David Heron 
121 
give fairly good results if we restrict their use to small values of A and k, while Qa 
may be used with safety for values of h and k as high as 1*5. 
It would be comparatively easy from the values given of the various 
approximations to obtain a formula* which would give still better results and 
could be used over a much larger range of values of h and k, but I have 
purposely refrained from doing so. In any work of importance, it is always best 
to calculate at once the actual coefficient of correlation with the help of Everitt's 
Tables. 
i , — , , 1 i 
1 2 3 4 5 
Fig. 7. Diagram to show the relative degrees of accuracy of various approximations 
to the correlation coefficient. 
* Thus the harmonic mean of Q :i and (for )' = -5) gives quite good results, and the arithmetic 
mean of Q 2 and Q' also. Best of all (for the same special case) appears the arithmetic mean of Qi and 
Q 3 , which cannot be adequately shown as differing from r on the cale of Fig. 7. 
Biometrika vm 16 
