232 
On Theories of Association 
From Table XVII. Ivy Leaf Length. 
First Leaf. 
Whorls of Woodruff*. 
Members of First Whorl. 
Under 6-95 
Over 6-95 
Totals 
Under 6-95 
Over 6-95 
3358 
3626 
3626 
49390 
6984 
53016 
Totals 
6984 
53016 
60000 
O o 
CO - C - 
u fe- 
ci) t> 
£ s 
cu o 
^ CD 
Under 8 
8 and over 
Totals 
Under 5 
7268 
2281 
9549 
5 and over 
2281 
1400 
3681 
Totals 
9549 
3681 
13230 
Actual Correlation '567. 
Yulean cp ... '412. 
Now let us put together these results in a Table 
Actual Correlation -173. 
Yulean 0 ... -141. 
Actual 
Yulean for 
r - <j> 
Percentage 
Correlation 
Fourfold 
Increase on c/> 
■925 
•686 
•239 
35 
•780 
•566 
■214 
38 
•780 
•531 
•249 
47 
•567 
•412 
•155 
38 
•518 
•308 
•210 
68 
•500 
•302 
•198 
66 
•333 
•243 
•090 
37 
•300 
•167 
133 
80 
•173 
•141 
•032 
23 
Now these results bring out the important point that whether the distribution 
of the frequency be Gaussian or not, we may have to add anything from 23 °/ c up 
to 80°/ o f to the value of as found from a fourfold table to obtain the true 
correlation. For values about - 33 we may have to add anything from 37 °/ 0 to 
80 °/o- For the tables for coat-colour in horses we must add to the Yulean at a 
moderate estimate something like 40°/ o > which gives a value, not near the - 33 of 
Mr Yule, but near our '46 and close to the value found by contingency or closer 
to the values originally assigned by the tetrachoric r, method. 
If Mr Yule continues to assert that the true value of the correlation of these 
tables is J, then he may as well argue from the <j> of the fourfold tables obtained 
* Selected as a case of irregular and skew correlation of a low product-moment value; see Phil. 
Trans. Vol. 197 A, p. 325. 
t One Ivy Leaf distribution as below actually gave Yulean </)='278 against actual correlation 
•567, requiring a 104 (l / n increase on the Yulean ! 
First Leaf. 
Under 11-95 
Over 14-95 
Totals 
TJjnder 14-95 
49502 
4054 
53616 
Over 14-95 
4054 
2330 
0384 
Totals 
53610 
0384 
60000 
