no. 3.] PSYCHOLOGICAL EXAMINING IN THE UNITED STATES ARMY. 



633 



"Tables for Statisticians and Biometricians," where tables for its use are given. Our contin- 

 gency tables, therefore, with respect to the jamming or limitations of the scales range all the 

 way from such tables as alpha 1 and beta 6 (Table 22), in which there is no jamming, to tables 

 like alpha 6 and beta 7 (Table 78), which is jammed on three sides. As indicated above, no 

 general method was applied, but each table was treated according to its own peculiarities and 

 limitations. Thus in curtailing these correlation surfaces two things were taken into account, 

 (1) the shape of the distribution of the two test scores, and (2) the way in which they were 

 disposed or scattered in the table. In the first cases it seemed desirable to eliminate all, or 

 nearly all, of the zero scores. In. some cases scores of 1 or 2 were eliminated with the zeros. 

 Further an effort was made to cut each distribution in such a place that if a normal curve were 

 fitted to the stump the number of cases cut off would just fill up the place provided for them 

 by the curve. This ideal condition was not always attained. It could have been attained 

 had it not been for the fact that it was just as necessary to consider the peculiar limitations of 

 each table separately, for in cutting a table an effort was made to cut deep enough so that the 

 arrays of the noncut variable would be nearly symmetrical. Thus it was necessary to cut a 

 given distribution in various places according to the distribution with which it was paired in a 

 table. In the table below when a distribution appears to be cut twice (each time below the 

 mean) it means that it was sometimes cut at one place and sometines at another, according to 

 the requirements of the table. Beta 7 was regularly cut twice in all tables above and below 

 the mean. This test shows decided limitations at both ends, and hence the first two and last 

 two class intervals were cut off and redistributed. 



Test. 



Alpha 1 • . 

 Alpha 2 . . 

 Alpha 2 . . 

 Alpha 3.. 

 Alpha 3.. 

 Alpha 4 . . 

 Alpha 5 . . 

 Alpha 5 . . 

 Alpha 6.. 

 Alpha 7 . . 

 Alpha 7 . . 

 Alpha 8.. 

 Betal.... 

 Beta 2.... 

 Beta 3. . . . 

 Beta 4.... 

 Beta 5.... 

 Beta 6... 

 Beta 7.... 

 Beta 7.... 



Place cut in class marks. 



Between 1 and 2 



Between and 1 



Between 1 and 2 



Between 1 and 2 



Between 2 and 3 



Between and 2 



Between and 1 



Between 2 and 3 



Between 2 and 3 



Between and 2 



Between 2 and 4 



Between and 2 



Not cut at all 



Between 1 and 2 



Not cut because of very peculiar distribution (see fig. 4) . 



Between and 2 



Between 5 and 6 



Not cut at all (see fig. 4) 



Between 1 and 21 



Between 8 and 9/ 



0.8558 

 .9369 

 .9007 

 .7860 

 .7392 

 .6246 

 .7669 

 .6714 

 .6829 

 .7827 

 .5740 

 .8481 



.9033 



.9198 

 .8672 



.6410 



1 This test was cut in but one table. 



The means and standard deviation used in this study were obtained by taking an arith- 

 metical average of all the possible means and standard of any given variable calculated directly 

 and indirectly. By "directly" we mean calculated from the truncated distribution. By 

 "indirectly" we mean the mean or standard deviation for any given variable calculated from 

 the correlation of that variable with other variables, when the variable in question is always 

 the nontruncated one. It is clear that if a correlation surface is truncated along one variable 

 the mean and standard deviation of the nontruncated variable can be obtained from the cor- 

 relation. The formulae for making these calcidations have already been given immediately 

 above. 



In some surfaces both variables were truncated and in other surfaces neither was truncated. 

 In all cases, however, in which neither or both variables were truncated we did not calculate 

 means or standard deviations indirectly. This fact will explain some apparent gaps in the 

 following tables. Other apparent gaps in the tables can be accounted for if note is taken of 

 the fact that in these tables the variable (i. e., test) in question is always the nontruncated one. 



121435°— 21- 



-41 



