138 Influence of " Broad Categories''' on Correlation 
Raw N<p = 766-887, corrected 0 2 = -761,0838 and G= '4550, 
r xy = •4550/07972 x -7540) = -7570, 
a result differing only by '02 from that of the product-moment method. 
It will be noticed that I have arranged the material so that the subranges 
are equal. If we work the 3 x 3-fold table out, using Sheppard's correction, we 
find by product-moment 
r xy = -7746, 
which is considerably nearer the mark than the corrected contingency value. 
In this case a poor result is given by the formula : 
the assumption that S (n st x st y st ) = S (n st x s y t ) being by no means satisfactory for 
(i) very non-Gaussian distributions, or (ii) high correlations, when the subranges 
if equal are very large. For equal ranges with a moderate approach to the 
Gaussian distribution and a correlation not much exceeding 0'5, it gives quite 
good results. Thus if we take the table for stature in Father and Son and 
arrange it in practically equal subranges thus : 
Stature of Father. 
58-5— 64-5 
04-5— 70S 
70-O—76-5 
Totals 
Under 67 '5 ... 
86-25 
269 
9-75 
365 
67-5— 73-5 ... 
39-25 
495-5 
129-25 
664 
73-5— 79S ... 
1 
22 
1 
26 
49 
Totals 
126-5 
786-5 
165 
1078 
a 
o 
m 
u 
+-> 
OS 
CO 
we find : 
x s = - 1-6780, --0540, +1-5439, 
^ = -1-0804, +-4387, +2-1022, 
^=•8353, 
l tyt\_.^ Aia±/L =-8454, 
S m ="697,738, 
(JffJ = -714,644, 
Sffe^M = -260,7392, 
Ncr x a y 
xy 
■5229, 
against 
The 
whence 
"5259 by the product-moment methods, 
same table yields by 3 x 3-fold contingency 
JV0 2 = 163 909, corrected <£- = -148,3386, 
G = -3594, 
r x , y = -5089. 
