ESTIMATION AND TESTING OF FINER GRADATIONS 123 



placed after the children lying in the upper section 

 of Group III. 



But, on the other hand, the principle of rank-ar- 

 rangement must not be carried so far as to insist on 

 assigning a precise place to every child at any cost. 

 Often enough, especially in the middle region, it will 

 be felt to be an arbitrary matter to give N a poorer 

 place than M, because it will have been impossible 

 to arrive at an unequivocal judgment as to the differ- 

 ence in the worth of the intelligence displayed by the 

 two children. The rule for such cases is to give the 

 same rank-number to individuals of equivalent abil- 

 ity, using the number that corresponds to the aver- 

 age of the places that they occupy. Thus, if four 

 individuals that would have occupied the stations 

 5, 6, 7 and 8 seem of equal intelligence, each one re- 



ceives the rank-number 6.5, i. e., - = 6.5. 



4 



In case this process has to be followed repeatedly, 

 the number of rank-differences that are at our dis- 

 posal is reduced, but this disadvantage is more than 

 compensated for by the advantage of avoiding arbi- 

 trariness in the arrangement. It is no misfortune 

 if no more than 20 or even a dozen different rank- 

 numbers are forthcoming in the ranking of a class of 

 30 pupils. 



We shall be obliged to dwell somewhat longer on 

 the matter, already broached, of the dependence of 

 the series of estimations on the pedagogical rank- 

 order. The greater the role played by the school's 

 rank-order in the ordinary management of the class, 

 the greater will be this dependence. But there pre- 



