No. 589] 



NOTES AND LITERATURE 



55 



lished. Pearson 3 has given a new approximate difference method 

 which is serviceable in special cases only. Harris 4 has suggested 

 a novel difference method for exact work with tables. An alter- 

 native method of calculating rough moments and product mo- 

 ments, given by Elderton, 5 seems to have attracted little atten- 

 tion, although it has certain advantages for use in adding-machine 

 computations. A product moment method which possesses 

 marked advantages for use with machines which allow of simul- 

 taneous multiplication and summation, and which obtains inci- 

 dentally the data necessary for testing linearity of regression or 

 computing the correlation ratio, v , is now available. 6 In the 

 special cases in which the two characters to be centered in the 

 correlation table are not differentiated, e. g., stature of pairs of 

 brothers, length of Paramecium, etc., the tables are ordinarily 

 rendered symmetrical by using each individual once as the x and 

 once as the y member of the pair. This may be done by actually 

 forming the symmetrical table, or by using the simple formula 

 proposed by Jennings. 7 If, as is frequently the case, more than 

 a single pair of individuals are associated, the labor of forming 

 tables becomes very great. Each individual of a family, each 

 organ of an individual, or each individual measured from a par- 

 ticular environment, must then be entered in the table m com- 

 bination with every other one. Since the number of combina- 

 tions in each class is n(n— 1) and the number of classes must 

 be at least moderately large, the total number of combinations is 

 very great. Thus the data for number of nipples in swine 

 recently published by Parker and Bullard 8 require a table of 

 34,884 combinations to determine the fraternal correlation for 

 number of nipples. In the case of the Hydra data analyzed by 

 Lashley, 9 tables with from one to nearly two hundred thousand 

 ,f Determining Correlation," 

 IV, Dulan and Co., 1907. 

 Calculating the Coefficient of 

 Correlation in the Case of integral Variates, " Biometrila, 7: 214-218 1909. 



s Elderton, W. P., "An Alternative Method of Calculating the_ Kougn 

 Moments from the Actual Statistics," BiometriTca, 4: 374-378, 1905. Also 

 in his "Frequency Curves and Correlation." 



« Harris J Arthur "The Arithmetic of the Product Moment Method of 

 Calculating the Coefficient of Correlation," Amer. Nat., 44: 693-699, 1910 

 7 Jennings, H. S., "Computing Correlation in Cases Where Symmetrical 

 Tables are Commonly Used," Amer. Nat., 45: 123-128, 1911. 



s Parker, G. H., and C. Bullard, Proc. Amer. Acad. Arts and Science, 49: 

 399-426, 1913. 



» Lashley, K. S., Jour. Exp. Zool., 19: 210, 1915. 



