no. 3.] PSYCHOLOGICAL EXAMINING IN THE UNITED STATES AKMY, 



639 



of each test on the total, for combinations of the first two tests, the first three, the first four, 

 etc. These multipliers are as follows: 



We shall assume that a total score value corresponding to the mid-point of each class 

 interval is typical of that interval. Therefore 2J points will be taken as characteristic of the 

 interval 0-4, 7h as characteristic of the interval 5-9, etc. Of course actual scores in half- 

 points do not exist, but this fact does not invalidate their theoretical use. 



Considering first the class interval 0-4, we can scarcely assume scores in a combination 

 of three tests to be typical, if we take its mid-point, 2\, as representative of all scores falling 

 within it, for points earned in three tests must necessarily total to three or more; but, since 

 we are dealing with fractional points, 2h might theoretically be composed of more than h point 

 in each of three tests. We therefore determine whether this is possible. On the assumption 

 of three components in a total of 21 points, d in the above formulae is the difference between 

 21 and the sum of the means of the three variables most likely to be involved, viz, tests 1, 2, 

 and 3. The sum of these three means is 19.5688, and consequently 



d = -17.0688 



Multiplying this value in turn by the values hi the second row of the above table (the first row 

 contains the regression coefficients of 2 and 1, respectively, on the sum of 2 and 1, the second 

 row the regressions of 2, 1, and 3, respectively, on the sum of 2, 1, and 3, etc.), we obtain 



^=-1.48355 



=2= -1.63687 



<r. 



1.55740 



But —1.5570 a for alpha 3 corresponds to 0.2293 points, and since this is less than i point, 

 3 should be rejected from the combination taken as typical of the class interval 0-4. We 

 therefore take tests 1 and 2 as the typical combination, and find the difference between the 

 sum of their means and 2 J. The new d is 10.7611, and using the regression coefficients in the 

 first row of the above table we find: 



^= -1.6283 



^=-1.6949 



Proceeding in exactly the same manner with the class interval 5-9 we find that, if a 

 combination of 1, 2, 3, 6, and 8 is assumed, a deviation of —1.2585 for test 8 results. This 

 value corresponds to —1.0995 points, so that test 8 must be rejected from the combination 

 taken as typical for this class interval. Using 1, 2, 3, and 6, we find: 



^i= -1.1448 ^=-1.2732 ^=-1.1562 

 (jj <r 2 <r 3 



all of which lie above the zero points of their respective scales. 



— 6 =- 1.2158 



