Scores on 12 aptitude and achievement tests for 11,743 subjects, subdivided into four groups according to intelligence and socioeconomic status, were used. A technique, developed by Jöreskog, for simultaneously factor analysing data from several populations was used to determine whether there was factorial invariance over the four groups. A model, in which the same factor pattern (matrix of factor loadings) is assumed to hold for the four groups, was fitted to the data. Goodness-of-fit indices suggested that the model fitted satisfactorily. Differences in the factor dispersion matrices and mean factor scores for the subpopulations are then examined and discussed.