On a method of determining correlation from the ranks of the variates

Abstract In the experimental psychology — and also in other branches of experimental researches — it is often asked for the correlation between two characters to which it is not possible to give quantitative values expressed in comparable units. Having, e. g., examined a g-roup of persons as to their power of adding numbers and their power of discriminating pitch, we can say that the faculty of adding numbers is greater by A than by B and greater by B than by C a. s. o., and in like manner we can arrange the persons according to their faculty of discriminating pitch, but we have no comparable units for measuring the faculties in question. The problem of finding a measure of the correlation between two such characters 1 The meaning of the correlation between such characters is not considered here. were, as far as I know, first treated by Spearman. 2 The American Journal of Psychology, Vol. XV and The British Journal of Psychology Vol. II. The formulae given by him are, however, in several respects open to objections and, as shown by Pearson 3 Drapers' Company Research Memoirs. Biometric series IV. in his paper “On Further Methods of Determining Correlation”, partly incorrect. In the same paper Pearson has also given some mathematically correct solutions of the problem but based on the hypothesis that the frequency distribution of the actual variates is normal. Now, in practice, a strictly normal distribution is rather to be regltrded as an exception than as a rule, and therefore, when only the ranks of the variates are given and nothing is known about the distribution, this assumption must, of course, restrict the availability of the method. Pearson does not overlook this fact, but he indicates that the frequency distribution can hardly be assumed to be other than normality. In this paper, however, I will give another solution which in most cases will be of greater generality.