Karl Pearson 
Southampton. 
137 
Si 
3 
Over 30-15 
30-15—29-95 
Under 29 -95 
Totals 
Over SO- 15 
545 
148-5 
26-5 
720 
30-15— 29-85 ... 
263-25 
340-75 
217-5 
821-5 
Under 39-85 ... 
83-75 
288-75 
1008 
1380-5 
Totals 
892 
778 
1252 
2922 
We have raw N<fr = 1449 - 52. 
</> 2 corrected for number of cells = "494,7023, G = '5753. 
•5753 
ThuS : Vxy ~ -8823 x 8736 
Found by the product-moment method* 
•7464. 
Without Sheppard : r xy = -7752 ± -0050, with Sheppard : r xy = "7802 ± '0049. 
Thus the difference is more than four times the probable error, but is not of a 
nature upon which any sweeping conclusions would be drawn. Indeed some 
might prefer the value drawn from the corrected 3 x 3-fold table, owing to the 
distrust of isolated outlying observations which often widely modify the constants 
of a distribution calculated by product-moment methods. 
To still further test the pliability of the method, I rearranged the data in 
a 3 x 3-fold table with markedly unequal frequencies but nearly equal ranges, 
thus : 
Southampton. 
3 
31-05—30-15 
30-15—29-25 
29-25—28-35 
Totals 
30-85—29-85 ... 
808-25 
733-25 
0 
1541 -5 
29-85—28-85 ... 
83-75 
1223-25 
45-5 
1352-5 
28-85—27-85 ... 
0 
14 
14 
28 
Totals 
892 
1970-5 
59-5 
2922 
A more unpromising series of totals is hardly likely to be met with ! We 
have 
x s = - 1-1479, -I--4467, + 2-4133. 
s(-|g) = -635,4498, ^='7972. 
y t = --75U, +-8044, +2-6797, 
^(fD = " 568 ' 5512 ' ^ = -7540. 
Thus we reach some of the lowest values we have come across for >'. r c x anf ' 
r yC in the case of threefold divisions. 
* In Phil. Trans. Vol. 190 A, p. 453, the value -7572 was printed in error for -7752. 
Biometrika ix 18 
