To account for observed sex differences on tasks such as the rod and frame test, the embedded figures test, and other related measures, the theory is advanced that a sex-linked recessive gene mediates or facilitates certain performances. This assumption is coupled with the concept of "a mixture of density functions" to provide a theoretical account of the continuity of observed performance scores, increases in magnitude of sex differences with development, and certain anomalies in cross-cultural data. The theory generates predictions concerning the shapes of the distributions of observed scores and the manner in which parameters of these distributions, for each sex, should be ordered. As an example of how these assumptions can be applied, rod and frame data from a previous study are fitted to the theory. Results are found to be in good agreement with theoretical predictions. (Author/RH)