BIAS IN COEFFICIENT-ALPHA ARISING FROM HETEROGENEITY OF TEST CONTENT

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