Figure 2.

Histograms of random variables ${\widehat{\alpha }}_1$, ${\widehat{\alpha }}_{1\mathit{adj}}$, and ${\tilde{\alpha }}_1$ based on 100,000,000 replicates under the null hypothesis that there is no association between the SNP and the secondary phenotype (Figure 1 (A)). The theoretical curves were plotted following normal distributions, with a mean of 0 and the estimated standard errors of ${\widehat{\alpha }}_1$, ${\widehat{\alpha }}_{1\mathit{adj}}$, and ${\tilde{\alpha }}_1$, respectively.