204 
On Theories of Association 
Any argument, as we have already indicated, which is valid when applied to 
the columns and rows of a fourfold table ought to be valid when applied to the 
columns and rows of a multifold table. Such a table should also not be affected 
by selection. Well, let us take the Table from the Census of the age of husband 
and wife and let us select so as not to change certain Q's and see what effect 
this has on the correlation. The following tables give Q and r before and after 
a series of selections. 
Let the divisions be at the same ages for both husband and wife, say under 30 
and over 30. 
Coefficient of Association = '9745 
Coefficient of Colligation = "7958 
Correlation before Selection = - 9136* 
Percentage of those over 30 years selected : 
Actual Correlation 
Actual Correlation 
100 % 
■9136 
5% 
•6969 
10% 
•8347 
4% 
•6479 
»7. 
•8175 
3% 
■5921 
8% 
•7961 
2 7. 
•5360 
7% 
•7698 
17. 
•4952 
6% 
•7369 
0 7. 
•4850 
In other words the selection which reduces the actual correlation from *914 
to "485 leaves Mr Yule's coefficients of association and colligation unchanged ! 
No, this is not true ; every other coefficient of association and colligation for 
the table is changed, except the particular two for the arbitrary division at 
30 years ! What legitimate inference of any kind can be drawn from the constancy 
of this individual pair ? 
Now let us select husbands and wives unequally but still at age 30 divisions: 
Husbands 
100 % 
10 7; over 30 
1 °/o over 30 
10 % under 30 
1 7. under 30 
•000 7„ under 30 
•000 °/ 0 over 30 
Wives 
100 7„ 
10 °/ 0 under 30 
10 7„ under 30 
1 7„ over 30 
0-1 7 o over 30 
•000 7„ over 30 
■000 7 0 under 30 
Actual Correlation 
•914 
■908 
•850 
•715 
•285 
- -009 
- -038 
During all these operations which reduce the actual relationship as measured 
by correlation from the very high value - 914 to zero and even to negative values, 
Mr Yule's association and colligation for his selected dichotomies show the constant 
"very high values" 975 and - 796. At other dichotomies of course they cover 
pretty well the whole possible scale. 
* Value without Sheppard's corrections, because in dealing with selection it is not clear that those 
corrections are always appropriate. 
