There are Many Greater Lower Bounds than Cronbach’s α: A Monte Carlo Simulation Study

Abstract

ABSTRACT A Monte Carlo simulation study was conducted to examine the performance of α, λ2, λ4, μ2, ωT, GLBMRFA, and GLBAlgebraic coefficients. Population reliability, distribution shape, sample size, test length, and number of response categories were varied simultaneously. The results indicate that α and λ2 perform the worst overall. However, the performance of α is improved if the population reliability is high. λ4 is relatively unbiased but the most imprecise. μ2 and ωT perform relatively well under most conditions. GLBAlgebraic outperforms other coefficients under many conditions. GLBMRFA is useful under few conditions if the population reliability is high. The results corroborate previous suggestions that large samples, longer tests, higher number of response categories, and normally distributed results can make reliability estimates more dependable. Some insights on the interaction of these factors are provided. We discuss the findings compared to previous research. The complete R code used for the simulation is provided in the online supplement.