230 
On Theories of Association 
The Mendelian £ should come at once by the simple division of the tables into 
Chestnut and not-Chestnut and it comes pretty closely indeed by taking only the 
Chestnut groups of the 3 x 3-fold tables, as indeed it must do if we remember the 
rarity with which a Chestnut x Chestnut gives other colours. Our four tables 
become : 
Sire. Sire. 
o 
O 
o 
O 
N.-C. 
C. 
Totals 
N.-C. 
C. 
Totals 
N.-C. 
C. ... 
742 
189 
179 
190 
921 
379 
N.-C. 
C. ... 
632 
146 . 
126 
146 
758 
292 
Totals 
931 
369 
1300 
Totals 
778 
272 
1050 
Dam. 
Dam. 
N.-C. 
C. 
Totals 
N.-C. 
C. 
Totals 
N.-C. 
C. ... 
575 
162 
122 
141 
697 
303 
N.-C. 
C. ... 
579 
152 
Ill 
158 
690 
310 
Totals 
737 
263 
1000 
Totals 
731 
269 
1000 
The pseudo-rank correlations, <p, are : 
Sire and Colt: -3094 
Sire and Filly : "3414 
Dam and Colt : -3030 
Dam and Filly : "3638 
Mean = -3294 
Could a better demonstration of the Mendelian ^ correlation be possible ? 
Now let us look at a similar arrangement of other data in which the true 
correlation is actually known. We take the following cases with approximately 
similar total frequencies : 
From Table XV. 
Stature of Father. 
From Table XIV. 
Gaussian Surface for '5. 
Son. 
1—4 
5-8 
Totals 
O 
1-4 
659 
97 
756 
<D 
Sh 
5—8 
143 
101 
244 
3 
Stat 
Totals 
802 
198 
1000 
1-4 
5—8 
Totals 
1—4 
658 
98 
756 
5—8 
144 
100 
244 
Totals 
802 
198 
1000 
Actual Correlation -518. 
Yulean <£ ... -308. 
Actual Correlation - 500. 
Yulean <f> ... -302. 
