The effects of skew on internal consistency
Description
The effect of skew on the standardized item alpha, an estimate of internal consistency closely related to Cronbach's coefficient alpha, was examined through Monte Carlo techniques. First, situations in which skew may exist were described, then attempts to address problems created by skew were discussed. Next, the logical relations among split-half reliability, Cronbach's coefficient alpha, and the standardized item alpha were examined and shown to be equivalent when all item variances are equal. Finally, results from Monte Carlo simulations were presented which compared alpha computed from standard normal variables to alpha computed from the same samples but where skew was induced by the lognormal transformation and finally to alpha computed from the ranks of the lognormal values. Both the extent and direction of skew were systematically varied as was the size of the population interitem correlation--rho. Since factorial complexity and the average interitem correlation have been shown to be related to alpha, the effect of skew on both of these was also examined. Results indicated that skew increases factorial complexity, decreases the average interitem correlations, and decreases alpha. These results were especially pronounced when rho was small. Transforming the values with a natural log transformation, which produces results equivalent to bivariate normal values, and ranking the lognormal values eliminated the skew as well as the liabilities associated with skew. However, ranking resulted in a slight decrease in the standardized item alpha compared to standard normal values