508 ILLINOIS STATE ACADEMY OF SCIENCE 



It is, therefore, necessary to take into account the type 

 of selection that is made as well as its random character. 

 It is not enough to make the selection of data in an un- 

 biased way. In addition, one must interpret the co- 

 efficient of correlation that is obtained with reference 

 to the particular type of selection that has been followed. 

 If all of the data have been obtained from the pupils be- 

 longing to a given half grade, the interpretation will be 

 generally on a distinctly different basis from that to be 

 followed if the data were selected in a random way from 

 the pupils belonging to a sequence of several grades. 



My second thesis is that the meaning to be attached 

 to the numerical value of a coefficient of correlation de- 

 pends upon the type of relationship being studied. For 

 example, if we were studying the relation between general 

 intelligence and quality of handwriting, a coefficient of 

 correlation between these two traits of .40 would be high. 

 If we were to obtain this result for a representative stud- 

 ent population drawn from the sequence of several 

 grades, we would be justified in asserting that for this 

 group the relationship between general intelligence and 

 quality of handwriting was very high. On the other 

 . hand, if we were studying the relation between first trial 

 and second trial scores on an intelligence test we would 

 consider a coefficient of .40 exceedingly low, if it was 

 based upon a representative group of pupils from a 

 sequence of several grades. In order for a coefficient of 

 correlation to be considered high in this case it would 

 need to be .80 or larger. 



When these two illustrations are analyzed with refer- 

 ence to the questions we are attempting to answer by 

 means of the coefficient of correlation, w^e find that we 

 are dealing with questions which are not identical. In 

 the case of the relationship between general intelligence 

 and handwriting we are primarily concerned with ascer- 

 taining whether or not any relationship exists. If any 

 does exist, it is very small. If we secure a positive co- 

 efficient of correlation which is three or four times larger 

 than its probable error, we have evidence of a positive 

 relationship between these two trials. We are, of course, 



