Karl Pearson and David Heron 
205 
Nor has the result anything to do with the division at ages 30. If we divide 
at 21 years we find : 
Percentage 
selected over 21 Actual Correlation 
100% -914 
10 7„ -939 
1 7 o -941 
•1 7 o -493 
•000 7 o -272 
Here the Q and a> of Mr Yule retain throughout the operations the values 
"987 and "853, which mark, we have been told, "very high association"! 
Nor is the absurdity in the least confined to ages of husband and wife. Let 
us take stature in Father and Son* and divide into a fourfold at Fathers 67'5" 
and over, and Sons at and over. The actual correlation is "520, Q = "683 
and tw = -395. 
Selection of Father Selection of Son Actual Correlation 
100 7„ 100 7„ -520 
10 7„ over 67-5" 10 °/ e over 68-5" -314 
10 °/ 0 under 67-5" 10 °/ a over 68-5" -275 
•000 7„ over 67"5" -000 °/ 0 over 68-5" '251 
1 7„ under 67-5" 1 °/ a over 68-5" -185 
The result is exactly the same as before, the real relationship is immensely 
modified by selection, while the colligation and association remain unchanged for 
one pair of arbitrary divisions and for this one only. What can be learnt from 
such a statistical method? We venture to believe that from the standpoint of 
common sense it is wholly without meaning. 
What is the precise physical character which is to be attached to this wide 
difference between "association" and correlation? That correlation is affected 
by selection we know only too well ; it is one of the factors of progressive 
evolution under natural selection, but what profitable meaning of any kind 
is to be attached to the statement that one out of an indefinite number of 
associations has remained unchanged by a special selection ? Does not the 
principle that " association " or " colligation " is unchanged by selection arise 
from the fact that Mr Yule has merely guessed a denominator to his coef- 
ficient, which denominator has no theoretical justification of any kind; and his 
principle that selection makes no change is a later discovery and has no validity 
at all, for it is not a "natural " selection and has no generality beyond the fourfold 
table ? 
We think we have sufficiently indicated that Mr Yule's coefficients of associa- 
tion and colligation fail entirely for any variates which may be suspected in any 
way of continuity, and the bulk of the variates to which Mr Yule has applied his 
methods undoubtedly have such continuity. 
* Biometrika, Vol. n. p. 415. 
