no. 2.] PSYCHOLOGICAL EXAMINING IN THE UNITED STATES ARMY. 459 



Table 126 gives the various coefficients of relationship between test performance and 

 military efficiency for the Camp Meade data. 



Table 127 presents the results of comparing special groups in other camps by the method 

 of ratios of differences of means to their probable errors. This table gives for every comparison, 

 first, the difference between means; second, the ratio of that difference to its probable error; 

 and, third, in parentheses, the rank of the test concerned with respect to the other seven tests. 



Table 128 presents the x 3 values for the same set of comparisons. The numbers in parenthe- 

 ses are the ranks of the tests for each comparison. Numbers single starred are those derived 

 from distributions which intersect more than once, and are consequently slightly affected by the 

 factors other than thoseof prime importance for the evaluation of tests. This inaccuracy, however, 

 is practically negligible. Numbers double starred are those which are affected in the same way 

 to a much greater degree. It will be noted, however, that such cases occur usually when the dis- 

 tributions compared are so nearly alike that their differences may be entirely due to chance 

 factors. No use, therefore, will be made of these cases in the interpretation of results. 



Figure 1 represents diagrammatically a comparison of the rank orders for tests derived 

 from the methods of analysis. The vertical dotted lines in the chart represent diagrammati- 

 caUy the various groups compared, as designated at the top. Two inset numbers are carried 

 by each double-pointed arrow. The number in the circle is the rank of the test with respect to 

 the others for the comparison of the two groups indicated by the points of the arrow by the 

 X 2 method of comparison. The number in the square is the corresponding rank for the method 

 of the ratio of the difference to its standard deviation. It will be seen that there is generally 

 close agreement between the two sets of ranks. As already pointed out, however, it seems 

 safer to base conclusions on the x 2 test. 



The outstanding result is a great variation of rank orders from one comparison to another 

 by either method of analysis. These variations in rank order can scarcely all be due to purely 

 chance factors. As a starting point the order of tests by length of effective range has been 

 compared with some of the orders of tests according to their effectiveness in differentiating 

 between two groups. The distributions for each test of the standard group of 984 cases show 

 that some tests clearly have much shorter ranges than others, with the result that large per- 

 centages of zero scores occur in some distributions since the limitation of range is at the lower 

 end. This order of tests according to range is given approximately by the middle column of 

 Table 129. Test 2 has probably the longest range and test 7 the shortest. It is reasonable to 

 suppose that tests failing to measure the lower grades of ability will be considerably handi- 

 capped by this fact in differentiating between low-grade groups. Those tests having the longest 

 range, other things being equal, may be expected to differentiate most sharply between low- 

 grade groups. Reference to table 129 shows that the pattern of differentiation denned by the 

 comparison "poorest" Infantry v. standard agrees rather closely with the order of tests accord- 

 ing to their lengths of range. The chief difference is that the differentiation by tests 4 and 7 

 is apparently better than was to be expected in view of their short range handicap. 



In the case of the next higher group, "poorest," Field Artillery, v. standard, tests 1 and 2 

 rank lowest, and 4, 7, and 8 (especially 7) show a greatly increased sharpness of differentiation. 

 A direct comparison of differentiation patterns for ' ' poorest," Infantry, v. standard and "poorest," 

 Field Artillery, v. standard (Table 130) indicates that these two differ in the relative positions 

 of 1, 2, 6, 7, and 8, while 4 has the same rank in both. Tests 1 and 2 differentiate most sharply 

 the ' ' poorest ' ' Infantry from standard and least sharply ' ' poorest, ' ' Field Artillery, from standard 

 while 6, 7, and 8 play relatively more important rdles in the differentiation pattern for "poorest, " 

 Field Artillery, v. standard. Next considering the two differentiation patterns "best," Field 

 Artillery, v. standard and "best," Infantry, v. standard (Table 131), almost a complete reversal 

 is found. Tests 6 and 7 for "best," Infantry, v. standard, and with the exception of 5 are 

 the smallest factors for "best," Field Artillery, v. standard. On the other hand, tests 1 and 2. 

 though not definitely least important for the "best" Infantry differentiation, are definitely infe- 

 rior to 6 and 7; and, though not clearly most important in the other comparison, do definitely 

 outweigh the least important ones which include 6 and 7. 



