Karl Pearson 
135 
although the frequencies are not symmetrical or equal, to state the value of r xC 
for the same number of groups with equal frequencies from the table on p. 121, 
and save the trouble of calculating r x g . 
Illustration III. I took the 3 x 3 table for correlation of health in pairs of 
sisters, i.e. 
First Sister. 
CO 
a 
o 
o 
<x> 
CO 
V. R. + R. 
N. H. 
R. D. + D.+V. D. 
Totals 
V. R. + R. 
428 
172 
87-5 
687-5 
N. H 
172 
411 
220-5 
803-5 
R. D. + D. + V. D. 
87-5 
220-5 
238 
546 
Totals 
687-5 
803-5 
546 
2037 
and I determined the contingency. The raw value of Nfi 2 = 4249285, and 
after correction for number of cells = 420'9285. Hence 
<£ 2 = -206,6414, 
0 = -4138. 
Therefore by the value just found for r x (j t'ov three health classes 
Vxy = -801,3866 = ' 5164 - 
I then worked uut r xy by aid of the approximate formula 
-Si 
> ay — 
which gives in this case 
r xy = -4940. 
The value as given in my Huxley Lecture* for the mean of two fourfold 
tables with divisions first between Robust and Healthy and then between Delicate 
and Healthy was "51. The agreement between the three methods appears 
reasonably good. I compared the last value with the same formula applied to 
the original 5x5 table (see Biometrika, Vol. III., p. 166). I found 
\N <j x (x y 
•392,7573*, 
and 
r X!l = -4880. 
It will be clear that fur the type of argument which is generally based on such 
numbers the accordance is very satisfactory. 
* In the case of the 3x3 table this product was -317,2398, which measures the amount of 
correction made by denominator. 
