Since tests for selection and guidance of students at American colleges and universities are widely and increasingly in use, information on the validity of various tests for predicting academic achievement is crucial, first in evaluating the effectiveness of program components, second in finding ways of improving test offerings in continuing programs, and third in aiding test users to make the best use of test results. Three studies are cited and described here, each of which emphasizes one the these three purposes. In the first study, done in cooperation with Norman Frederiksen, the chief aim was to determine the effectiveness of mathematical aptitude and achievement materials for predicting average grades and mathematics grades earned during the first term of engineering school. The second study, done in cooperation with Marjorie Olsen, was aimed directly at improving the efficiency of the Law School Admission Test. The third study is not an experiment, but a discussion of the use of expectancy tables to aid in interpreting test scores. Seven principles, most of them familiar statistical concepts, that have seemed of major importance in carrying out these and other validity studies are listed and described. These principles are considered to be "the critical concepts in planning and interpreting validity studies of testing programs." The criterion used in test validation is also discussed, and it is noted that though college grades remain a crucial criterion for the validation of selection tests, the criterion should be broadened in two ways: 1) to include other major outcomes of college and professional education and 2) to cover a longer time span to permit validation of test scores in terms of adult success. Paper read at meeting of ASA, December 28, 1953.