228 
On Theories of Association 
We have seen that the corrected contingency gives a good practical approach 
to the actual correlation, even if the material be skew as in the Husband and 
Wife or in the Barometric Data ; are we to argue from the entirely fallacious 
reasoning of Mr Yule that the method is in this case on the average 44 °/ 0 in 
error although in the skew Mendelian table it is only - 06 °/ 0 in error and in 
the Husband and Wife data only 3 - 8 °/ 0 in error ? We shall need some far better 
reasons for believing that the value usually assumed for the correlation of eye- 
colour in brothers, i.e. circa - 50, is in error, than such as Mr Yule seems able to 
adduce. 
Another piece of remarkable special pleading on the same lines is that 
provided by Mr Yule in the case of Pearson's tables for parental heredity in coat- 
colour in horses*. Those tables are remarkable in their nature, because although 
16 classes are formed, there are practically no entries except in the three main 
groups Brown, Bay and Chestnut. Here is the frequency distribution for sires, 
where bl. = black, br. — brown, b. = bay, ch. ■= chestnut, ro. = roan, gr. = grey : 
bl. 
bl.jbr. 
br.jbl. 
br. 
br.jb. 
b.jbr. 
b. 
b.jch. 
ch./b. 
ch. 
ch.jro. 
ro.jch. 
ro. 
ro.fgr. 
gr.jro. 
gr. 
7 
4 
1 
209 
0 
19 
G91 
0 
0 
362 
1 
0 
0 
0 
0 
6 
Now Mr Yule arranges this in 11 classes : 
7 j 5 209 I 19 691 | 6 362 1 0 | 0 | 6 | 
and also in three classes, presumably as : 
j 0 | — | 221 j — | 710 j — | 369 | — j 0 | — | 0 | 
He then obtains sensibly the same values for the two groupings and speaks 
of the equality of the pseudo-correlation of ranks thus obtained as marking in 
some way a limit to the correlation of the variates ! Naturally he would obtain 
almost identical values, because the whole calculation of products and moments 
turns on the three dominating groups of brown, bay and chestnut and practically 
all he has done in his arrangements of three groups and eleven groups is to call 
his sub-range unity in one case and two in the other ! 
There is, we believe, only one classification possible of these tables on the 
reasonable assumption that the amount of pigment forms a continuous variatef; 
namely that which makes a 3 x 3-fold division between brown, bay and chestnut 
* Phil. Trans. Vol. 195 A, pp. 122 et seq. 
f I still see no error in my original classification by amount of pigment ; there are more melanin 
pigment granules in the brown hairs than in the bay, and, — if we disregard the black chestnuts, which 
are very rare among thoroughbreds as compared with hackneys, — more in the bay than in the chestnut; 
the latter colour depends more, and in some cases almost entirely, on diffused pigment. K. P. 
