The Correlation Coefficient and its Prognostic Significance
Clark Leonard Hull · The Journal of Educational Research · 1927
There are numerous points of view from which the correlation coefficient may be regarded; one of these is that of trigonometry. According to this view, the correlation coefficient is the natural tangent of one of the lines of regression with the vertical, say. This is a fundamental fact. To the trained mathematician this fact is doubtless illuminating and satisfying, but for the psychologist or the student of educational research, to whom mathematics is a means rather than an end, the trigonometric aspects of correlation are likely to be neither illuminating nor satisfying. A second point of view considers the relations among the factors which may produce a tendency to correlation. This is of interest to persons concerned with the theory of mental testing. Suppose that two variables are each produced by the joint action of ten independent factors or determiners, that each determiner is of equal importance, and that two of these determiners are common to both variables. This overlapping of the two variables will ob viously produce a tendency to correlation. If we let Nc represent the number of common determiners and N1 and N2 the total number of determiners in the respective variables, then the correlation be tween the two variables will be given by the formula, N x