Karl Pearson and David Heron 
245 
c 
2+* 
4 
5 + 6 
7+8 
Totals 
1+2 
471 
278 
94 
48 
40 
931 
3 
278 
300 
140 
86 
97 
901 
4 
94 
140 
78 
55 
76 
443 
5 + 6 
48 
86 
55 
42 
06 
297 
7 + 8 
40 
97 
76 
66 
149 
428 
Totals 
931 
901 
443 
297 
428 
3000 
Now mark what change must be made in A to correct it to B ; this is 
given by the scheme : 
B-A 
1+2 
3 
4 
5 + 6 
7 + 8 
1 + 2 
+ 98 
- 59 
- 50 
+ 2 
+ 9 
'J 
-59 
+ 137 
-38 
-31 
-9 
4 
- 50 
- 38 
+ 96 
- 3 
- 5 
5 + 6 
- 31 
- 3 
+ 31 
_2 
7 + 8 
XI 
- 9 
- 2 
+ 7 
Can there be any doubt that the scheme B — A marks immensely increased 
correlation ? To pass from A to B, we must accumulate 372 individuals along the 
diagonal as against 11 individuals drawn towards the corners away from this 
diagonal. We take it that only the most captious person could possibly deny 
that to reach B from A, we must transfer individuals in a manner which markedly 
increases the correlation. 
Now consider the change which must be made in G to obtain B. It is given 
by the scheme : 
B-C 
1+2 
3 
4 
5 + 6 
7 + 8 
1+2 
+ 25 
- 54 
-31 
+ 20 
+ 40 
-54 
+ 118 
-43 
-30 
+ 9 
4 
-31 
- 43 
+ 90 
- 8 
- 8 
5+6 
+ 20 
- 30 
- 8 
+ 28 
-10 
7+8 
+ 40 
+ 9 
- 8 
-10 
-31 
To pass from O to B we must transfer 261 individuals to the diagonal ; but 
there is an outward movement of 69 to each corner and a resulting defect of — 31 
in the fifth diagonal cell. There is a total movement of 261 individuals towards 
greater, and of 169 towards lesser correlation. We should have no hesication in 
saying that the correlation of B is higher than that of the C table. We would go 
further and say that until we find a table D in which these movements towards 
the diagonal and towards the outer corners nearly balance we have not yet reached 
a table with a correlation equal to that of B. Consider the table : 
