An analysis of covariance structural factor model was posed that allowed for tests of invariance across populations of (1) similarity of the factor pattern, (2) equivalence of units of measurement, (3) standard errors of measurement of each factor, (4) reliability of each factor, and (5) a factor mean structure. The analysis of the SAT®-V and the SAT-M indicated support for the hypothesis that the respective factors for SAT-V and M were measuring the same things across populations in the same units with equivalent accuracy as measured by the standard error of measurement. The factor analysis of item type classifications indicated that little useful information would be obtained if the scores were reported by item type. This is particularly true for the SAT-M. The verbal item type analysis did suggest the possibility that the analogy scores be reported separately and the remaining item types be combined in a single reading-vocabulary score.