Testing the Difference between Reliability Coefficients Alpha and Omega

Reliable measurements are key to social science research. Multiple measures of reliability of the total score have been developed, including coefficient alpha, coefficient omega, the greatest lower bound reliability, and others. Among these, the coefficient alpha has been most widely used, and it is reported in nearly every study involving the measure of a construct through multiple items in social and behavioral research. However, it is known that coefficient alpha underestimates the true reliability unless the items are tau-equivalent, and coefficient omega is deemed as a practical alternative to coefficient alpha in estimating measurement reliability of the total score. However, many researchers noticed that the difference between alpha and omega is minor in applications. Since the observed differences in alpha and omega can be due to sampling errors, the purpose of the present study, therefore, is to propose a method to evaluate the difference of coefficient alpha (alpha-hat and omega-hat statistically. In particular, the current article develops a procedure to estimate the "SE" of (omega-hat - alpha-hat) and consequently the confidence interval (CI) for (omega-alpha). This procedure allows us to test whether the observed difference (omega-hat - alpha-hat) is due to sample error or omega-hat is significantly greater than alpha-hat. The developed procedure is then applied to multiple real data sets from well-known scales to empirically verify the values of (omega-hat - alpha-hat) in practice. Results showed that in most of the comparisons the differences are significantly above zero but cases also exist where the CIs contain zero. An R program for calculating omega-hat, alpha-hat, and the "SE" of (omega-hat - alpha-hat) is also included in the present study so that the developed procedure is easily accessible to applied researchers.