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A certain level of measurement invariance (MI) is required before conducting factor mean comparisons. When assessing MI, researchers frequently modify their models based on modification indices, which can yield unreliable results. Studies have shown that incorrectly imposing invariance constraints can lead to biased estimates of factor mean differences and incorrect alphas for tests of these differences. Past literature has not focused on examining a wide variety of analysis models in the assessment of factor means. We systematically manipulated the number of invariance constraints imposed on loadings and intercepts of analysis models for data generated with varying levels of non-invariance. The results should inform researchers about the effect of decisions made in assessing MI on the evaluation of factor mean differences.