Figure 3: Effects of selection.

Simulation to illustrate the bias and skewness of selected distributions with different correlation parameters. For D = 2 and c = 0.2, we simulate data from Z = (Z₁, Z₂) ~ N ((0, 0), (1, ρ; ρ, 1)), and separate cases where the region 1 : 2 was selected (full circle). The left plots show the bivariate distributions for ρ = 0 and ρ = 0.8. The right plot displays the density of the observed effect-size ${\overline{Z}}_{a:b}$ for all data (dash-dot) versus the selected data (full). Although ${\overline{\theta }}_{a:b}=0,{\overline{Z}}_{a:b}$ is biased away from 0 in the case of selection. Furthermore, the conditional distribution and the selection bias are different for each correlation regime. Without selection there is no bias and the effect of correlation amounts to rescaling.