iz4 



THE QUARTERLY REVIEW OF BIOLOGY 



believing in the physical existence of g 

 and s. 



Another point which seems important 

 is the following. Professor Spearman 

 writes m ax = r aa g x + r asa s ax , in which 

 r ag and r asa are constant for all individuals. 

 Now, even if we allow that the relation 

 connecting m a with g and s is linear for 

 any individual, it seems to involve an 

 additional, and a rather considerable, as- 

 sumption to say that the relation shall be 

 the same for all individuals tested. As- 

 suming that g and j- really correspond to 

 physical quantities, is there a priori any 

 reason for assuming that they must have 

 the same coefficients for all individuals 

 tested? Must we have 



m ax = r ag g x + r , a s ai 



and 



Way — r a g gy + f a s a Say 



rather than this relation? 



max = Ag x + BSax 



Way = Cgy -f DSay 



Of course, we return immediately to the 

 proof of the existence of the (g, s) system 

 provided (ab, cd) vanishes throughout. 

 However, it appears that Spearman himself 

 recognizes that r ag and r aSa remain constant 

 only so long as the populations tested are 

 sufficiently homogeneous. We find him 

 saying (p. 2.17 et seq_.~): "Another impor- 

 tant influence upon the saturation of an 

 ability with g appears to be the class of 

 person at issue. The most drastic example 

 of this is supplied by a comparison be- 

 tween normal children and those who are 

 mentally defective The corre- 

 lations are much smaller in the case of the 

 normal children. This indicates that with 

 these the influence of the energy [g\ has 

 gone down and that of the engines [s] 



has correspondingly gone up 



No less marked is the tendency on com- 



paring children with adults. As exempli- 

 fying this may be taken the correlations 

 obtained by Otis and Carothers re- 

 spectively for what appear to have been 

 similar tests in each case: 



Analogies 



Completion 



Directions 



Digits, memory 



CORRELATIONS 

 WITH ,5 



Otis, 



Grades 



iv-vm 



0.86 



0.41 



Cat-others' 

 students 



O.71 



53 

 0.45 



"Similarly, Stead has found that even 

 motor abilities have considerable corre- 

 lations with tests of g up to about 1 i-iirj 

 years of age, but not later." 



We seem to find, then, that while in 

 deriving our theory we showed that r a9 <\ 

 and r ata should be constant for all indi- , 

 viduals, in actual practice they vary from 

 group to group. But if from group to 

 group, why not within the group? In 

 fact, we find Spearman going on from 

 what we have just quoted as follows (p. 

 119): "Now, all the changes we have been 

 considering follow a general rule. The-, 

 correlations always become smaller — 

 showing the influence of g on any ability 

 to grow less — in just the classes of persons 

 which, on the whole, possess this g more 

 abundantly." But there seems to be no I 

 clear reason for supposing, if this is true 

 for different classes, that it is not true for 

 individuals within the class; and if this be 

 true, it would appear that any theory 

 which involved a linear relation between 

 achievement, g, and s, could not be cor- 1 

 rect. 



Of course, we still need not throw the 

 theory overboard. It may well be that, 

 provided we keep our group sufficiently 

 homogeneous, we can maintain our lin-| 

 ear relation; which amounts to saying that 





