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MEMOIRS NATIONAL ACADEMY OF SCIENCES. 



[Vol. XV, 



The best method of calculating the correlation between ratings and scores would therefore 

 be one which takes account only of those cases which the officer felt justified in rating higher or 

 lower than " average." Such a method consists in calculating a " biserial " r. 1 Two such values 

 may be calculated from the present data, one by taking all cases rated above average as the 

 subgroup, and the other by taking all cases rated below average as the subgroup. The following 

 results were obtained: 



Officer 1: 



Subgroup— Above average r=0.202±0.104 



Subgroup — Below average r=0.142±0.094 

 Officer 2: 



Subgroup— Above average r=0. 304 ±0.101 



Subgroup — Below average r=0. 539 ±0.080 

 Officer 3: 



Subgroup — Above average r=0. 549 ±0.089 



Subgroup— Below average r=0. 656 ±0.072 



Evidently the correlation of score with the ratings of officer 1 is insignificant, but the 

 relatively high correlation of scores with the ratings of officer 3 lends support to the theory 

 that this officer made his ratings very carefully, but followed the principle of rating all, con- 

 cerning whom he had insufficient knowledge, 4, or "average." Presumably his inability to 

 differentiate among the great majority of cases was due to the short period of time for which 

 they had been under his observation. Officer 2 seems to have followed the same principle, 

 but less rigidly. Officer 1 must have made his ratings very largely by sheer guess. This 

 statement seems warranted by the evidence of the contingency coefficients given above, 

 showing that his ratings agreed less with those of officers 2 and 3 than the ratings of these two 

 agreed with each other. One more point seems worthy of notice. It is that both officers, 

 whose ratings agree significantly with the total alpha scores of the men they rated, have chosen 

 low-grade men more accurately than high-grade men, unless we suppose that the alpha exami- 

 nation discriminates between grades of ability in the lower end of the scale more efficiently 

 than in the upper end of the scale. Other evidence indicates that the reverse of this is true, 

 for some of the tests are so difficult that individuals of low intelligence fail to score on them, 

 so that their total scores are simpler, and consequently less reliable composites. 



It seemed not desirable to dismiss the ratings of officer 1 finally as being mere guesswork, 

 until their correlation with the beta examination scores had been worked out. The standard 

 deviation of scores of this group was found to be 4.04685 and r=0.2231. This value when 

 adjusted to the com m on basis of "selectedness," as indicated by scores, becomes 0.2S94. 

 Thus, this officer's ratings have a slightly higher correlation with the beta scores than with 

 the alpha scores of the same individuals, but the correlations in both cases are so low and 

 subject to so many accidental factors that they need not be taken into account further. 



After obtaining the relatively good results with the biserial r for the ratings of officer 3 

 it seemed desirable to work out similar coefficients for each alpha test. The following values 

 were obtained: 



Table 99. — Company H, Fifth Battalion, Infantry Replacement Camp, MacArthur. — Officer S, with scores. — (Biserial.) 



1 Pearson, Biometrika, vol. 7, p. \ 



