Thorndike, E. L.—Educational Psychology; 3 vols. Teachers College, Columbia University, 1913.
CHAPTER II
The Relationships among Capacities
I. THE COEFFICIENT OF CORRELATION
The question is: How are mental capacities mutually related, with regard to amounts of each found in given individuals?
Before verifiable facts can be established in a field of knowledge, it is necessary to introduce therein methods of enumeration and measurement. The question above propounded has waited long for answer, because of the great difficulty of applying mathematics to mental phenomena. The answer required first that single functions be accurately scored, and then that a measurement be obtained of the relationship between and among the single functions.
It seems well agreed that the quantitative determination of the relationship between and among mental characteristics began with Galton, about 1885. Various scholars have presented discussions of the subject since then, notably Baerwald in 1896, Spearman in 1904, Stern in 1911, Meumann in 1913, and Thorndike in 1913, each of whom summarized the findings up to the time of writing, with original interpretations.
The methods of quantitative measurement used to study the constitution of mental abilities, or functions, as related to each other, are chiefly those of correlation—simple correlation, multiple correlation, and partial correlation.
It is not within the scope of the present volume to give consideration to these methods as such. Highly technical instruction in the theory and practice of measurement is necessary for complete understanding of them. The results may be comprehended for our purposes, without complete knowledge of the methods. Much of the evidence we now have in the matter of relationships among mental functions has been obtained by the method of simple correlation. A brief exposition of how a relationship is established between two variable functions within a group, by simple correlation, will suffice to give a general understanding of the term coefficient of correlation, which is used here, and which frequently appears in modern texts of educational psychology. The interpretation of coefficients of correlation should not, however, be undertaken independently without full knowledge, as competent interpretation for practical purposes must take into account all the conditions under which they have been derived.
Below are listed fourteen school children, each of whom has been measured in each of two mental functions: (1) mental age, determined by a standard scale for measuring general intelligence (Stanford-Binet), and (2) spelling ability, as measured by a standard spelling scale (Ayres’ scale). These children were selected for study, because they appeared to be characterized by special discrepancy between the two functions.
We wish now to know whether and to what extent the child who falls high in the distribution of mental ages also falls high in the distribution of spelling ability. According to the formula which is most useful in this case,[[1]] we arrange these pupils in their order of merit for one of the functions measured, e.g. for mental age. We then find the rank for each, within the group, in the second function, which is here spelling ability. The difference in rank between the paired functions is then found for each pupil, and the correlation formula is applied.[[2]]