no. 2.] PSYCHOLOGICAL EXAMINING IN THE UNITED STATES ARMY. 439 



ample, in the same class in our contingency table, whether they are all rated by the same 

 person or not, the computed measure of relationship will be affected by factors other than those 

 relevant to the problem. 



The effect of such fortuitous factors is best seen from the following formula expressing the 

 correlation and standard deviations of a combination of two distributions in terms of the com- 

 ponent r's and standard deviations, and the difference of means : 



N N 

 N<r x <r y r XT = N 1 <j I1 o- yi r Iiyi + N 2 o- I2 <r y2 r I2 y 2 + —^ (x, - x 2 ) (y t - y 2 ) . 



Thus the means of both variables being different in the two distributions, the third term of 

 the above formula is not zero, and contributes to the magnitude of the correlation coefficient 

 of the combined distribution. If, as in the present study, one of the variables, say x, is "rat- 

 ing," and we suppose ratings to be not absolute quantities, but class ranks, then the contribu- 

 tion of the third term in the formula to the correlation of the combined distribution is wholly 

 irrelevant. It is necessary, therefore, to equalize the mean ratings of all groups before they are 

 combined. This may be done by treating the class intervals on the rating scale as intervals 

 on the axis of abscissae of a normal probability curve, their lengths determined by their fre- 

 quencies, and their deviation values as best expressed by the deviation from the center of the 

 normal curve of the mean of the segments whose bounding ordinates are thus fixed. 



Summarizing, then, with reference to the three points raised on page 432: 



(a) Qualitative differences in ratings do quite evidently exist, and it is suggested that in so 

 far as one is limited to subjective estimates of intelligence for a comparison of tests, he should 

 work for a qualitative mean, if such a term is permissible, by obtaining ratings made by as many 

 different individuals as possible, rather than by multiplying the number of cases rated by the 

 same individual. The latter procedure evidently reduces the accuracy of the ratings, whereas 

 the greatest possible accuracy of each kind of rating Is necessary. The point is again empha- 

 sized that, speaking in statistical terms, the kind of sampling dealt with is not of individuals 

 tested and rated, but of individuals rating those who are tested. 



(b) The analysis of the ratings of officer 3, Infantry Replacement Camp, MacArthur, brings 

 out the relation between extensiveness of observation of the subject to be rated and the accuracy 

 of this rating. The low correlations obtained from most of the Beauregard and MacArthur 

 data are, therefore, to be regarded as mainly accounted for by the known brevity of period 

 during which the officers had an opportunity to become acquainted with their men. Con- 

 versely, the same considerations lead to the conclusions that the Meade ratings are rather un- 

 usually accurately made. 



(c) Ratings are essentially class ranks rather than absolute measures and should be treated 

 accordingly. The low correlations from the Beauregard and MacArthur material are probably 

 partially due also to the mixture in the same contingency table of many different sorts of ranks, 

 thrown into classes according to the purely arbitrary class symbol with which they happened 

 to be labeled. 



The final problem is to obtain a correlation coefficient for each alpha and beta test from a 

 composite mass of data, with the conditions that as many different kinds of ratings as possible 

 shall be represented, and that these ratings shall be as accurate as possible. These conditions 

 eliminate the Beauregard and MacArthur data, owing to the probable inaccuracy of the ratings, 

 although by this elimination we sacrifice (probably, but not certainly) a great variety of ratings. 

 In the Camp Meade material there are alpha and beta records of men from five different com- 

 panies, so that at least five different rating officers are represented. There are 672 alpha cases 

 and 416 beta cases available. 



One further point needs to be considered. Thus far all correlations have been calculated 

 without regard to the different lengths of effective range of the different tests. In other words, 

 all correlations given so far are class-index correlations, and not correlations of the variates 

 represented by the class indices. Thus the zero class interval has been treated as if of length 

 equal to any other class interval. 



