had never been thoroughly examined. The present study investigated (1) the difference of MCFA and MIMIC in terms of Type I error rate and power when testing the mean difference of the higher-order latent factor (Δκ) in a second-order confirmatory factor analysis (CFA) model; and (2) the impact of data parceling on the test of Δκ between groups by using the two approaches. The methods were introduced, including the design of the models, the design of Monte Carlo simulation, the calculation of empirical Type I Error and empirical power, the two parceling strategies, and the adjustment of the random error variance.