no. 2.] PSYCHOLOGICAL EXAMINING IN THE UNITED STATES AEMY. 441 



The deviations for the rating classes used in the calculation of Table 101 were obtained for 

 each company separately, taking into account all ratings in the company, even though some of 

 the cases are not actually in the contingency tables. This was considered a logical requirement 

 of the supposition that ratings were to be treated as class ranks, rather than as absolute values. 

 Since all of the men in a company who were rated at all were probably ranked individually, to 

 a greater or less extent, as well as in classes, it seemed best to determine the deviation values 

 for each rating class on the basis of the total frequencies in each class in the company. Thus 

 the frequencies of each rating and the deviation values of the latter for each company are as 

 follows: 



Rating. 



7 

 6 

 5 

 4 

 3 

 2 

 1 



1.7137 

 .6533 



- .1319 



- .7895 

 -1.4954 

 -2.3532 



2.0983 



1.35715 



.8711 



.0675 



- .9586 



-1.8987 



-2.6655 



2.1646 

 1. 2525 

 .3914 

 - .6617 

 -1.7249 

 -2. 1298 

 -2. 6655 



2. 0626 

 1.2063 

 .5242 

 - .3379 

 -1.2923 

 -1.6230 

 -2.4394 



2. 1749 

 1. 3356 

 .6810 

 - .1521 

 -1.0592 

 -1.7230 

 -2.3857 



166 



160 



The data of Table 101 are the results of correction of the corresponding values of incomplete 

 contingency tables for the limitations of range displayed by the various tests, in all cases except — 



(a) Test 3, beta: The wide departure of the distribution of scores for this test from the 

 approximately Gaussian type of all other distributions precludes correction of the type used for 

 other tests. 



(6) The range of test 6, beta, was clearly not limited, so far as this particular group of cases 

 was concerned, as indicated by the vanishing frequencies at both ends of the scale. 



(c) Beta total score: Although the component scales of beta are in most cases limited at 

 one or both ends, the distribution of total scores of course does not show high terminal frequen- 

 cies, and consequently the need for correction is not present. The results for beta total score 

 are, however, not directly comparable with the results for its components; as, for example, 

 mean total score with sum of separate test mean scores, owing to the fact that the latter are 

 corrected, in one case for limitation at upper end (test 1), in another case (test 7) for limitations 

 at both ends, and other cases, except tests 3 and 6, for limitations at lower end. The sum of 

 these means, therefore, is the mean value of scores of constant heterogeneity at all levels, which 

 beta raw scores obviously are not. 



The corrections for several of the alpha and beta tests of nearly unlimited range actually 

 result in values differing only insignificantly from the values that would have been obtained if 

 the small degree of limitation had been ignored. But it has been considered best to treat all 

 tests uniformly, in view of the necessity of special treatment of some, in order that the results 

 may be more uniformly comparable. 



The corrected value of the constants given for alpha total score are based on the incomplete 

 contingency table of individuals scoring 30 points or more, on the supposition that toal scores 

 below this value are unreliable, since usually not all of the component tests are represented. 

 For comparison the uncorrected constants determined from the complete table, ignoring the 

 obvious foreshortening of the scale, are given. The difference between corrected and uncor- 

 rected values is not great, but in agreement with the supposition of unreliability of the lower end 

 of the alpha raw total scale. 

 121435°— 21 29 



