224 
On Theories of Association 
Here again for practical purposes the mean square contingency gives quite 
good results. It is very unlikely that in practical statistical work stress would be 
laid on a difference of "05 occurring in a correlation of this magnitude. 
We now turn to the table of ages of Husband and Wife taken from the Census 
of 1901. We have first arranged an 8 x 8-fold table in unequal frequency 
groups, as follows : 
TABLE XIX. 
Age of Wife. 
73 
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 
Totals 
15—20 
21—29 
30—39 
40—44 
45-49 
50—54 
55 — 64 
65— 
(1) 15-24 
44112 
194620 
4962 
162 
40 
16 
8 
1 
243921 
(2) 25—34 
15763 
881320 
590180 
14046 
2669 
645 
186 
17 
1504826 
(3) 35-U 
873 
98200 
910238 
388586 
78648 
13986 
3362 
240 
1494133 
(4) 45-49 
90 
6584 
85583 
178474 
251519 
58699 
12223 
576 
593748 
(5) 50—54 
43 
2573 
27000 
56976 
146990 
194509 
53322 
2027 
483440 
(6) 55—5.9 
29 
1166 
10275 
17810 
46192 
110115 
176506 
7847 
369940 
(7) 60—69 
16 
788 
6570 
10233 
21314 
50238 
261167 
102356 
452682 
:(8) 70- 
184 
1257 
1780 
3290 
6759 
36251 
125302 
174830 
Totals 
60933 
1185435 
1636065 
668067 
550662 
434967 
543025 
238366 
5317520 
The following cases were investigated by contingency : 
Order of 
Tcable 
Division 
Contingency 
uncorrected 
for classes 
Wife 
r C x x 
Husband 
r c v y 
6x6 
1 + 2 
3:4:5:6: 7+8 
•7821 
•9470 
•9346 
•88 
5x5 
1+2 
3:4: 5+6 : 7+8 
•7677 
•9447 
•9327 
•87 
4x4 
1 + 2 
3 : 4+5 : 6+7+8 
•7405 
•9312 
•9223 
•86 
3x3 
1 + 2 
. 3+4+5 : 6+7+8 
•6995 
•8959 
•8954 
•87 
The true value of the coefficient of correlation by product-moment method 
= "925. These values in an extreme case of skewness, rendered more complex by 
heterogeneity of the material*, so far from discrediting the method of contingency 
are definitely in its favour. On material given by a 3 x 3-fold or 4 x 4-fold table 
no reasoning is likely to be based which would be modified by a change of - 03 
to "05 in the correlation. We think that for even these exceptional cases — which 
rarely occur without warning in practical statistics — the corrected contingency 
will not lead any one astray f. 
* Skewness of wife's ages = - 71; skewness of husband's ages = -76. The heterogeneity depends 
on the fact that the table represents the ages of all married couples without regard to second or later 
marriages. 
t Here are a few comparisons of results reached by the method of pseudo-ranks with those deduced 
by contingency : 
