Karl Pearson and David Heron 
249 
Mean Son 
Eye-Colour 
Stature 
Group 1 
% 
3 . ... 
4 
» 5 + 6 
8 
- -4336/i 
- -5065A 
- -0166A 
+ '1319/t 
+ -6704A 
+ -7513/i 
+ 1 -14147? 
- -8255A* 
- 4778/i 
- -0246/i 
+ -2686A 
+ -361U 
+ -7353/i 
+ 1 -0455/r* 
Standard Deviation o> 
•8247/t 
"8932/i 
•8247A 
'8932/i 
ij uncorrected from above 
77 corrected 
Slope of Regression Line, from r) used as r ... 
True value of r 
Tetrachoric r t \ 
•5217 
■5420 
•5870t 
1 
•5503 
•5074 
•5224 
•5658 
•5189 
•5104 
Can any one continue to assert with Mr Yule that the correlation for eye-colour is 
about i and that for stature is \ ? Is it not clear that for eye-colour in Father 
and Son the value given by Pearson in 1900 is within '02 of the true value ? 
A similar figure (Diagram X) is given on p. 250 for Mother and Son. This is more 
irregular in the terminal groups (which contain 3 - 6 % and 4'6 % 0i ' tne frequency 
only), but it shows the same points. The uncorrected 77 = "4930, the corrected 
r) = '5109 and the regression is - 5459. These are in quite good agreement with 
the value of r as found from contingency, i.e. "4885 (see p. 241), but differ slightly 
in excess from the value given by the tetrachoric r t for the "Mendelian" table, 
i.e. correlation '4817 and regression '5145. It is clear from the diagram that r, 
as regards 77, has been lessened by the deviations from linearity in the terminal 
classes^. Still the slope of the regression line shows that we are far from dealing 
with a correlation of i for there is approximate equality in the variations of the 
eye-colour in mother and son, a M = - 8574 h and a s = 9161 h. 
(12) The Vaccination Data. 
We now turn to the question of vaccination and recovery from small-pox. 
Mr Yule apparently considers either his coefficient of association, or his coefficient of 
colligation, to be the right coefficient to use here. Now both these coefficients are 
* The means in the case of the two terminal arrays had to be somewhat differently treated as there 
is no frequency in the first array of groups 5 — 8 and in the last array of groups 1 + 2. Accordingly if the 
h of the table be 7)3+4, the mean of the first array was found in terms of h- 2 , i.e. the range of group 2 
for that array, and the mean of the last array from 7i6+6+7 for that array, i.e. the range of groups 5 + 6 + 7 
for that array. h 2 and /ig + 6+7 were then expressed in terms of h 3+i , i.e. of h of the table by means of 
the relations between these subranges in the marginal total frequencies for sons. 
t To four figures the value as given in 1900 was -5159. 
£ For divisions as originally given in the Phil. Trans, memoir, Vol. 195 A, p. 106. 
§ See remarks, p. 164 above, on the true measure of correlation. 
Biometrika ix 32 
