SHORTER ARTICLES AND CORRESPONDENCE 



COMPUTATION OF THE COEFFICIENT OF 

 CORRELATION 



In Dr. Harris's recent note 1 suggesting a helpful modification 

 of the method of computing the coefficient of correlation, the only 

 objection mentioned is the fact that his method results in very 

 large product-numbers. This difficulty can be considerably re- 

 duced by a procedure based on the fact that the calculation of 

 the standard deviation and the coefficient of correlation does not 

 depend upon the absolute dimensions of the things measured. 

 All that is required is a given series of successive grades; the 

 standard deviation will then be obtained in terms of the units 

 separating the grades, whatever they are; while the coefficient 

 of correlation is a relative numher. quite independent of the 

 value of the units. We may therefore give to the lowest grade 

 of both sets of measurements (x and y) the value 0, for the 

 succeeding ones the values 1, 2, 3, 4, etc., instead of the real 

 values; the labor of computation will then be greatly reduced, 

 while the same value will be found for the two constants in 

 question. The values which Dr. Harris calls A, and A, will by 

 this method not be the means of x and y (so that they may well 

 be designated rather d x and d y ) , but the means can be obtained 

 from them without labor by simply adding to each the absolute 

 value of the lowest grade of x and of y, respectively (since we 

 had reduced all grades by this amount, in substituting for 

 the lowest grade). 



This much simplifies the computations when the absolute di- 

 mensions are represented by numbers considerably greater than 

 unity. Thus, in Dr. Harris's Table III., in finding the standard 

 deviation we should for the third grade have to multiply by but 

 4, instead of by the square of 28. 



NOTE ON BATRACIIOSEPS ATTEXUATUS ESCH. 

 Batrachoseps attenuatus is the most abundant salamander in 

 the vicinity of Stanford University. During the rainy season 

 •This journal. November, 1910. 



413 



