Karl Pearson and David Heron 
237 
more adequate than the Yulean pseudo-ranks method. It must give better results 
than a process which concentrates at unit-distances and renders any attempt at 
class-index correction impossible. 
Groups 
By Gaussian 
By Yulean 
Value 
Deviation 
Value 
Deviation 
29 S 
29 '6 to 29-9 
30-0 to 30-1 
30-2 
30 -8 to 30-5 
30-036 
30-006 
29- 998 
29'997 
30- 007 
+ -055 
+ -025 
+ •016 
+ -016 
+ •026 
29- 695 
30- 128 
30-039 
30-095 
29-784 
-•287 
+ •147 
+ •058 
+ •113 
- -198 
Mean 
From whole Range 
•028 
29-750 
•161 
- -231 
It may be said that Mr Yule has not used the Yulean to find means ; in 
appearance perhaps not; in actuality he certainly has, for all product-moment 
processes reduce in actuality to rinding the means of arrays. In fact : 
S(n xy xy)/N - xy 
= S(n x xy x )/N-xy 
a x a y 
Here x in the summation term should be really the mean x of the individuals 
in the class n x . Thus in finding r we actually use the means x and y of the two 
variates, the means y x of the y variate for all individuals in the class n x of x's, and 
the mean x of all the individuals in the class n x . Mr Yule's method, as we have 
just seen, must lead to big errors in all these means; it also as we have seen leads 
to big errors in a x and a y . Hence if r comes out near the true value, this can 
only arise from a compensation of errors, the exact measure of which has so far 
only been determined for the case of a Gaussian distribution. 
(11) The Eye-Colour Data. 
We now turn to the eye-colour data for parent and offspring where we think 
Mr Yule has been led into precisely the same fallacies by his method of pseudo- 
ranks as in the coat-colour of horses. The colour shades recognised by Francis 
Galton in his inquiries were : 
1. Light Blue. 5. Light Brown. 
2. Blue, Dark Blue. 6. Brown. 
3. Grey, Blue-Green. 7. Dark Brown. 
4. Dark Grey, Hazel. 8. Very Dark Brown, Black. 
The book of data presented by Francis Galton to Pearson in 1899 contains 
under these entries a record of each family, grandparents, parents, offspring, uncles 
and aunts. No other data concerning the family were provided ; — only quite 
