172 
On Theories of Association 
Length of First Leaf. 
T5 
fl 
o 
O CD 
bp 
S 
Under 6 - 95 mm. 
Over 6-95 mm. 
Totals 
Under 14 '95 mm. 
Over 1^95 mm. 
6,943 
41 
46,673 
6,343 
53,616 
6,384 
Totals 
6,984 
53,016 
60,000 
The true correlation of the material is "5672 and the tetrachoric r = \5572 ± "0058. 
It may be presented in any one of the three forms (i) as A above, (ii) in one of 
Mr Yule's " natural forms * " e.g. 
B. 
Or, again, as 
6,636 
1,383 
8,019 
1,383 
6,636 
8,019 
8,019 
6,943 
8,019 
4-6673 
16,038 
6,947-6673 
410,000 
6,343 
416,343 
416,943 
6,347-6673 
423,290-6673 
Now Q is the same = - 9167, "very high association" for all these forms, and 
a posteriori given Q we should not know whether it had arisen from A, B or C. 
The values of the Boas-Yulean coefficient for these tables are : 
A. 0 = 1183, 
B. 0 = -6551, 
C. </>=0152. 
Which of these values are we to adopt ? Are we to use the table as it originally 
is given ? Or the " natural " form B ? Or the selected form C ? How can two 
coefficients ever lead to the same results, when an adjusting process which does 
not modify one, a property claimed as one of its advantages, changes the other to 
any value we please from zero up to Mr Yule's new coefficient of colligation f ? 
* See Journal R. Stat. Soc. Vol. lxxv. p. 590. 
t Taking the usual form of the fourfold : 
a 
b 
a + b 
c 
d 
c + d 
a + c 
b + d 
n 
