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Researchers often compare groups of individuals on psychological variables. When comparing groups an assumption is made that the instrument measures the same psychological construct in all groups. If this assumption holds, the comparisons are valid and differences/similarities between groups can be meaningfully interpreted. If this assumption does not hold, comparisons and interpretations are not fully meaningful. The establishment of measurement invariance is a prerequisite for meaningful comparisons across groups. This paper first reviews the importance of equivalence in psychological research, and then the main theoretical and methodological issues regarding measurement invariance within the framework of confirmatory factor analysis. A step-by-step empirical example of measurement invariance testing is provided along with syntax examples for fitting such models in LISREL.