What is a good g?

Abstract

We have examined the stability of psychometric g, the general factor in all mental ability tests or other manifestations of mental ability, when g is extracted from a given correlation matrix by different models or methods of factor analysis. This was investigated in simulated correlation matrices, in which the true g was known exactly, and in typical empirical data consisting of a large battery of diverse mental tests. Theoretically, some methods are more appropriate than others for extracting g, but in fact g is remarkably robust and almost invariant across different methods of analysis, both in agreement between the estimated g and the true g in simulated data and in similarity among the g factors extracted from empirical data by different methods. Although the near-uniformity of g obtained by different methods would seem to indicate that, practically speaking, there is little basis for choosing or rejecting any particular method, certain factor models qua models may accord better than others with theoretical considerations about the nature of g. What seems to us a reasonable strategy for estimating g, given an appropriate correlation matrix, is suggested for consideration. It seems safe to conclude that, in the domain of mental abilities, g is not in the least chimerical. Almost any g is a “good” g and is certainly better than no g.