506 ILLINOIS STATE ACADEMY OF SCIENCE 



THE USE AND INTERPEETATION OF COEFFI- 

 CIENTS OF CORRELATION 



Walter S. Monroe, University of Illinois 



Within the last few years the statistical device known 

 as the coefficient of correlation has become extensively 

 used in various phases of educational research. As a 

 result, the interpretation of the coefficient of correlation 

 has become a matter of major iiiportance. In the brief 

 time that is allotted to me I desire to call attention to 

 two conditions which affect the meaning to be attached 

 to a given value of the coefficient of correlation. 



In the first place, the magnitude of the coefficient of cor- 

 relation is affected by a selection of the population from 

 which it was calculated. When studying general rela- 

 tionships it is obvious that we must resort to sampling. 

 For example, if we wish to ascertain the relation between 

 success in Latin and success in English, it is necessary 

 for us to answer this question on the basis of the relation 

 that exists between these two achievements in a limited 

 population. If two populations are selected in a random 

 or unbiased manner the resulting coefficients will not be 

 identical, except by chance. The differences, however, 

 will not generally be large, and if we are justified in as- 

 suming that the selection is a random one, the fluctuations 

 of the resulting coefficients of correlation conform to a 

 general law. For any given value of the coefficient of cor- 

 relation calculated from a known number of cases we 

 can determine the probable error due to sampling by 

 means of the formula 



1 r 2 



P. E.r = .6745 — 



Vn 

 In certain types of educational research the magnitude 

 of the coefficient of correlation is affected by other as- 

 pects of the selection of the population group from which 

 it is calculated. In the case of certain traits, the range 

 of the magnitude of the traits is a potent factor in de- 

 termining the magnitude of the coefficient of correlation. 

 For example, if we are studying the relation between in- 



