Now that we have introduced the topic of latent means in SEM, we can revisit the topic of CFA, with the addition of latent means analysis in CFA. We will do so within the framework of invariance testing, a topic first introduced in the initial discussion of multi-group SEM. This is an important topic that needs additional exploration. Although it is possible, perhaps even common, to test for aspects of invariance without examining measured and latent means, here we will first focus on invariance testing with means and intercepts. Thus, this chapter will focus in some detail on the steps needed to test for invariance in constructs across groups, including invariance in measured variable intercepts, which will allow the testing of differences in latent means. Part of this discussion will concern what is tested conceptually at each step, and why one would want to do such testing. We will then back up a little and focus in less detail on the steps you might take if you were interested in invariance testing without focusing on means. Finally, we will (as in the previous chapter) see how some of this same information can be obtained by the addition of a categorical variable to the analysis, but with the addition of some assumptions that may or may not be valid.