UK ATTRIBUTES IN STATISTICS. 287 



error. If the dividing joints be taken to be the means, this is not so, and the 

 probable error of Q would be increased. 



41. The standard error of the surplus ratio comes very simply 



_ (A) - (.) __ 2(A) 



i= -ir~-~ir -1-2*- 



8*1 = 2 . 8< 



...... (13), 



so that the probable error of Sj is the smaller the larger ,. 



42. It remains to determine the correlations between errors in surplus ratios 

 and between errors in surplus ratio and errors in association. The first problem 

 proceeds exactly as in the case of finding the correlation between errors in two non- 

 ultimate groups (p. 284, equations (5)-(8)). 



(A) + (B) - N = (AB) - (off} 

 or say 



^i + <l>2 1 = T\ T-A 



.'. &, + 8 2 = 2 (877-! - Sir.,) 



where s l s } are the surplus rations of A and B. Proceeding as in the previous case 



(14). 



Whence 



R.,,- 1 = 



'* *< l _-*'l (16) . 



These regressions are positive if A and B be positively associated. Thus if A lie, for 

 example, genius in father, B genius in son, and, if in a sample of the population there 

 l>e found to be a surplus of genius differing from the average by 8s 1( then we should 

 expect to find in the sons of the sample a surplus s., + 8.s 2 , where 



43. To proceed to find the correlation of errors in Q 12 and, say, *,. 

 SO 2 S * 



d ^ 18 - " (i + y 



2* f?*t,?*i_8i_tyl 



" a + f I * " " *i " * " * r 



