132 Influence of "Broad Categories" on Correlation 
Therefore 
S f^yt\'_. 240,51548, 
\Jy a x (Jyj 
•240,51548 
= -•2762, 
and 
•9661 x -9014 
r C x C,J( r x C x r y C y ) = - '3171 
In the above table each row is first multiplied by the y t on the left and the 
final sign at once given to the product; this forms the lower half of the table. 
The columns are then added up with the results given at the foot. The column 
sums are then multiplied by their respective x s 's, shown at the top of the first 
half of the table, regardless of the sign of x s , and the sum divided by 1725 as a 
continuous operation on the calculator, which shows finally -240,51548. 
The value ultimately obtained, -32, is somewhat less than the "33 of the con- 
tingency result but of the same order for all practical purposes. 
I next reduce my table to a 4 x 4 table as follows : 
Intelligence. 
be 
g 
!S 
o 
o 
B+C 
D 
E 
F+G 
Totals 
I 
81 
113 
209 
233 
636 
II 
141 
202 
255 
153 
751 
III 
97 
70 
61 
37 
265 
IV and V 
.30 
22 
10 
11 
73 
Totals 
349 
407 
535 
434 
1725 
We have 
x s = - 13934, --4758, + -2428, +1-2674, 
y t = - 1-0066, +-2173, +1-2130, +2-1317, 
S ( ) = -868,606, 
8 
r rCj = -9320 
Proceeding as before by formula (xvii) we find 
- -228,76485 
•812,475, 
r vG =-9014. 
' xy ~ -868,606 x -812,475" ' 3242, 
a result which is again in excellent agreement with the previous ones. 
Lastly I convert my table into a 3 x 3 table : 
Intelligence. 
fee 
g 
IS 
+= 
JO 
O 
B+C+B 
E 
F+G 
Totals 
I 
194 
209 
233 
636 
II 
343 
255 
153 
751 
III + IV+V 
219 
71 
48 
338 
Totals 
756 
535 
434 
1725 
The negative sign shows that worse intelligence is associated with the poorer clothing. 
