no. 2.] PSYCHOLOGICAL EXAMINING IN THE UNITED STATES ARMY. 435 



The actual values of the product-moment coefficients from these tables axe as follows: 



Table 96, Officer 1, r = 0.171 

 Table 97, Officer 2, r = 0.321 

 Table 98, Officer 3, r = 0.411 



but for the reasons stated above probably only the first of these is even approximately correct. 

 We might apply a correction or class index correlation, by dividing each one of these coefficients 

 by the corresponding ryC 7 for the vertical marginal frequencies. The values of r y C y for each 

 table are (Pearson, Biometrika, vol. ix, pp. 116-139): - Officer 1, 0.9662; Officer, 2, 0.8242; 

 Office 3, 0.7523. The resulting corrected values of the correlation coefficients are: Officer 1, 

 0.177; Officer 2, 0.397; Officer 3, 0.546. But suspicion is aroused against even these results 

 by the results of application of the same corrections to contingency coefficients for each possible 

 pair of officers. 



To measure the agreement between officers in their ratings the following three contingency 

 tables were formed : 



The raw coefficients of mean square contingency calculated from these tables are as follows: 

 Officers 1 and 2, 0.5045; officers 1 and 3, 0.4029; officers 2 and 3, 0.7390. 



If we attempt to correct these contingency coefficients for class index correlation, we obtain 

 an absurd result for the third, a quantity greater than 1. This result is due to the very low 

 class index correlations for officers 2 and 3, 0.8242 and 0.7523, respectively. In other words, 

 the assumption upon which the class index correction is based does not hold, for these two series 

 of ratings at least. It is evident that both of these officers have given the rating of 4 (average 

 intelligence) to a much greater proportion of individuals than might be reasonably supposed to 

 be of average intelligence, even without taking their scores into consideration. Now the most 

 reasonable explanation of this state of affairs is that these officers have rated a great many 

 individuals 4 because they were required to give some rating, and their observation of the indi- 

 viduals in question had not been extensive enough to furnish them any reliable data upon which 

 to base an estimate of intelligence. They therefore "played safe" and gave all such individuals 

 ratings of 4. 



