An examination of two methods of forming confidence intervals for coefficient alpha

Coefficient alpha (Cronbach, 1951) is a commonly used measure of reliability. Feldt (1965) and Hakstian and Whalen (1976) developed methods of forming confidence intervals for coefficient alpha. In this thesis, three issues related to these confidence intervals were examined. First, their performance under fixed and random sampling of conditions (e.g., items, raters) was compared. When conditions were fixed, the confidence intervals were accurate for the kinds of data studied. When conditions were random, as few as 77% of the .95 confidence intervals included the parameter. Second, some researchers have recently questioned what constitute the necessary assumptions of these confidence intervals. In response, it was shown in this thesis that, contrary to what has been claimed, sphericity is not sufficient, although compound symmetry is. Compound symmetry may, in fact, be necessary, but no definitive proof of this can be offered at this time. Third, the performance of the two confidence intervals under random sampling of conditions was explored in more detail. Neither the type of confidence interval used nor heterogeneity of conditions means had any effect on the performance of the confidence intervals. However, heterogeneity of variances reduced the proportion of confidence intervals including the population value. This effect was most pronounced when the population value was high (.90) and when the number of conditions was low (5). The following conclusions were reached. Researchers conducting Monte Carlo studies of coefficient alpha should simulate the type of sampling that they are most interested in, as results depend on the type of sampling used. The Feldt (1965) and Hakstian and Whalen (1976) confidence intervals are precise when conditions are fixed; however, when conditions are random and variances heterogeneous, these intervals should be used with caution, especially if the data contain fewer than 20 conditions. The two types of confidence intervals perform very similarly, and hence the choice of method is left to the researcher. Lastly, a call is made for more robust procedures to be developed, and one possible approach to such a robust procedure has been identified.Arts, Faculty ofPsychology, Department ofGraduat