Statistical work not requiring the class grades of students has now been completed for the tests given in July 1948. Appreciable relationships were found between hours or lessons of refresher work and mathematics achievement test scores. Comparisons of the Postgraduate School results with those for College Entrance Examination Board candidates for five tests taken by both groups revealed the distinct superiority of the Postgraduate group. One verbal test had been given also to a Naval Academy entering class, and here again the average score for the Postgraduate group was markedly the higher of the two. Comparison of the Postgraduate School group with the 1947 freshman class at the Coast Guard Academy revealed that for three tests the groups were quite similar, while each group excelled the other on one of two other tests. The Postgraduate group was found to be markedly superior on the same tests, and on one other test, to a group of freshman liberal arts students at a large Eastern university. Comparisons of the test performances of six instructional groups at the Postgraduate School revealed only small differences among groups except for the Applied Communications group, which did not do nearly as well on certain of the tests as did the other groups, especially on tests in the quantitative area. The findings indicating the superiority of the Postgraduate School group over most of the other comparison groups point to the need for the study of the test performances of the total group of applicants. The group tested in July was a select one, and hence the present data cannot be used by themselves to decide upon the appropriate level of difficulty for future tests.