Karl Pearson and David Heron 
27o 
colligation &> (it is quite easy to deduce another " coefficient of association " from 
Q, which will have a still less probable error than co, or one from tetrachoric r t 
having a less value than both : see p. 262 ftn.). Further we do not consider that the 
product-moment method (i.e. <f> which Mr Yule erroneously terms the correlation 
coefficient) has any application to these eye-colour data ; it is purely idle to deal 
with the difference between a 'light brown' and 'dark brown' eye as a discrete 
' unit/ 
We next turn to the Father and Son Eye-Colour data. The table for 
16 divisions is: 
For Father. 
6—7 
^=•316 ±'041 
§=•487+ -064 
r t = -421 + -038 
§=•579 ±-045 
r t ='bVl± -037 
§=•684+ -035 
r t =-512+-039 
§=•695 ±-037 
In this case we find : 
Weighted Mean 
Weighted 
Standard Deviation 
Tetrachoric r t 
Association § 
•443 
•605 
•086 
•086 
If we thought range was a measure of variation we should have : 
Range of tetrachoric r t = "31. 
Range of association Q = '34 
It is clear that for these eye-colour tables Q is almost as stable as tetra- 
choric r t . Indeed judged by the probable error test Q is slightly better than 
tetrachoric r t , for we have 
Mean value of 
* 
Brothers and Brothers 
Fathers and Sons 
(r«-r t )/(p.e. of r t ) ... 
(§-§)/(p.e. of§) ... 
3 5 
32 
2-2 
1-9 
35—2 
2—3 
3—4 
4—5 
2—3 
r< =-504+-029 
§=-616± -030 
r t = -405 ±-031 
§=•528 ±-038 
r ( =-385+-035 
§=•549 ±-050 
3—4. 
r t = -391 + -031 
§=•500 ±-038 
,•,,= ■550+ -027 
§=•658 ±-027 
r t = -493 ± -032 
§=•632 ±-034 
4—5 
r t =-276+ -035 
§=•381 ±-049 
r t =-466+-031 
§=•590 ±-034 
r ( =-575+ -032 
§=•716+ -028 
6-7 
r t =-266± -040 
§=•402 ±-062 
^=•374+ -038 
§=•519 ±'047 
>-,= -457 ±-040 
§=•622+ -040 
