Karl Pearson and David Heron 227 
TABLE XX. 
First Brother. 
1 
2 
3 
4 
5 + 6 
7 
S 
Totals 
1 
16 
38 
19 
10 
3 
6 
6 
98 
2 
38 
404 
205 
53 
65 
41 
27 
833 
3 
19 
205 
418 
97 
56 
78 
28 
901 
k 
10 
53 
97 
168 
47 
50 
18 
443 
5 + 6 
3 
65 
56 
47 
70 
42 
14 
297 
7 
6 
41 
78 
50 
42 
72 
8 
297 
8 
6 
27 
28 
18 
14 
8 
30 
131 
Totals 
98 
833 
901 
443 
297 
297 
131 
3000 
variates. Now it is clear that there is no such general rule about the correlation 
of pseudo-ranks always moving in one direction. It is possible within certain 
limits to vary that correlation in an almost endless manner according to where 
we take our divisions. It is far more influenced by the size and position of our 
"brackets" than by whether we work with a 3 x 3-fold or a 7 x 7-fold classification. 
We can choose in this case a 3 x 3-fold table to give this spurious coefficient of 
Resemblance of Eye-Colour in Brothers. 
Order of 
Table 
Nature of Divisions 
Pearson's 
Contingency 
Yule's 
Pseudo-Ranks 
7x7 
1:2:3:4:5+6:7:8 
•51 
•29 
1st 6x6 
1+2:3:4: 5+6 : 7 : 8 
•52 
•29 
2nd 6 x 6 
1:2:3:4: 5+6 : 7+8 
•49 
•29 
5x5 
1+2:3:4: 5+6 : 7+8 
•50 
•30 
1st 4x4 
1+2:3:4: 5+6+7+8 
•51 
•33 
2nd 4x4 
1+2+3 : 4 : 5+6 : 7+8 
. -53 
•27 
3rd 4x4 
1 + 2 : 3 + 4 : 5 + 6 : 7 + 8 
•44 
•27 
1st 3x3 
1+2+3 : 4 : 5+6+7+8 
•54 
•29 
2nd 3x3 
1+2 : 3+4 : 5+6+7+8 
•44 
•30 
3rd 3x3 
1+2:3: 4+5+6+7+8 
•50 
•36 
Mean 
•498 
>-28* 
Mr Yule any value from "19 to almost '-iO. This flows from the fact that the 
class-index correction may take a wide range of values according to the arrange- 
ment of the classes, and Mr Yule makes no allowance whatever for this factf. 
* " Can we have any hesitation in similarly estimating the correlation for the eye-colour table, if we 
were in a position to adopt a finer and more uniform grouping (without assuming that we will compel 
that grouping to give us a normal distribution) as something slightly less than 0-28?" Yule, loc. cit. 
p. 619. 
t It is not possible to correct the Yulean pseudo-ranks correlation (i) for"passing from ranks to 
variates, because Mr Yule not only rejects any appeal to the Gaussian, for which we know the proper 
correction, but because his assumption of unit ranges precludes the use of that curve, nor (ii) for class- 
index correlation, because the same assumption hinders any rational method of finding the class-index 
correlations. 
29—2 
