220 On Theories of Association 
TABLE XIV. 
Gaussian Surface for r — - 5 adjusted to give whole units in cells. 
1 
2 
3 
4 
5 + 6 
7 
8 
Totals 
1 
7 
20 
5 
2 
34 
2 
21 
145 
79 
36 
10 
9 
1 
301 
3 
6 
94 
85 
54 
19 
22 
4 
284 
4 
2 
32 
39 
31 
12 
17 
4 
137 
5 + 6 
18 
28 
25 
11 
18 
5 
105 
7 
11 
22 
24 
12 
22 
7 
98 
8 
■2 
6 
8 
5 
13 
7 
41 
Totals 
36 
322 
264 
180 
69 
101 
28 
1000 
magnitude of stature and divided up the frequencies of Father's and Son's stature 
exactly in the eye-colour groups. The following contingency table resulted. 
TABLE XV. 
Stature of Father and Son in Eye-Colour Groups. 
Stature of Father. 
1 
2 
4 
5 + 6 
? 
8 
Totals 
1 
4 
22 
7 
1 
34 
2 
23 
154 
84 
26 
8 
6 
301 
8 
87 
75 
66 
22 
24 
2 
284 
4 
1 
29 
36 
37 
14 
14 
6 
137 
5 + 6 
18 
27 
26 
11 
18 
5 
105 
7 
9 
26 
19 
7 
29 
8 
98 
8 
3 
9 
6 
6 
10 
7 
41 
Totals 
36 
322 
264 
180 
69 
101 
28 
1000 
We have thus one table which for practical purposes is absolutely Gaussian, 
one Gaussian table modified to give units in the cells, and one table typical of 
what occurs in, perhaps, 9 out of 10 cases in every-day statistics. 
The next table gives the results obtained by the method of mean square 
contingency with the appropriate corrections. It will be seen that 3x3 tables 
give as good results as 7 x 7 tables and the method is thus justified for Gaussian 
material and for the bulk of such tables as occur in statistical practice. 
It will be seen not only how closely the mean of the contingency values 
agrees with the product-moment value of the correlation, but how little the 
individual values differ from the mean. Worse cases may possibly be found by 
those who go to seek them by extreme divisions — we have taken them as they 
came, and feel convinced by a wide experience that contingency gives in practice 
remarkably satisfactory results. 
We now take a step further and ask, if we depart from the ordinary run of cases 
and pick out skew distributions, can we place equal reliance on the contingency 
