OF ATTRIBUTES IN STATISTICS. 



291 



Getting out the number of pairs in the same way for fraternities of all the sizes 

 given, I find the totals : 



Good-good 330 pairs. 



Good-bad and bad-good . . . 255 each. 

 Bad-bad 454 



Q = 



330 x 454 - 255 x 255 



330 x 454 + 255 x 255 

 = '395. 



This value seems rather low ; the fraternal correlation of '4 should correspond to 

 an association of about '49, or more as the axes of division are not taken through 

 the medians. 



47. Inheritance of Artistic Faculty ("Natural Inheritance," p. 218). The data 



are :- 



Number of artistic children with artistic parentage 296 



,, non-artistic parentage . . . . 173 



non-artistic children with artistic .... 372 



non-artistic parentage . . 666 



We have called the parentage artistic where either parent is so entered. Mr. 

 GALTON'S table does not separate the sexes. The above is consequently a kind of 

 " mid-parentage " inheritance table. The association coefficient is 



Q = -508 -029. 



The correlation of offspring with mid-parent is '42, corresponding to an association 

 of '51 or remarkably close to the above ; but the close agreement must be more or 

 less accidental. As we have seen (p. 276, and example), shifting the axes of division 

 of a correlation surface towards the extremities of the surface, so as to increase or 

 decrease the surplus ratio of each attribute, increases the association between them. 

 This ought to have made the association somewhat higher in the present case, as 

 there are only 469 artistic children to 1038 non-artistic, or s = '378. It is interesting 



2 P 2 



