Confidence Intervals for the Coefficient Alpha Difference From Two Independent Samples (Groups)

Four different bootstrap methods for estimating confidence intervals (CIs) for a coefficient alpha difference from two independent samples (groups) were examined. These four CIs were compared to the most promising non-bootstrap CI alternatives in the literature. All CIs were assessed with a Monte Carlo simulation with conditions similar to previous research. The results indicate that there is a clear order in coverage performance of the CIs. The bootstrapped highest density interval had the best coverage performance across all simulation conditions. Yet, it was impacted by unequal sample sizes when one of the groups had the smallest sample size investigated of 50, or when items came from a compound symmetric correlation matrix with $\rho = 0.64$. Regardless of the simulation condition, the percentile bootstrap is a good alternative as long as both group sample sizes were 200 or more