Coefficient Alpha as an Estimate of Test Reliability Under Violation of Two Assumptions

Through use of computer simulation, the central tendency and variability of coefficient alpha were examined under violation of two assumptions made in the derivation of the formula. When assumptions were satisfied, the mean value of coefficient alpha was extremely close to the population reliability coefficient, but values were highly variable. This result was independent of the shape of the population distribution of test scores. Coefficient alpha underestimated reliability under violation of the assumption of essential tauequivalence of subtest scores and overestimated reliability under violation of the assumption of uncorrelated subtest error scores. In both cases, the bias of the estimates varied systematically with the degree of violation of assumptions, while the variability of the estimates remained constant. All these results were independent of the number of persons and the number of subtests.