Karl Pearson and David Heron 
233 
by taking as classes Chestnut and non-Chestnut. But in that case his only 
logical standpoint is to assert that inside the Chestnut and outside the Chestnut 
there are no hereditary differences of pigment, that Chestnut is a unit character 
that differs by a unit from all other shades in Bay and Brown. This, however, is 
not a fact as a very little microscopic examination of horse hair would show him, 
Pearson's tables themselves indicate that excluding Chestnut, there is correlation 
of intensity of pigmentation between parent and offspring ; further unpublished 
material indicates that within the Chestnut and for different shades of it the like 
relation holds. If there be a correlation between parent and offspring inside and 
outside Chestnut the value for the fourfold tables in the Chestnut and non-Chestnut 
unit classes must be a minimum and not a maximum value as Mr Yule asserts, and 
his criticism collapses with the fallacies on which he has constructed it. 
The chief of these fallacies is the principle that stress of some kind can be laid 
on the Yulean, or pseudo-rank coefficient proceeding to a limit; the fact is that it 
can be made anything we please by a suitable choice of divisions. The divisions 
which for a given number of cells give it a maximum value are those which make 
the sub-range frequencies of the two variates equal. Every deviation from this 
equality lessens the value of the Yulean, whether the deviation consists in heaping 
up the frequency at one or both ends or in the middle of the variate range. 
In the following table are a few results for the pseudo-ranks coefficient for 
3 x 3-fold divisions of the Husband and Wife Table (see our p. 224). They fully 
substantiate the view that it can be made to take almost any value by a proper 
choice of grouping in the scale classes : 
Wife Groups 
Husband Groups 
Yulean 
Coefficient 
1 
2 : 3—8 
1-6 : 7:8 
•184 
1—6 
7 : 8 
1 : 2 : 3—8 
•254 
1—3 
4 : 5—8 
1 : 2—7 : 8 
•268 
1 
2—7 : 8 
1—2 : 3—4 : 5—8 
•297 
1 
2—7 : 8 
1 : 2—7 : 8 
•551 
1—4 
5 : 6—8 
1_4 : 5 : 6—8 
•605 
1—2 
3_4 : 5_8 
1—2 : 3—4 : 5—8 
•809 
The whole fallacy becomes at once obvious in the light of the class-index 
correlation correction, for even with a 6x6 or 7x7 table wide changes may 
be made owing to changes in the classification influencing the class-index 
correlation*. 
Mr Yule has selected the following Series A for Brother-Brother's eye-colour 
in order to show that decreases to a limit of less than "28. But why should 
he not have taken Series B in order to show that it increases to a value greater 
than -28 ? 
* Cf. Table XI, p. 218. 
Biometrika is 30 
