Bias in Coefficient Alpha Arising From Heterogeneity

Abstract

A necessary and sufficient condition of coefficient alpha as an estimate of test reliability is that the part scores be essentially tau equivalent. This condition implies that the test is unidimensional in the factor analytic sense, and all parts must measure the same unitary trait or ability. This article examines the cruciality of this assumption. It is shown mathematically that the negative bias introduced by multidimensionality is likely to be quite small. Empirical data are cited from a standardized achievement test battery to corroborate this inference. It is concluded that the usual formula for coefficient alpha is quite robust with respect to alpha's cardinal assumption. Where bias is substantial, the stratified version of coefficient alpha can be used to accommodate to multidimensionality.