PAPERS OX PSYCHOLOGY AND EDUCATION 509 



interested somewhat in the closeness of this relationship, 

 bnt since it is slight we have answered the question in 

 so far as we are able when we have determined that a 

 positive relationship does exist. On the other hand, 

 when we are dealing with the relation between first trial 

 scores and second trial scores on the same test we are 

 not concerned with ascertaining whether a positive re- 

 lationship exists between these sets of facts. We know 

 from onr general experience with educational tests that 

 a relatively high positive relationship exists between 

 first and second trial scores. The question which we 

 wish to answer in this case is how nearly perfect is this 

 relationship, or perhaps to put it into a more effective 

 form, how great are the departures from a perfect re- 

 lationship. If we comjjare the coefficient of correlation 

 with its probable error due to sampling we obtain little 

 or no assistance in interpreting it in snch case. For ex- 

 ample, we might have a coefficient of correlation of .65 

 with a probable error of ± .03. In this case the coefficient 

 of correlation is more than 20 times its probable error, 

 but the relationship between the first trial scores and the 

 second trial scores is far from perfect. 



In order to secure a measure of departure from a 

 perfect correlation the probable error of estimate has 

 been proposed for use instead of the coefficient of corre- 

 lation. It mav be calculated bv means of the formula. 



p. E.E.. = .6:45 P ^' 1 — r,,. 

 The calculation of the probable error of estimate, if the 

 coefficient of correlation is known, involves some very 

 simple arithmetic. It gives a measure of the magnitude 

 of the departures from perfect correlation, or to put it 

 in another way, it measures the amount of change which 

 would be necessary in one set of data in order to bring 

 them into perfect correlation with the other. For ex- 

 ample, the correlation between the number of questions 

 answered by eighty fourth grade children on forms 1 

 and 3 of the Courtis Silent Beading Test Xo. 2. was 

 found to be .87 = .02. In this case the coefficient of cor- 

 relation is 43 times its probable error. This will be 

 recognized as a very high correlation since it is based 



