One of the assumptions required to estimate genetic parameters using the diallel mating design is that the genes in the parents must be independently distributed. The objective of this study was to test the validity of the assumption that the genes in the parents must be independently distributed. Two different diallel experiments representing a fixed sample and a random sample were conducted in maize (Zea mays L.). In the first experiment, an eight-parent diallel among four Reid Yellow Dent inbreds and four Lancaster Sure Crop inbreds was produced (original diallel). For the second experiment, 96 unselected single-seed descent lines from a random mating population in linkage equilibrium were used to produce 12 eight-parent diallels (pooled random diallels). Both experiments were evaluated together in a replication-within-sets randomized incomplete block design in six environments. The 12 eight-parent diallels were pooled and combined across environments and the original diallel was combined across environments. Estimates of additive and dominance variances from the original diallel always had greater standard errors than estimates from the pooled random diallels. Estimates of additive and dominance variances from the pooled random diallels were significantly different from the original diallel for half the traits. For six traits the average level of dominance was overestimated in the original diallel relative to the pooled random diallels. The average level of dominance for grain yield was 2.0 times greater for the original diallel than for the pooled random diallels. Estimates of additive variance appear to be affected more than estimates of dominance variance by repulsion phase linkages. Since non-independence distribution of genes caused differences in additive and dominance variances, the diallel mating design should only be used to estimate genetic parameters when the parents of the diallel have been randomly selected from a population in linkage equilibrium.