Karl Pearson and David Heron 
267 
mean of such method when applied is only '048 in error, the contingency method 
giving -3288 and the true value being -3333. We see that, judged by weighted 
standard deviations, the relative variabilities are as 176 to 840, or the stability of 
the tetrachoric r, is 4-8 times as great as that of Mr Yule's coefficient. 
Diagrams XIX and XX. No Q differs by less than its probable error from the weighted mean, 
only one r t differs by more than its probable error. 
•7- 
■5 
■4 
! ! <*> 
" ft 
66 00 
Weighted mean Q 
99 
Weighted mean r t 
** 
34 56 789 10 11 
Percentage of total in smallest quadrant. 
12 13 14 15 16 
We can look at this from the standpoint of the diagrammatic representation 
of the probable error (see Diagrams XIX and XX). In the lower figure we have 
the 16 points given by tetrachoric r t ; only a single one (shown by the individual 
linked with the non-black circle) is at a distance more than once the probable 
error from the weighted mean. In the upper figure not a single case occurs in 
which Q differs by so little as its probable error from the weighted mean value. 
34—2 
