OF ATTRIBUTES IN STATIST! 299 



certain age, has certain {>ercentages of defectives and exhibits certain associations 

 between defects. Another group, of another mean age, has different percentages !' 

 ilffects and different associations. Such differences are due to all three of the above 

 causes of change acting together, superposed in general on wholly uukm>\\ u initial 

 differences between the groups, due either to their being differently gathered 

 samples, or to a secular change taking place in the population. It becomes, then, 

 impossible to separate, except conjecturally and in a more or less tentative manner, 

 the effects of selection from those of growth including under this term all processes 

 of change that take place in the individual. 



54. Let (AB),, (A/3),, (a/8),, (aB), be the four second-order frequencies observed for 

 any pair of defects for an early age, and let ( AB) 2 , (A/8).,, ()8).,, (B) 2 be the frequencies 

 at a later age in the same individuals, or in an older age group of the same population. 

 Then if Q, Q., 1x5 the association coefficients for the two groups, *, jr., the values of 

 the corresponding ratio of the cross products 



Q*< Qi 



if K. 2 > K! 



(B),(A/3), (B),(A/3X 

 (AB);( ay 8), * (AB\(a/3\ 



(B), . (Aft), (AB), _ 

 (B), (A0), * (AB), 

 Let 



(AH),' '> 

 Then 



Q*<Q, 



so long as 



s, s 3 < *, s 4 . 



If we are dealing with a population subjected solely to selection, s { n 2 s 3 .<r + are the 

 survival rates for the four classes ; the quantities 4 2 /*i s z/ s \> s J s i we ma y 

 " survival figures " for the three classes, and the condition may be written 



That is, if the survival figure for the class with two defects be less than the product 

 of the survival figures for the singly defective classes, the association will decrease. 

 A priori I could not say whether this condition should hold or not ; it appears 

 possible that selection might either decrease or increase association. Practically the 

 condition does seem to hold,* but, as mentioned above, the evidence is not complete 

 nor certain, for we cannot, amongst present data, find a single case in which change 

 is certainly due to selection alone without other causes. 



When we are comparing one age group with another of the same population the 



* Below p. 312-315. 

 2Q2 



