NEW BIOLOGICAL BOOKS 



iz 5 



for relatively small changes in g, the varia- 

 tion in achievement will be linear. But 

 it would appear that for any complete 

 theory we should require something much 

 more elaborate than the linear (g, s) 

 system. 



So far we have not been concerned at 

 all with what, if anything, g and s really 

 are; with what physical facts they may be 

 identified. Spearman, after rejecting the 

 various explanations which have been 

 made, suggests that we may regard g 

 as a general mental energy, while the vari- 

 ous /s may be taken as the various en- 

 gines in which this energy is utilized. 

 The language, especially as applying to 

 the engines, is somewhat vague; but 

 Spearman nowhere, so far as I have found, 

 explains his conception clearly. The hy- 

 pothesis as stated seems scarcely likely to 

 attract a physicist; to assume that output 

 is given by the sum of the energy input 

 and the efficiency of the engine is an un- 

 usual formula. We might, of course, say 

 that we are dealing with logarithms; but 

 there would appear to be difficulties here. 

 In any case, the hypothesis seems scarcely 

 of vital concern in the present state of the 

 whole theory. If, of course, it were found 

 possible to measure mental energy directly, 

 the case would be different; but until we 

 have some means for measuring it, it seems 

 idle to waste much time identifying it 

 with a factor g, whose very existence, even 

 as a matter of mathematics, is still ques- 

 tionable. 



There are other difficulties which will 

 occur to any reader. One such lies in the 

 highly variable nature of the measurements 

 obtained, and of the results deduced from 

 them. For example, on pages zoz and 

 2.03 Spearman cites the correlations with 

 g which have been found by various 

 workers for different tests. The test of 

 "Opposites" appears three times, with cor- 

 relations with g of 0.89, 0.71, and 0.37. 



Obviously, such values, if obtained in any 

 biometric investigation, would indicate 

 that something was radically wrong. 

 Whether they really indicate that here, it 

 is impossible to say, because we do 

 not know that the three "Opposites" 

 were really the same thing. However, 

 we may reasonably infer from the fact that 

 Spearman refers to them all under the 

 same names, and without indicating in 

 any way that they are different tests, that 

 they are intended to be similar tests and 

 to measure the same thing; and we are 

 forced to conclude, either that the tests 

 themselves were badly devised, or that 

 the quantities correlated cannot be meas- 

 ured in this manner. 



This difficulty, of the large variability 

 of the measurements obtained in similar 

 mental tests on the same subject, has of 

 course attracted the attention of psy- 

 chologists, and Spearman has devised a 

 formula for eliminating its effect. This 

 formula he calls the correction for "atten- 

 uation. ' ' The proof of it, and the circum- 

 stances under which it may legitimately 

 be used, would lead us too far; and ac- 

 cording to Spearman, it is unnecessary to 

 use it in order to establish the vanishing 

 of the tetrad difference. A remark of 

 Spearman's about it (Appendix, p. i, 

 note) may, however, be quoted: "It 

 should be noted that the correction for 

 attenuation only has, and only can have, 

 the virtue of producing on an average 

 the true amount of correlation. Hence, 

 if this true amount is close on unity, the 

 correction will in nearly half the cases 

 produce values greater than unity ', although 

 no such amounts of correlation are actually 

 possible." (Spearman's italics.) With- 

 out questioning the validity of the cor- 

 rection, one can merely report a certain 

 uneasy visceral sensation when correla- 

 tion coefficients greater than unity are 

 mentioned. 





