Karl Pearson and David Heron 
277 
Yet according to Mr Yule cf> is " applicable in its entirety to the 2 x 2-fold 
table." Of course we may "apply" any method to any problem, but whether 
we shall obtain anything of value from the application is another question, 
and Pearson's original statement about Boas' coefficient that "it differs in the 
simplest cases from the true coefficient of correlation, and often differs con- 
siderably... and its use is liable to be misleading, especially if compared with 
values of the true coefficient found by other processes*" was amply justified and is 
well illustrated by this case. The tetrachoric r t values cluster round the true 
value, the Boas-Yulean never reaches it. In the following table the values of 
the tetrachoric r t , of the coefficient of association Q, of the coefficient of colligation 
<B, and of the Boas-Yulean, Pearson's </>, are recorded with their probable errors for 
all divisions at like ages, since these are the divisions selected by Mr Yule. 
Ages of Husband and Wife. Values of the various Coefficients 
proposed to measure Association. 
Division 
of age 
h 
Q 
0 
18 
? 
•9991 + 
•00018 
•9587 + -0004 
•0711 + 
•0097 
19 
% 
•9965 + 
•00020 
•9197+ -0022 
•1240 + 
•0042 
20 
•7755 + 
0025 
•9932 + 
•00016 
•8895+ -0012 
•2128 + 
•0024 
25 
•8813 + 
0030 
•9734 + 
•00010 
•7919+ -0003 
•5644 + 
•0005 
30 
•9302 + 
0001 
•9745 ± 
•00006 
•7958+ -0002 
•7137 + 
•0002 
35 
•9522 + 
0001 
•9795 + 
•00005 
•8151 + -0002 
•7735 + 
•0002 
Ifi 
•9535 + 
•0001 
•9821 + 
•00004 
•8265 + -0002 
•7948 + 
•0002 
45 
•9630 + 
•0001 
•9846 + 
•00004 
•8381 + -0002 
•8003 + 
■0002 
50 
•9601 + 
•0001 
■9850 + 
•00004 
•8401 + -0002 
•7867 + 
•0002 
55 
•9570 + 
■0001 
•9863 + 
•00004 
•8468+ -0002 
•7658 + 
•0002 
60 
•9471 + 
•0001 
■9864 + 
•00005 
■8471 + -0002 
•7260 + 
•0003 
65 
•9350 + 
•0002 
•9881 + 
•00005 
•8565 + -0003 
•6733 + 
•0005 
70 
•9159 + 
•0003 
•9897 ± 
•00006 
•8656 ± -0003 
•5947 + 
•0007 
75 
•8917 + 
•0006 
•9922 + 
•00006 
■8823 + -0005 
•4932 + 
•0012 
80 
•8450 + 
•0020 
•9946 + 
•00008 
•9013+ -0007 
•3512 + 
•0024 
85 
•8081 + 
•0024 
•9975 + 
•00010 
•9317+ -0013 
•2046 + 
•0046 
The first two divisions were not used because the work of calculating tetra- 
choric tables to the large number of terms in r t required for getting results even 
approximately correct is excessive when r t is large and the dichotomies extreme. 
It will be seen that we very frequently differ by a unit in the second figure of 
r t from Mr Yule's results and that our diagram (Diagram XXI) differs from his 
for r t by being sensibly nearer to the true correlation. He has stopped his series 
before it began to converge properly. 
The following gives the percentage in the least quadrant at each age division : 
18 
19 
20 ■ 
25- 
30 
35 
40 
45 
50 
55 
60 
65 
70 
75 
80 
85 
•0003 
•005 
•031 
•962 
1-92 
2-13 
2-12 
1-88 
1-69 
1-35 
1-10 
•734 
•444 
•216 
•081 
•009 
* Science, Vol. xxx. p. 24. 
