An Information-Theoretic Alternative to the Cronbach's Alpha Coefficient of Item Reliability

TL;DR

This paper introduces an information-theoretic reliability measure based on entropy, suitable for nonnumeric response scales, offering advantages over Cronbach's alpha while maintaining similar tracking performance.

Contribution

It presents a novel entropy-based reliability index that is applicable to nonnumeric scales and offers advantages over traditional Cronbach's alpha.

Findings

The index tracks Cronbach's alpha uniformly.

It is suitable for nonnumeric response scales.

Offers advantages over existing reliability measures.

Abstract

We propose an information-theoretic alternative to the popular Cronbach alpha coefficient of reliability. Particularly suitable for contexts in which instruments are scored on a strictly nonnumeric scale, our proposed index is based on functions of the entropy of the distributions of defined on the sample space of responses. Our reliability index tracks the Cronbach alpha coefficient uniformly while offering several other advantages discussed in great details in this paper.