This thesis examines the relationship between measurement invariance in psychometrics and effect invariance in the machine learning and causal inference literatures. It provides a formal algebraic bridge mapping where the two frameworks align and where they differ. The Wald-E test for conditional treatment effect invariance is then applied to a large-scale psychological replication dataset assessing whether previously studied psychological effects generalize across countries. Despite being motivated by a different concept of invariance, the Wald-E procedure yields conclusions that closely match those of the original psychological analyses. Finally, a simulation of a simple latent trait–proxy setting demonstrates that measurement invariance and effect invariance can diverge in both directions: a proxy may appear effect invariant even when the underlying latent trait differs across environments, while a proxy for an invariant latent trait may fail to satisfy effect invariance. These findings illustrate the relationship between the two notions of invariance and highlight the importance of considering the measurement process when drawing conclusions about causal invariance.