Cumulative deficit is an hypothesis concerning the cause of lower mental test scores of groups considered environmentally deprived. It presupposes a progressive decrement in test scores, relative to population norms, as a function of age. Clarification of the theoretical issues and the methodological problems involved in establishing the progressive decrement phenomenon are discussed in relation to the relevant research on disadvantaged groups, especially American Negroes. In this group in particular there is no methodologically adequate evidence in the literature for a progressive decrement in IQ or other mental measurements. The study reported here used differences between younger and older siblings, which satisfies rigorous methodological requirements for the detection of progressive decrement. The entire Berkeley Unified School District's elementary school population, consisting of some 8,000 children in 17 schools, was given a battery of tests by 20 specially trained testers (12 whites and eight Negroes). From school records and from questionnaires sent to the children's parents, all full sibships within the elementary school population were identified. The only tests considered in this study are the Lorge-Thorndike IQ tests, because they were the only tests in the battery for which published nationwide age norms are available. The results indicated a slight but significant decrement in Verbal but not in Nonverbal IQ among a large sample of Negro elementary school children. The same method detected no progressive decrement in the white school population. (Author/JM)