Assessment of Item and Test parameters: Cosine Similarity Approach

Abstract

The paper proposes new measures of difficulty and discriminating values of binary items and test consisting of such items and find their relationships including estimation of test error variance and thereby the test reliability, as per definition  using cosine similarities. The measures use entire data. Difficulty value of test and item is defined as function of cosine of the angle between the observed score vector and the maximum possible score vector. Discriminating value of test and an item are taken as coefficient of variation (CV) of test score and item score respectively. Each ranges between 0 and 1 like difficulty value of test and an item. With increase in number of  correct answer to an item, item difficulty curve increases and item discriminating curve decreases. The point of intersection of the two curves can be used for item deletion along with other criteria. Cronbach alpha was expressed and computed in terms of discriminating value of test and item.  Relationship derived between test discriminating value   and test reliability as per theoretical definition. Empirical verifications of proposed measures were undertaken. Future studies suggested.re to enter text.