Structured means analysis is a very useful approach for testing hypotheses about population means on latent constructs. In such models, a z test is most commonly used for testing the statistical significance of the relevant parameter estimates or of the differences between parameter estimates, where a z value is computed based on the asymptotic standard error estimate associated with the parameter of interest. In the current article, a series of population analyses demonstrate that the z tests for latent mean structure parameters or, more directly, the standard error estimates upon which those z tests are based are, not invariant to how factors are scaled. As such, circumstances exist in which latent mean inference is compromised solely as a result of scaling decisions. This problem is illustrated in the context of between-subjects (i.e., multisample) latent means models and within-subjects latent means models. Recommendations for practice are also offered.