The Recursive Alpha (RAlph) Coefficients: Quantifying Inter-Item Cohesion under Indirect Range Restriction

Year: 2015       Vol.: 64       No.: 2      

Authors: Michael Van B. Supranes; John Francis J. Guntan; Joy Pauline Adrienne C. Padua; Joseph Ryan G. Lansangan

Abstract:

Range restriction is a known cause of underestimation in the Cronbach’s Alpha reliability coefficient. The estimate of the Cronbach’s Alpha is usually adjusted to minimize bias, but existing methods require information about the population. In the case of indirect range restriction however, such information may not be readily or intuitively available. A data-driven bootstrap-based estimator that requires minimal assumptions about the unrestricted population, called the Recursive Alpha (RAlph) coefficient, is therefore proposed. Based on the simulation studies, the two versions of the Ralph coefficient perform best when the information associated to the range restriction is strongly correlated with the characteristic being measured, and when the true reliability coefficient Alpha is high. Also, the RAlph coefficients are found to be effective in minimizing the error in estimating Alpha under strong presence of range restriction. Moreover, considerations on the length of the instrument, scale of the responses, and sample size aid in minimizing the error of the proposed coefficients. In support of the simulation results, an empirical study using behavioral data on social media users is carried out, and evidently, the RAlph coefficients are far better than the ordinary Cronbach’s Alpha estimate.

Keywords: Range Restriction, Adjusted Cronbach’s Alpha, Bootstrap Sampling

Download this article: