The previous chapters, from Chapter 5 on, have presented a survey of first-order cognitive ability factors found in the database for this project. They are “first-order” factors in the sense that they emerged from direct analysis of the correlation matrices of the datasets. The factorial procedures chosen for use in the project, however, dictated that when first-order factors rotated to simple structure were found to have substantial intercorrelations, their correlation matrices were to be subjected to further analysis to find one or more “second-order” factors. This process could continue for a further step when second-order factors had substantial intercorrelations, to produce “third-order” factors – in principle, possibly more than one for a given dataset, but it was never the case, for my datasets, that more than one meaningful third-order factor emerged in the analysis. (This was true even for reanalysis of one dataset, HAKS01, whose authors, Hakstian and Cattell, 1978, believed it necessary and desirable to extract three oblique factors at the third order.)

The present chapter reports the results of the higher-order analyses conducted, wherever applicable, on the 467 datasets selected for study in this survey. The chapter thus constitutes a study of the higher-order structure of cognitive abilities. The complete orthogonalized hierarchical factor matrices for the datasets are shown in Appendix B.