Using data from the same source as that employed in Herrnstein and Murray's book, "The Bell Curve," this study reexamined links between the test scores of mothers and children, paying close attention to what the scores measure and whether these measurements mean the same things for blacks and whites. The study replicated Herrnstein and Murray's finding that a mother's score on the Armed Forces Qualification Test (AFQT) is a powerful predictor of her child's score on the Peabody Picture Vocabulary Test (PPVT). After controlling for AFQT, however, results showed racial gaps in PPVT scores. This suggests that AFQT is not the only factor influencing PPVT scores. Child's test scores differed dramatically in correlation with maternal education and income. In addition, scores differed with the test, the child's age, and the child's race. The child's background also significantly affected grade repetition after controlling for child test scores and maternal AFQT scores. Maternal scores of different achievement tests have different effects on the PPVT scores of black and white children. The conclusion is that nature and nurture both matter. (Includes 9 statistical tables and 23 references.) (JW)