PAPERS ON PSYCHOLOGY AND EDUCATION 507 



telligence and achievement in silent reading, the co- 

 efficient of correlation will be much smaller when calcu- 

 lated from a random selection of the pupils belonging to 

 a single half grade than when it is calculated from a 

 random selection of pupils taken from grades three 

 to eight, inclusive. In a recent study the coefficient 

 of correlation between these two traits was calculated 

 for each half grade from 3B to 8A, inclusive. The co- 

 efficients of correlation range from — .12 to .57. Since 

 there were from 200 to 400 cases in each half gi'ade the 

 probable errors of these coefficients of correlation are re- 

 latively small. When the data from all grades were com- 

 bined the coefficient of correlation for the same two 

 traits was found to be .76. This is distinctly larger than 

 the average of the coefficients of correlation for the 

 separate half grades. 



A more striking illustration is obtained from the cor- 

 relation between chronological age and mental age. In 

 the investigation referred to above, the coefficients of cor- 

 relation were calculated between these two traits for each 

 half grade. These range from — .12 up to — .44. In other 

 words, the correlation between mental age and chronolo- 

 gical age for the pupils belonging to a single half gi-ade 

 is inverse. In general, the pupils who are older chro- 

 nologically tend to be the ones who are younger mentally, 

 and vice versa. "When the pupils from gi-ades 3B to 8 A, 

 inclusive, are grouped together the correlation betv\-een 

 chronological age and mental age was found to be .56. 

 In this instance the coefficient is not only larger but it is 

 positive, although when the pupils were taken by sepa- 

 rate half grades all of the coefficients were negative. It. 

 however, does not always happen that the coefficient of 

 correlation is alfected by the grade range from which the 

 population is selected. For the same pupils the correla- 

 tion was calculated between the intelligence cpiotient and 

 the achievement quotient for arithmetic. When the pupils 

 are taken by separate half grades, these coefficients range 

 from — .19 to — .62. TThen all grades are taken together, 

 the coefficient of correlation was found to be — .41, which 

 is essentially the average of the coefficients of correlation 

 for the separate half grades. 



