42 STATISTICAL METHODS. 



CHAPTER IV. 

 CORRELATED VARIABILITY. 



Correlated variation is such a relation between the magni- 

 tudes of two or more characters that any abmodality of the 

 one is accompanied by a corresponding abmodality of the 

 other or others. 



The methods of measuring correlation given below are 

 applicable to cases where the distribution of variates is 

 either symmetrical or skew. 



The principles upon which the measure of correlated varia- 

 tion rests are these. When we take individuals at random we 

 find that the mean magnitude of any character is equal to the 

 mean magnitude of this character in the whole population. 

 Deviation from the mean of the whole population in any lot of 

 individuals implies a selection. If we select individuals on 

 the basis of one character (A , called the subject) we select also 

 any closely correlated character (B, called the relative) (e.g., 

 leg-length and stature). If perfectly correlated, the index of 

 abmodality (p. 23) of any class of B will be as great as that of 

 the corresponding class of A , or 



Index abmodality of relative class _ 

 Index abmodality of subject class ~~ 



If there is no correlation, then whatever the value of the 

 index of abmodality of the subject, that of the relative will 

 be zero and the coefficient of correlation will be 



Index of abmodality of relative class _ _ 

 Index of abmodality of subject class ~~ m ~ ' 



The coefficient of correlation is represented in formulas by 

 the letter r. We cannot find the degree of correlation be- 

 tween two organs by measuring a single pair only; it is the 

 correlation "in the long run" which we must consider. 

 Hence we must deal with masses and with averages. 



