Complex diseases are often highly heritable. However, for many complex traits only a small proportion of the heritability can be explained by observed genetic variants in traditional genome-wide association (GWA) studies. Moreover, for some of those traits few significant SNPs have been identified. Single SNP association methods test for association at a single SNP, ignoring the effect of other SNPs. We show using a simple multi-locus odds model of complex disease that moderate to large effect sizes of causal variants may be estimated as relatively small effect sizes in single SNP association testing. This underestimation effect is most severe for diseases influenced by numerous risk variants. We relate the underestimation effect to the concept of non-collapsibility found in the statistics literature. As described, continuous phenotypes generated with linear genetic models are not affected by this underestimation effect. Since many GWA studies apply single SNP analysis to dichotomous phenotypes, previously reported results potentially underestimate true effect sizes, thereby impeding identification of true effect SNPs. Therefore, when a multi-locus model of disease risk is assumed, a multi SNP analysis may be more appropriate.