SHORTER ARTICLES AND DISCUSSION 



THE ARITHMETIC OF THE PRODUCT MOMENT 

 METHOD OF CALCULATING THE COEFFI- 

 CIENT OF CORRELATION 

 In view of the increasing application of refined statistical 

 methods to scientific problems of all kinds it seems highly de- 

 sirable to point out any simplification of arithmetical method 

 which may lighten the necessarily formidable labor of calcula- 

 tion. 



The statistical constant which has proved a most powerful 

 tool in many fields of work is the coefficient of correlation. Be- 

 sides the contingency constant 1 , the correlation ratio 2 and the 

 well-known four-fold table and product moment methods, sev- 

 eral alternative processes of determining correlation in the case 

 of special data have been suggested. 3 In recent numbers of 

 Science Dr. Boas 4 and Professor Pearson*"' have discussed the 

 formula? to be used in the calculation of r, and in another place 

 I have suggested methods 6 which in some cases materially 

 shorten the labor of calculation. 



"When the nature of the material permits, the best method of 

 calculating correlation is the product moment one. 



As conventionally described in the books, 7 this requires for the 



1 Pearson, K., ' ' On Contingency and its Kelation to Association and Nor- 

 mal Correlation," Draper's Co. Research Memoirs, Biometric Series, 1, 1904. 



•Pearson, K, "On the General Theory of Skew Correlation and Non- 

 linear Regression," ibid., 2, 1905 . 



3 For instance, K. Pearson, "On Further Methods of Determining Corre- 

 lation," ibid., 4, 1907; K. Pearson, "On a New Method of Determining 

 Correlation," Biometrika, Vol. VII, pp. 248-257, 1910; K. Pearson, "On 

 a New Method of Determining Correlation," Biometrika, Vol. VII, pp. 

 96-105, 1909. 



N. S., Vol. XXIX, pp. 823-824, 1909. 



"Pearson, K., "Determination of the Coefficient of Correlation," Science, 

 N. S., Vol. XXX, pp. 23-25, 1909. 



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