It has been stated that though all, or nearly all, mental functions so far measured and correlated, yield positive coefficients, all do not show an equal amount of positive correlation. Certain mental functions, for example, are shown to yield coefficients of as much as .80, for a total correlation with others of a series; while some yield coefficients as low as .10, approaching absence of relationship. To explain these facts, Spearman formulated the concept of a hierarchy of relatedness to a “general factor.” Those abilities showing slight correlation with others in series of tests, were thought of as but loosely related to “general intelligence,” and as constituting “special abilities.” They might be displayed by persons inferior in general, or might be lacking in persons otherwise superior. Here again, the facts are not in question. It is admitted by all that functions show different amounts of positive correlation with one another, and of total correlation with members of a series. Not all experts agree, however, with Spearman’s theoretical explanation of the phenomena. Thomson has recently shown, by tossing dice of various colors, that in this game of chance (in which there is no “general factor,” but only many independent factors), hierarchical order of correlation coefficients is almost sure to be obtained, for combinations resulting from throws. Thomson, therefore, holds that the theory of a “general factor,” participating in all the separate performances of an individual, is not proved from the facts about correlation coefficients. He proposes the following, regarded by him as an alternative: “The mind, in carrying out any activity such as a mental test, has two levels at which it can operate. The elements of activity at the lower level are entirely specific, but those at the higher level are such that they may come into play in different activities. Any activity is a sample of these elements. The elements are assumed to be additive like dice, and each to act on the ‘all or none’ principle, not being in fact further divisible.” It is not quite easy to see that this theory, finally proposed by Thomson, which might be termed the “two level” theory, is very different from Spearman’s “two factor” theory, nor why the terms “higher” and “lower” should be introduced. But demonstration of the probability of obtaining a hierarchy of correlations simply from the tossing together by chance of independent factors, as with dice, adds new data for consideration. It might be that non-biological principles of probability are sufficient to explain the hierarchical order of correlations, among many tests administered to a given group, just as they are apparently sufficient to account for the particular form in which ability in any single test is distributed through the human species.