r,2 



THE AMERICAN NATURALIST 



[Vol. L 



culation of approximate probable errors which are sufficiently 

 exact for all practical purposes. 



Finally, the most important recent development in the theory 

 of correlation is probably Pearson's novel method of dealing with 

 variates classed in alternate categories only. 40 



The fundamental conception of this method is exceedingly 

 simple. Given the table, 



where the large letters represent any alternative (e. g., Men- 

 delian) characteristic of an individual, and the small letters 

 denote the frequency of occurrence of the several possible combina- 

 tions, it is clear that 



a + c b_±d a + b c + d 

 N ' N ' N > N 

 give the independent probabilities of the two pairs of character- 

 istics. The four pertinent products of these ratios give the 

 chances on the assumption of the independence of the two char- 

 acters A and B, of the four possible combinations. Then if there 

 be no correlation, within the limits of the errors of random 



e which would be expected 

 )endent, gives the familiar 

 • The significance of this 

 Iderton's tables, 41 and this 

 correlation. It has been 



ng the Association of 



jodness of Fit of Theory 

 Also reprinted in Pear- 



