652 



MEMOIRS NATIONAL ACADEMY OF SCIENCES. 



Table 164. — Table of partial correlations between all pairs of alpha tests. 



[Vol. XV, 



Comparing the coefficients of table 164 with those in the alpha-alpha section of table 155, 

 we see at once the extent to which the correlation there exhibited between any pair of alpha 

 tests is actually due the correlation of each member of the pair with other alpha tests. Table 

 164 shows the amounts of actual resemblance between tests so far only as the alpha system is 

 concerned. 



It is entirely beyond the limits of time to attempt a general discussion of the interrelation 

 of tests as displayed in the above table. However, these correlations have yielded some rather 

 unexpected results. For example, the highest coefficient in the table is that between A4 and 

 A8. The high partial correlation between A5 and A7 is also surprising. On the surface the 

 task set by test 4 does not appear to resemble that of test 8, nor does test 5 seem to resemble 

 test 7, yet the facts are otherwise. Another interesting feature of the above table is that, aside 

 from the high partial correlations just referred to, the table shows that the alpha tests consti- 

 tute a fairly discontinuous system. The tests also show another and somewhat contrary tend- 

 ency, viz, that the system would not be seriously injured by omitting as many as three or four 

 of the tests. 



Section 3. — Application to main groups of principal sample. 



Unfortunately the foregoing method was not completed in time to permit its application 

 to all of the subgroups of the principal sample. It was applied, however, to the main groups 

 of the sample. The results are exhibited in figure 7 and in table 165. In each group the 

 alpha distribution was distributed on the combined scale by the use of table 159, the beta dis- 

 tribution by table 162, and the Stanford-Binet mental age distribution by table 163. The 

 performance scale distributions and the point scale distributions were handled in the following 

 way: The performance distributions were first transformed into Stanford-Binet mental age 



distributions by the use of the regression formula: M. A. (in years) =— ^ -• This 



formula was derived from the correlation of a sample of 350 cases who had both Stanford- 

 Binet mental age ratings and performance scale ratings. The point scale distributions were 

 transformed into Stanford-Binet mental age distributions by the use of the table in the examiner's 

 guide, Part I, pages 195ff . These transformations only approximate the truth, but owing to the 

 fact that the performance and point scale cases constitute less than 3 per cent of any group 

 handled it would take a considerable error in transformation seriously to affect the whole. 



