222 
On Theories of Association 
We have <j> 2 = -1251373 and C, = "3335 against actual r = '3333. A better illustra- 
tion of the value of C 2 properly used could hardly be imagined. 
TABLE XVI. 
Mendelian Inheritance of Recessive Couplets on Pearson's Theory*. 
Case of Four Couplets. 
Number of Recessive Couplets in Parent. 
> 
go 
cd .2 &o 
" a 
<4-( CO • rH 
O ■+=> H 
Id 
iZ5 
We now take 
0 
1 
2 
3 
4 
Totals 
0 
625 
500 
150 
20 
l 
1296 
i 
500 
800 
360 
64 
4 
1728 
2 
150 
360 
276 
72 
6 
864 
20 
64 
72 
32 
4 
192 
4 
1 
4 
6 
4 
1 
16 
Totals 
1296 
1728 
864 
192 
16 
4096 
TABLE XVII. 
4x4 Table for Hoinotyposis in Ivy Leavesf. 
First Leaf. 
(1) 
Under 6-95 
(2) 
6-95—10-95 
(3) 
10-95—14-95 
(4) 
Over 14-95 
Totals 
(1) Under 6-95 
3358 
3133 
452 
41 
6984 
(2) 6-95— 10-95 
3133 
13566 
7497 
1124 
25320 
(3) 10-95—14-95 
452 
7497 
10474 
2889 
21312 
(4) Over 1^95 
41 
1124 
2889 
2330 
6384 
Totals 
6984 
25320 
21312 
6384 
60000 
CP 
a 
o 
o 
<D 
CO 
In the original paper Pearson gives the correlation as "562 + -009. Reworking 
the original table with use of Slieppard's correction it is found to give '567. The 
Table is extremely skew, arid owing to its method of construction — i.e. taking pairs 
of leaves out of 25 gathered from each of 100 plants — it is markedly lumpy. 
The massing into a 4 x 4 table has removed this lumpiness and the result probably 
represents the organic relation between leaves of ivy from the same spray better 
than the original table. We find : 
cj) 2 = -353,307 when corrected for random sampling, (7. 2 = - 51095, and the class- 
index correlation given by r 2 c x x = *870,404, which leads to - 587 for the corrected 
contingency. No investigation has been made of the linearity of the regression, 
but it seems to us that the value of the correlation in its general sense may be 
* Phil. Trans. Vol. 203 A, p. 60. Here is another illustration of Mr Yule's peculiar methods. This 
table takes some calculating, but Mr Yule does not give the table, so that his results might be verified. 
Further any reader of his memoir would suppose that Pearson had applied on this occasion or on 
other occasions tetrachoric r t to tables of this character, whereas the exact contrary is the fact, Pearson 
having been the first to apply product-moment formulae to theoretical Mendelian data, including this case. 
t Phil. Trans. Vol. 197 A, p. 351. 
