Karl Pearson and David Heron 
305 
state of affairs, although the correlation is negatively high. But in such a table 
as Table II the whole character of the correlation is changed by inserting a 
frequency x, less than "5, in this d quadrant. 
The first question to be answered is : If we put a small frequency x in d, how 
are we to take it from the other quadrants ? The only reasonable answer here 
seems to be : " Take it in proportion to their frequencies." Thus Table II 
becomes of the form : 
TABLE IV. 
5 -looo) 
1000/ 
- '-Woo) 
#+23 1 
x 
1000 
! -Togo) 
x + Q 
x 
looo 
1000 
Now can we choose x so that ah — cd = 0, for this Table ? For this we must 
have : 
x 
x 6 1 
x \ 
ToooV 
which leads to x= "1421. 
This shows us that on the Gaussian hypothesis a value of x absolutely 
consistent with a zero being recorded in that quadrant leads to zero association. 
This for most practical purposes would be sufficient. But a little further con- 
sideration here is desirable ; we may write the table in the form : 
TABLE V. 
970-8620 -* 
22-9967 +x 
993-8587 
5-9992+* 
•1421 -x 
6-1413 
976-8612 
23-1388 
1000 
Here x — 0 gives a table of zero association, x = '1421 gives, if we can only 
record to a unit individual, the table of experience, i.e. 
TABLE VI. 
971 
23 
994 
6 
0 
6 
977 
23 
1000 
Now 7) of Table V = - 
Therefore the probable error of x= 1000 times 
1000' 
that of r]. If we find 0 a n for x = 0 in Table V, we have for its value '0003714, 
Biometrika ix 39 
