316 



MEMOIRa NATIONAL ACADEMY OF SCIENCES. 



[Vol. XV, 



rating for general intelligence to the extent of nearly 0.7, in the case of the lower half of the National Army. For higher 

 grades the test is not so useful. The low correlations in the Brooklyn, and Officers' Training Camp groups show this. 

 Also the correlation with marks attained by aviators in the studies of the ground school is under O.3. 1 



Table 2 shows the inter-correlations of the ten tests for 313 National Guard men. 



Table 2. — The intercorrelations of the 10 tests for a group of 313 enlisted men. 

 [Table shows coefficients of correlation (r) and their P. E.'s.] 



The last column in table 2 shows the average correlation of a test with the other nine tests. 

 These averages all fall between 0.47 and 0.64. Only those for tests 2 and 8 are as low as 0.50 

 and only those for tests 4, 5, and 6 are as high as 0.60. A test which failed to show a fairly 

 high average correlation with intelligence tests picked by competent judges would probably 

 not be worth much as a measure of intelligence. On the other hand, if a test correlated almost 

 perfectly with some other test in the battery, it could be omitted without loss. Accordingly, 

 the intercorrelations of the tests and their correlations with officers' ratings are important in 

 determining the proper weight to be given to the separate tests. 



The following is quoted from Thorndike's report as chief of the statistical unit in the initial 

 experiment with the group examination: 



The group test is to be used to prophesy the mental ability which a man will display in the Army. Our best attain- 

 able measure of that is the rating for mental ability given to men by their company commanders. If any one of the 

 10 tests correlates zero with officers' ratings, it deserves zero weight in the composite score used for the prophecy. If 

 it correlates highly it deserves much weight, other things being equal. The other things to be equal are its correlations 

 with the other nine tests. The general principle is that the lower it correlates with them, the greater weight it should 

 have in the composite. For, in proportion as two tests intercorrelate closely, they are repetitive — i. e., are measures 

 of the same fact — and a high weight to each of them will mean an undue weighting of the same fact. The lower the 

 correlation of this fact with the fact to be prophesied, the more excessive would the weighting be. 



A fair approximation to the weighting discoverable by a full treatment of partial correlation coefficients and a fully 

 derived regression equation may then be secured by simply observing which tests correlate relatively closely with 

 officers' ratings and relatively little with other tests of the 10. 



The facts secured by us in the case of companies C, D, and L of the National Guard (tested by E. K. Strong in 

 July and August) justify these conclusions: (1) That any convenient weighting of the 10 tests will give a prophecy not 

 much inferior to that obtained from the best possible weighting. (2) That any convenient system for giving tests 2, 

 7, and 9 less, and test 3 more weight than the others will improve the prophecy. The correlations of each test with the 

 officers' ratings and the averages of its nine correlations with the other nine tests are as shown in table A. The points of 

 importance may be still better seen by expressing the facts of table A as differences from the average correlation as is 

 done in table B. Thus test 1 is seen to be somewhat above the average in closeness of correlation with the officers' 

 ratings, but also to be somewhat too repetitive of the other tests. It is intrinsically a good symptom of mental ability 

 in the Army, but its contribution is in large measure contained in or duplicative of the other nine tests. Test 2 is not 

 intrinsically a very good symptom of mental ability, but it does have the merit of contributing a good deal that the 

 other nine tests do not include. Test 3 is above the average of the 10 tests in its closeness of correlation with officers' 

 ratings; it also is less repetitive of the other nine than the average. So it is clearly a test to be given extra weight. 



' The conventional letter "r" is used in this report to represent a coefficient 0/ correlation. A probable error is designated by "P. E." 



