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Propensity Score Analysis (PSA) is an important method for estimating intervention effects in educational research based on the large secondary datasets. Therefore, educational studies sometimes focus on treatment effect estimation not only controlling observable covariates but for latent covariates. Even though previous studies have provided the information for treating latent variables as covariates and outcomes in PSA and presented basic requirements concerning reliability and measurement invariance assumptions, few studies are dealing with testing the effect of measurement invariance different from testing the effect of lack of reliability in covariates. This study will investigate specific consequences of lack of measurement invariance, which will inform analyses of applied researchers using PSA and PSA-SEM.