452 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [vol. xv. 



The complete partial correlation of each a test with officers' ratings has been carried out. 

 The results are of little use as far as the purpose for which such work is usually done is concerned. 

 Inspection of the ninth order coefficients presented in table 124 shows that (1) none of them is 

 large enough compared with its probable error to be clearly significant ; (2) at least two are totally 

 absurd results and can only be taken as invalidating the whole final result. The negative 

 partial coefficients of tests 4 (arithmetic) and 6 (synonym-antonym) mean, if accepted, that to 

 get the best total score the appropriately weighted scores in these two tests must be subtracted 

 from the weighted sum of the others. It is true, of course, that the partial coefficient for test 

 4 is numerically so small that its negative sign is unimportant, but the coefficient for test 6 is 

 numerically one of the largest of the whole series, and had the same result been obtained from 

 1,000 cases instead of 236, its mathematical significance would have been practically as great 

 as that of any of the other partial coefficients. This result can mean one or both of two things — 

 (1) that the "intelligence ratings" upon which these results are based are not qualitatively 

 acceptable as intelligence ratings; (2) that the zero order coefficeints obtained from the original 

 data are erroneous measures of the intercorrelations of tests, and of the correlations of tests 

 with ratings. That (2) is very probably, at least partially, explanatory of the results of table 124 

 is apparent when we take into consideration the fact that none of the zero order coefficients was 

 corrected for length of range of test. It is impossible to guess what effect such correction would 

 have upon the value of the partial correlations of the ninth order, but it is clear that the omission 

 of corrections that effect very considerable changes in the values of some of the zero order 

 coefficients makes any computations based upon them wholly unreliable. 



It may also be pointed out that the 236 cases upon which these results are based were not 

 all members of the same company, and were consequently not rated by the same officer, nor 

 even ranked with respect to each other. That this fact adds one more item of unreliability 

 to the case against our results is clear in the light of the results of the study of the alpha tests. 



The total maximum correlation as determined from the partial coefficients, between the 

 sum, with best weights, of the score in all 10 tests of examination a with intelligence ratings by our 

 particular group of officers is 0.5644. The coefficient was 0.546 with the old weighting (not based 

 on partial correlation) and with tests 2 and 10 omitted and all others weighted equally 0.530. 

 That no great gain over unweighted scores by any system of weighting would result was to 

 be expceted in view of tthe very high intercorrelations, but the actual gain is scarcely even 

 significant for the sample. 



The net result is therefore a negative one. The futility of attempting to estimate the rela- 

 tive values of tests, and their corresponding weights in a composite score when all intercorrela- 

 tions are high is clear. Further, the results strongly suggest, if they do not prove, the falla- 

 ciousness of a partial correlation system based upon zero order coefficients that are not reduced 

 to a common basis of comparability by correction for the limitations of range of measurement 

 of the different methods of measurement they represent. 



The foregoing discussion of the relation of subjective ratings to test performance has not 

 been given without appreciation of one important respect in which such ratings may have 

 a great advantage over intelligence ratings based on psychological tests. The psychological 

 test admittedly measures only what might be termed instantaneous intellectual capacity, 

 whereas what we want to predict is mean effective intellectual capacity, which is the resultant 

 of instantaneous capacity and all of the instinctive and emotional factors which constitute 

 the motivation of the individual. It is not at all improbable that a very high degree of accu- 

 racy has already been attained in the measurement of instantaneous intelligence, but only 

 in a competent observer's estimate of intelligence based upon a considerable period of observation 

 are the factors of motivation taken into account. Herein lies a reason why most correlations 

 between ratings and test performance are between 0.50 and 0.60 instead of between 0.90 and 1 . 



