Studies involving the effects of single genes on quantitative traits may involve closed populations, selection may be practiced, and the quantitative trait of concern may also be influenced by background genes that are inherited in a polygenic manner. It is shown analytically that analysis of such data by ordinary least squares, the usual method of analysis, can lead to finding an excess of spurious significant effects of single genes, when no effect exists, for both randomly and directionally selected populations and can lead to bias in estimates of single-gene effects when selection has been practiced. The bias depends on heritability of the polygenic effects on the trait, selection intensity, mode of inheritance, magnitude of gene effect, gene frequency, and data structure. It is argued that when genotypes of individuals can be identified for all individuals with observations on the trait, use of mixed-model procedures under an animal model treating single-gene effects as fixed effects can provide unbiased estimates of single-gene effects and exact tests of associated hypotheses for pedigreed populations, even when selection is practiced. Results are illustrated through computer simulation.