224 On the Probable Error of a Coefficient of Contingency 
In the examples given below it will be seen that this is only a small part of the 
total correction and thus the main part of the correction is due to the retention 
of the squares and products in the value of (S</)^)^ used in (5). 
(8) Numerical Illustrations. 
I. Contingency between Handwriting and Intelligence in Girls. 
The probable errors of the contingency constants in this table have been worked 
out both in the 1905 and in the 1914 papers and below is given a table showing the 
effect of the corrective terms of the present discussion. 
The new summations required are found to be 
S 
12-788, 
93-144, 
S 
(f ) - ''''' 
.(f) ^57270, 
and in the following equation the numerical values of the various terms of equa- 
tion (xiv) are given in the same order as their corresponding algebraic terms : 
cr% = [-14865 + -09580 - -00918] 
+ [r)58-864 + 97-404 - 1-784 + 58-205 - 22 - 5-365 - -092] 
(1801) 
+ ^yglyyya [57270 + 15982 + 164 - 186 + 870 + 1224]. 
The other calculations are summarised in the table below : 
TABLE I. 
</.2 = -09580, 
1 +<^^ 
•2957. 
Various formulae used 
Blakeman and 
Pearson 
(1905) 
1st Term of 
(xiv) or Pearson 
(1914) 
1st and 2nd 
Terms of (xiv) 
All Terms of 
(xiv) 
V 
•02023 
•02286 
•02709 
•02729 
Probable error of 0-^ 
■01365* 
•01542 
•01827 
•01841 
o"c 
•0285 
•03219 
•03815 
•03844 
Probable error of C 
■0192 
•02171 
•02573 
•02593 
In this table the work has been carried out to four significant figures with a view 
to showing the corrective effects of the various terms. It is apparent that the 
fineness of approximation given by (xiv) in full is more than is required in practice, 
Incorrectly given as ^0042 in Blakeman and Pearson's paper, loc cit. footnote p. 19G. 
