This note summarizes the main results of three recent studies on the heritability of mental traits: (1) The inferences Jinks and Fulker (1970) derived from Shields's (1962) twin data are invalid since the assumptions of the genetic model are consistently violated by these data. A purely environmental model fits them better by a factor of 2. (2) Holzinger's heritability coefficient W) is invalid since his derivations imply that dizygotic twins share no genes. (3) In contrast, Nichols's (1965) heritability coefficient (HR) follows from a strictly additive genetic model. (4) However, the needed assumptions are consistently violated by Osborne's (1980) personality data, which produce an excessive number of inadmissible HRs. A purely environmental model fits these data better by a factor of 14. Jointly, these results suggest that heritability estimates of mental traits in the literature should be viewed with caution.The purpose of this advance note is to put some recent results about the heritability of mental traits on record until more complete accounts of this work can be published in the appropriate journals. In the meantime, the reader is referred to SchOnemann (1987SchOnemann ( ,1988 and Schonemann and Schonemann(1988) for more detailed empirical evidence and the proofs of formal claims. IDENTICAL TWINS RAISED TOGETHER AND APART (SmELDS'S DATA)In 1962, Shields published a set of twin data, which has been reanalyzed by numerous other investigators, including Jinks andFulker (1970) and, more recently, Farber (1981). Shields recorded the values of various physical and four psychological variables: the Dominoes Intelligence Test, a synonyms section of the Mill Hill Vocabulary Scale, and two self-rating scores for extraversion and neuroticism. The sample comprised 44 pairs of monozygotic twins raised apart (MZAs), 44 pairs of monozygotic twins raised together (MZTs), and 32 pairs of dizygotic twins raised together (DZTs). On reanalyzing these data , Jinks and Fulker (1970) concluded, among other things; (1) that "it is reassuring to fmd that [correlated environments and genotype-environment interactions] are by no means universal phenomena" (p. 347) ; (2) " high heritabilities recorded in Table 30" (p. 347) for the four measures employed by Shields; and (3) that "the high number of genes estimated to be controlling IQ (> 20 and approximately 100) fully confirms that this trait is under polygenic control" (p. 348) . According to Eysenck (1973, p . 262 where rA denotes the intraclass correlation (based on mean squares) for MZAs, and rr denotes the intraclass correlation for MZTs. These predictions are violated by Shields's (1962) data (a) in 7 out of8 cases (88%), (b) in 8 out of8 cases (100%), and (c) in 7 out of8 cases (88%) . 175