In psychological research, populations are commonly assumed to be homogeneous; however, populations can contain qualitative or quantitative subtypes. Mixture models can be used to capture unobserved population heterogeneity. After obtaining class membership, a researcher may be interested in seeing how classes of people differ on a background variable or covariate. In this study, three types of covariates are investigated: continuous, binary and ordered categorical. Factor mixture modeling is a statistical procedure, where class membership is probabilistic and frequently imperfectly inferred. The first aim of the study was to understand the extent to which incorrect class assignment decreases the power of detecting a significant post hoc effect. Second, a series of different models that a researcher could choose from are compared with respect to the proportion of correct assignment. The final and most significant focus of the study was to investigate whether a post hoc mean comparison has more power when the class probabilities are used to weight the covariate by the posterior probability or when it is not weighted.