Psychometric theory has been one of psychology's stronger foundations and a major contributor to the recognition of psychology as a scientific discipline. Basic principles of psychometric theory led to the development of respected intelligence tests and large and comprehensive testing and assessment programs. This paper synthesizes major developments in psychometric theory, focusing on the issues of reliability and validity. The synthesis is developed from: (1) Cattell's basic data relation matrix (BDRM) of 10 coordinates for describing psychological events and the reliability and generalizability (Cronbach) coefficients derived from it; (2) the four box conception of data (predictor, criterion, experimental treatment, and nonexperimental treatment) to depict psychological research problems; and (3) a hierachical version of Brunswik's lens model in which correlations between boxes can only be optimal under conditions of good reliability and symmetry. The paper concludes with an empirical example from intelligence and school achievement research: predicting school grades and other kinds of aggregated criteria from the Berlin model of intelligence, the most prominent intelligence model in German-speaking Europe. (BS)