30 STATISTICAL METHODS. 



CHAPTER IV. 



CORRELATED VARIABILITY. 



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Correlated variation is such a relation between the magni- 

 tudes of two or more characters that any abmodality of the 

 one is accornpained by a corresponding abmodality of the 

 other or others. 



The methods of measuring correlation depend upon the 

 assumption that the variates of the characters compared are 

 distributed normally about the mode. The method is approxi- 

 mately applicable to cases where the distribution of variates is 

 slightly skew. 



TThe principles upon which the measure of correlated varia- 

 tion rest 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 of B will be as great as that of A or 



Index abmodality of relative 1 

 Index abmodality of subject 



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

 index of modality of the subject, that of the relative will be 

 zero and the coefficient of correlation will be 



Index of abmodality of relative 

 Index of abmodality of subject " m 



The coefficient of correlation is represented in formulas by 

 the letter p. "\Ve cannot find the degree of correlation between 

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

 tion '-'in the long run " which we must consider. Hence we 

 must deal with masses and with averages. 



