510 ILLINOIS STATE ACADEMY OF SCIENCE 



upon data of children from a single school grade. The 

 probable error of estimate is 4.6. This means that in 

 tifty percent of the cases one set of scores departed from 

 perfect correlation with the other by more than 4.6 nnits. 

 Since the average score is approximately 40 this amounts 

 to about twelve per cent of the magnitude of the aver- 

 age scores. 



In the formula for the probable error of estimate it 

 will be noted that its magnitude depends upon the stand- 

 ard deviation of the distribution of the data from which 

 the coefficient of correlation is computed as well as upon 

 the coefficient of correlation. For this reason there is 

 far from perfect correspondence between the magnitude 

 of the probable error of estimate and the magnitude of 

 the coefficient of correlation, even when the difference 

 in the size of units is recognized by taking the ratio of 

 the probable error of estimate to the average. For ex- 

 ample, a certain collection of paired facts yielded a co- 

 efficient of correlation of .52. The probable error of 

 estimate was 6.4 and the ratio of this to the average was 

 .33. Another collection of data yielded a coefficient of 

 correlation of .8, a probable error of estimate of 1.4 and 

 the ratio of the probable error of estimate to the average 

 of .14. A third collection of data yielded a coefficient of 

 .51, a probable error of estimate of 17.6, and a ratio of 

 .37. It will, therefore, be seen that widely different 

 probable errors of estimate may be obtained for coeffi- 

 cients of correlation of approximately the same magni- 

 tude. 



