Confirmatory composite analysis (CCA) is a subtype of structural equation modeling that assesses composite models. Composite models consist of a set of interrelated emergent variables, i.e., constructs which emerge as linear combinations of other variables. Only recently, Hair et al. (J Bus Res 109(1):101–110, 2020) proposed ‘confirmatory composite analysis’ as a method of confirming measurement quality (MCMQ) in partial least squares structural equation modeling. As a response to their study and to prevent researchers from confusing the two, this article explains what CCA and MCMQ are, what steps they entail and what differences they have. Moreover, to demonstrate their efficacy, a scenario analysis was conducted. The results of this analysis imply that to assess composite models, researchers should use CCA, and to assess reflective and causal–formative measurement models, researchers should apply structural equation modeling including confirmatory factor analysis instead of Hair et al.’s MCMQ. Finally, the article offers a set of corrections to the article of Hair et al. (2020) and stresses the importance of ensuring that the applied model assessment criteria are consistent with the specified model.