Cosine similarity approaches to reliability of likert scale and items /

Abstract

Based on cosine similarities, the paper proposes two non-parametric methods of finding reliability of Likert items and Likert scale from single administration of the questionnaire, considering only the frequency or proportion for each cell of the Item-Response category matrix without involving any assumptions of continuous nature or linearity or normality for the observed variables or the underlying variable being measured. Each method enables to find reliability irrespective of distribution of the observed or underlying variables and avoiding test of uni-dimensionality or assumption of normality for Cronbach's alpha or bivariate normality for polychoric correlations. The proposed methods thus are considered as improvement over the existing ones. Reliability as per Bhattacharyya's measure appears to be preferred over the Angular Association method as the former expresses test reliability as a function of item reliabilities. In addition to offering the computational steps, empirical verification with real data is given to illustrate the concepts and usefulness of the proposed non-parametric reliability procedures.