This paper provides an analysis of the measurement invariance of the items on the Academic Aptitude Test (PAA, for its initials in Spanish) at the University of Costa Rica (UCR). The measurement invariance was analyzed according to two classifications: by high school (public-private) and by sex. The analysis were realized considering the dichotomous nature of items, for that reason the study was delimited to the analysis of the weak and strict invariance. Each people classification reached strict invariance, thus, it was concluded that the test scores have the same unit of measurement for men and women, and among students from public and private high schools. Finally, these results are evidence of the validity of the PAA scores for proposed uses from the perspective of fairness.