“The correlations thus established between the several school subjects may legitimately be attributed to the presence of common factors. Thus, the fact that the test of Arithmetic (Problems) correlates highly with the test of Arithmetic (Rules) is most naturally explained by assuming that the same ability is common to both subjects; similarly, the correlation of Composition with Arithmetic (Problems) may be regarded as evidence of a common factor underlying this second pair; and so with each of the seventy-eight pairs. But is the common factor one and the same in each case? Or have we to recognise a multiplicity of common factors, each limited to small groups of school subjects? “To answer this question a simple criterion may be devised. It is a matter of simple arithmetic to reconstruct a table of seventy-eight coefficients so calculated that all the correlations are due to one factor and one only, common to all subjects, but shared by each in different degrees. Such a theoretical construction is given in Table XIX. In this table theoretical values have been calculated so as to give the best possible fit to the values actually obtained in the investigation, and printed in Table XVIII. It will be seen that the theoretical coefficients exhibit a very characteristic arrangement. The values diminish progressively from above downwards and from right to left. Such an arrangement is termed a ‘hierarchy.’ Its presence forms a rough and useful criterion of the presence of a single general factor. “On turning to the values originally obtained (Table XVIII.) it will be seen that they do, to some extent, conform to this criterion. In certain cases, however, the correlations are far too high—for instance, those between Arithmetic (Rules) and Arithmetic (Problems), and again Drawing and both Handwork and Writing (Quality). Now these instances are precisely those where we might anticipate special factors—general arithmetical ability, general manual dexterity—operating over and above the universal factor common to all subjects. These apparent exceptions, therefore, are not inconsistent with the general rule. Since, then, the chief deviations from the hierarchical arrangement occur precisely where, on other grounds, we should expect them to occur, we may accordingly conclude that performances in all the subjects tested appear to be determined in varying degrees by a single common factor. “Nature of the Common Factor.