrated examples of spreadsheets with step-by- step descriptions of their creation and the commands used. Thus, the work hopes to contribute to the understanding of IRT and, consequently, of the educational indicators produced by large-scale assessment programs, as well as benefit educators in their practice and reflection on methods of educational evaluation.