A strong developmental theory of field dependence-independence

Assume an X-linked gene in two alleles mediates performance on field dependent-independent tests such as the rod-and-frame test. Only the recessive gene with relative frequency q facilitates field independence. Other genotypes lead to field dependence. Under a simple genetic model, field dependence-independence may be viewed as outcomes of a discrete random variable B with field independent and dependent probabilities π_iq and 1 ? π_iq for men, and π_iq² and 1 ? π_iq² for women, respectively. The parameter π_i is a maturational ageindexed parameter, 0 < π_i ≤ 1, monotonically increasing with development until maturity when π_k = 1. Observations of performance are made on a random variable W of the form W = B + N, where N is normal in distribution independent of B; N represents a composite of influences including error. The model implies testable age-related between- and within-sex predictions regarding E(W) and Var(W), predictions which appear to coincide with major empirical findings; it also generates novel predictions. For instance, W is a mixture of normals distribution. The model is briefly evaluates in two data sets.