Karl Pearson and David Heron 
229 
and either excludes the few roans and greys or, as done below, throws them into 
the lightest group. The threefold tables are then : 
Sire. Sire. 
79 
132 
47 
258 
105 
426 
132 
663 
37 
152 
190 
379 
O 
221 
710 
369 
1300 
58 
66 
25 
149 
102 
406 
121 
99 
146 
629 
272 
187 
571 
292 
1050 
Dam. 
Dam. 
o 
Q 
82 
101 
33 
73 
319 
129 
23 
99 
141 
178 
519 
303 
63 
106 
34 
83 
327 
118 
23 
88 
158 
169 
521 
310 
216 
521 
263 
1000 
203 
528 
269 
1000 
And the corrected contingency coefficients are : 
Sire and Colt: 41, Dam and Colt: 45, 
Sire and Filly : '47, Dam and Filly : "46, 
Mean : "45. 
Mr Yule states that the correlation is in this case of the order '33. Are we 
again to assert that the mean of the contingency coefficients shows an error of 
•12, or is 36 °/ 0 in excess of the true correlation, when as we have seen the error 
we find in even extremely skew distributions is of the order of 4 °/ 0 and under ? 
Mr Yule says that the correlation of his pseudo-ranks is '33. Well and good, 
then the correlation for variates would be about "35, probably more for skew 
variation, and the factor for correction of class-indices about '80, or the true 
correlation is of the order '35/'80 = '44, which brings it strangely nearer to the 
value found by contingency than to Mr Yule's £ ! 
It is quite true that the values obtained in the original memoir were higher 
than "45, but the theory of contingency was not then developed; when a fourfold 
table had to be formed there were very good reasons for dividing it in the way 
actually selected. In the first place the division between Chestnut and Bay was 
physiologically more reasonable than one between Brown and Bay, which would 
throw the Chestnuts into the Bays. In the next place it was the division nearest 
to the median and so liable to the least error from either random sampling or skew- 
ness. The other, the asymmeti"ical, divisions are less reasonable because they 
give one quadrant with only 2 to 3 °/ 0 of the total frequency in it, they divide 
parent and offspring differently, and mix in one or other case Bays with Chestnuts. 
Let us suppose with Mr Yule that these tables did show a correlation of ^ (which 
they certainly do not), then we fail to grasp why Mr Yule should not get his 
Mendelian \ quite directly without elaborating an erroneous theory of pseudo- 
ranks and using 3 x 3-fold and 11 x 11-fold tables to show approach to a limit. 
