Discriminating Value of Item and Test
The paper proposes methods of obtaining discriminating value of items and scale consisting of binary items and also for Likert items, from a single administration making no assumption of continuous nature of data or linearity or normality for the observed or the underlying variable being measured. Relationships derived between difficulty and discriminating values of binary items and test and relationship between test reliability and test discriminating value.
Discriminating value of Likert items and questionnaire were computed considering seven dissimilarity measures using the operations which are permissible for a Likert scale i.e. considering frequency or proportion for each cell of the Item- Response category matrix. Major features of the methods discussed and comparison of the proposed methods in terms of desired properties was undertaken. Condition for monotonically increasing was derived 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 and is recommended. Moreover, it is easy to estimate population CV and undertake other statistical inferences. Reliability as an association of two vectors and discrimination as a distance between the vectors showed a negative relationship.
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