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Discriminating Value of Item and Test
Keywords
Discriminating value, K-L distance, Hellinger measure, Co-efficient of variation, Chi-square
Abstract
The paper proposes new measures of difficulty and discriminating values of binary items and also test consisting of such items. The measures consider length of two vectors and angle between them. Relationships between difficulty and discriminating values of items and test were derived including relationship between test reliability and test discriminating value. Quantitative evaluation of discriminating value of Likert item and questionnaire have been presented for seven dissimilarity measures which can be computed from a single administration of the questionnaire and using the permissible operations for a Likert scale i.e. considering only the frequency or proportion for each cell of the Item-Response category matrix. Important features of the methods discussed along with comparison of the proposed methods in terms of desired properties. Each proposed method is monotonic subject to satisfying specific condition which is different for different approaches. Theoretical derivation of condition for monotonically increasing was undertaken separately for each method. Based on theoretical advantages, measure based on CV appears to be best method for discriminating values of Likert items and scale. Both the conditions for zero discriminatory value of an item are satisfied by CV. Moreover, it is easy to estimate population CV and undertake other statistical inferences.