Karl Pearson and David Heron 
265 
It will be seen that the mean weighted tetrachoric r t differs only by - 0086 from 
the true product-moment value ( - 7800). Further the variability of the association 
coefficient marks an increase of 42'4°/ 0 on the variability of the tetrachoric r t * ; 
there can be no doubt that in this first of Mr Yule's selected markedly skew cases 
the tetrachoric coefficient is far more stable than the association coefficient. 
Another method of approaching the problem will also illustrate this point. Let 
us express the deviations from the means in the case of both coefficients in terms 
Diagram XVIII. Comparison of r t and Q for Correlation of Barometric Heights, 
nine cases, r t only one case outside 2-5 times the probable error. 
Barometer Heights. Southampton and Laudale. 
Q ha 
0 1 2 3 4. 5 6 
Percentage in smallest quadrant. 
of their probable errors, and then average these deviations : the mean value of 
(Q - mean Q)/(probable error of Q) = S'S5, the mean value of (r ( - mean r t )j 
(probable error of r t ) = I."63. Clearly Q is 100 °/ 0 worse than r t . This is indicated 
on the accompanying Diagram XVIII, where the values of Q and r t are plotted to 
the percentage frequency of the smallest quadrant of the table, a matter which 
* As both Q and r t have the same possible range of variation - 1 to + 1, in such a case the standard- 
deviation and not the coefficient of variation properly measures the variability. 
Biometrika ix Si 
