Results on the Standard Error of the Coefficient Alpha Index of Reliability

Abstract

In this research, we investigate the behavior of Cronbach's coefficient alpha and its new standard error. We systematically analyze the effects of sample size, scale length, strength of item intercorrelations, and scale dimensionality. We demonstrate the beneficial effects of sample size on alpha's standard error and of scale length and the strengths of item intercorrelations (effects that are substitutes in their benefits) on both alpha and its standard error. Our findings also speak to this adage: Heterogeneity within the item covariance matrix (e.g., through multidimensionality or poor items) negatively impacts reliability by decreasing the precision of the estimation. We also examined the question of "equilibrium" scale length, showing the conditions for which it is optimal to add no items, or one, or multiple items to a scale. In terms of "best practices," we recommend that researchers report a confidence interval or standard error along with the coefficient alpha point estimate.