\ III l\l 



Introduction 



lix 



It is, we think, clear that a difference of the order 0*223 is not of much statistical 

 importance in a cell containing 2*, and thus the formula (a) might have been used 

 throughout. We have given the work up to third differences, which much increases 

 tin labour, in order to show the reasonable effectiveness of the shorter hyperbolic 

 formula. 



The following table shows the order of differences from the observed values : 



The ratio (vii) is in no case beyond the bounds of random sampling, and since 

 n u contains n u ', n v ' contains n w ' and n v contains n u , n u ' and n v ' we should expect a 

 high correlation between all these deviations. The actual number 27 in the chosen 

 cell might easily occur in a random sample from a population containing either 28*4 

 or 28-8 in this cell. 



We will now take illustrations of the reverse process of finding r from the 

 observed d/N. 



Illustration (iii). The following table indicates the relation between Athletic 

 Capacity and Intelligence in 1708 Schoolboys : 



A 2 



