no. 3] PSYCHOLOGICAL EXAMINING IN THE UNITED STATES ARMY. 575 



tions. As a matter of fact, the relationship between alpha total scores and beta total scores, 

 treated as simple variables, is of such a nature that it is very doubtful if good regression equations 

 can be obtained. 



Prof. Karl Pearson has very kindly attempted this problem. Using contingency tables for 

 total scores only he has obtained the equations and curves shown in figures 1 and 2. His 

 material included, besides the data of the special experimental Group X, data from a more 

 highly selected group of 1102 infantrymen from Camp Meade. The equation for the regression 

 of beta on alpha gives very good results both as a fit to the observation points and, as nearly as 

 can be judged, as an extrapolation curve. But Prof. Pearson, however, points out an impor- 

 tant difficulty in dealing with the other regression, that of alpha on beta. He considers (with 

 excellent grounds as will appear later) it unsafe to calculate mean alpha scores for beta arrays 

 below 50 points. (Table 154.) The cubic equation fitted to the arrays above 50 turns out to 

 be impossible as an extrapolation curve, while a straight line serves practically as well within 

 the range for which the cubic is satisfactory, and probably gives good results in extrapolation. 

 Using this straight line for extrapolation we find an alpha score of about —71 for a beta score 

 of zero. 



Unfortunately, Prof. Pearson was not provided with distributions and contingency tables 

 for scores in the component tests of alpha and beta, analysis of which shows clearly the nature 

 of the relationship between alpha and beta total scores, and suggests a method of avoiding some 

 of the difficulties met hi treating total scores as simple variables. 



From Group X of the principal sample, contingency tables for all pairs of variables, i. e., 

 ei^ht alpha tests, seven beta tests, Stanford-Binet mental age ratings, and each of these with 

 total alpha score and total beta score, have been obtained. Of these tables those showing 

 contingency of each beta test with Stanford-Binet mental age and of total beta score with 

 Stanford-Binet mental age are shown hi Part II, chapter 7, table 52. The other contingency 

 tables are printed herewith as tables 10 to 154. The distribution of scores in each test and 

 examination is shown by the histograms of figures 3, 4, and 5. 



Table 10. — Variables: Alpha score, test 1 X alpha score, test 2. Group X: Special experimental group. 



ALPHA TEST 2. 



Table 11. — Variables: Alpha score, test 1 X alpha score, test 3. Group X: Special experimental group. 



ALPHA TEST 3. 



