A Note on Simple Correlation
Maurice Fréchet, C. de la Menardiere · Mathematics Magazine · 1959
In Volume 22, No. 2, 1958, pp. 57-69 of Mathematics Magazine, appeared an article by C. D. Smith entitled, On the Mathematics of Simple Correlation. aim, as given in the article, is to state the problem as it usually occurs and show how the measures of correlation may be derived by elementary algebraic calculations. This aim was completely fulfilled. purpose of this Note is to add some comment regarding interpretation of measures of correlation which follow from theoretical cons iderations. paper states, p. 58, The method of correlation is designed to measure the strength of commnon influences between two variables.' We may rnote first that the coefficient of correlation r does not always indicate what influences may exist. Yule, and others, (1), have found cases where the measure has a value near. its maximum where no common influience is known to exist between the two variables under consideration. iTl fact, the thing that can best measure the coefficient of correlatio is the thing that can measure a good index of correlation. We seek the total accuracy of the determination of one of the twovariables when the other is given. In other words, an index of correlation has nothing to say as to the causes of this accuracy or the lack of accuracy, not even the existence of the causes. It gives a numerical fact. For instance X I is more or less determined by knowing X2* This is why the term, 'nonsense correlation, seems deceiving to us. In all cases, the value of an index of correlation has a meaning if the numerical data from which it has been extracted have been correctly taken. But that meaning is only one of the characteristics of the numerical table of correlation. When a good index is equal to 1, we may state four conditions, namely: I. To all values of X2 there corresponds only one value of X II. Conversely when it is equal to 0. III. X1 is constant when X2 varies. IV. And conversely Moreover it is known that the classic coefficient, r, verifies only two of 265