54 



THE AMERICAN NATURALIST 



[Vol. L 



In this review we shall limit ourselves strictly to * 

 progress which has been made in the theory of the i 

 of the interrelationship of two variates, leaving for considera- 

 tion at a later time the far more complex subjects of correction 

 for grouping, partial and multiple correlation, variate differ- 

 ence correlation and some other topics. 



The detailed advances may be most easily understood by con- 

 sidering the kinds of data with which one has to deal in deter- 

 mining the degree of interdependence, association or correlation 

 (to use these terms in a broad sense) between two variates. 



An arrangement of the literature according to a key similar to 

 that familiar in taxonomic works will perhaps be of service to 

 the biologist who desires to locate at once the literature perti- 

 nent to the particular kind of data with which he has to deal. 



Suppose first of all that the two characters are both suitable 

 for measurement (or counting) on a quantitative scale and that 

 for both the measurements form several classes. The choice of 

 methods for measuring the correlation between them will then 

 depend upon whether the average values of the y character as- 

 sociated with serially arranged values of the x character lie in 

 sensibly a straight line or whether they can best be represented 

 by some more complex curve. Linearity of regression, as it is 

 technically called, has therefore a two-fold significance, (a) 

 Biologically, -it shows that an associated character changes at a 

 uniform rate (however slight this rate may be) with the varia- 

 tion of a selected character, (b) Statistically, it justifies the 

 application of the familiar product-moment method of determin- 

 ing the correlation coefficient. 



Both Characters Measurable on a Quantitative Scale, Regres- 

 sion Linear.— So satisfactory has the product-moment method 

 proved for data in which both characters are measurable and 

 regression is sensibly linear, that no fundamental advance has 

 been made for several years. Boas V first formula is, as pointed 

 °u t 7^ Pearson ' 2 merel y another form of the difference method, 

 which has been in use for many years. 



Several modifications of a purely technical nature which facili- 

 tate calculation or are useful in special cases have been pub- 



N^. F 82^" D ° f ^ C ° effiCieDt ° f ~ 

 2 Pearson, K., "Determination of the Coefficient of Correlation » W™v 



