180 On Theories of Association 
Combine b + c, d + e, f+ g, h + i together ; /3, 7 + 8, e + £, r/, and we deduce 
(F) 
a 
b+e+d+e+f+g+h+i 
j 
Totals 
a 
40 
0 
0 
40 
0 
1920 
0 
1920 
e 
0 
0 
40 
40 
Totals 
40 
1920 
40 
2000 
The Yulean has now reached perfect correlation, or r = + 10000. 
Combine a, b, c, d, e together and /, g, h, i, j ; a, j3, 7, S and e, f, tj, 6, and we 
have 
(G) 
a+b+e+d+e 
f+g + h + i+j 
Totals 
e + f +r) + d 
240 
760 
760 
240 
1000 
1000 
Totals 
1000 
1000 
2000 j 
The Yulean is now negative and —"5200. 
But if we write the table as a fourfold thus : 
(H) 
a+b+c+d+e+f+g+h+i 
j 
Totals 
a + /3-(-y + a + f + (+rj 
6 
1960 
0 
1960 
0 
40 
40 
Totals 
1960 
40 
2000 
the Yulean would be again unity and mark perfect correlation of a positive kind. 
Mr Yule's coefficient of association would also be positive and mark perfect 
association. 
Now it is not open to Mr Yule to turn round and assert that such tables are 
extremely unlikely in practical statistics, first because his condemnation of the 
coefficient of contingency is based solely on the creation of an artificial table 
in exactly the same way, and secondly because he asserts that once we dismiss 
the idea of Gaussian frequency the method of correlating ranks with big 1 brackets ' 
becomes applicable. Our tables bring out, however, three important points : 
(i) that two variates with an actual correlation of —'112 may exhibit any corre- 
lation between - '52 and + 1*00 when treated by the Yulean process of pseudo- 
ranks ; (ii) that Mr Yule's coefficient of association may cover under the heading 
' perfect association ' almost any value of the real relationship, it is merely an 
association of common names, i.e. class-indices, and not of the real variate beneath 
these class-indices; and (iii) that the assumption that a fitting measure of 
association should give unity for a fourfold table of the form ^ | ^ is by no 
