Estimating reliability: A comparison of Cronbach's α, McDonald's ωt and the greatest lower bound

Cronbach's alpha as a reliability estimate for a set of items has been repeatedly criticised. Using McDonald's omega or the Greatest Lower Bound (GLB) has been suggested instead. A simulation study using a single scale was performed on data with n = 60, 80, 120, 200, 300, 500 and 900 cases utilizing 4, 8, 16 or 32 items. A total of 10% of each item had missing values vs. there were no missing data. Skewness of the items were 0, 1 and 2. Correlations were homogenous vs. heterogeneous. Standard deviations were homogenous vs. heterogeneous. Underlying constructs were homogenous vs. heterogenous. Conditions were combined in a block design, and 1000 replications for each one were calculated. As a result, alpha slightly underestimated reliability in some cases, omega minimally overestimated in large samples, the GLB overestimated strongly in small samples. Additionally, GLB estimates had less precision within the 1000 replications, i.e., standard deviations were almost double as large as for alpha and omega. Interestingly, the performances of alpha and omega were basically similar. However, various programs showed different results particularly in cases with missing data on the items. Out of the programs examined, the R package MBESS displayed best results.