Figure 3.

Correlation coefficients obtained from a pool of N heteroskedastic groups. r_xy was obtained from pooling N groups of simulated data (shown in red), and ${\overline{r}}_{\mathit{\text{xy}}}$ was obtained from averaging within groups correlation (shown in blue); ρ is the true correlation within each group. This plot shows that the error between ${\overline{r}}_{\mathit{\text{xy}}}$ and ρ is smaller than the error between r_xy and ρ. Simulation parameters: μ_xy,i = (2,2), ${\sigma }_{x,i}^2=i^2$, −0.9 ≤ ρ ≤ 0.9, n_i = 10, λ_i = λ, and 0.01 ≤ λ ≤ 0.1 for i = 1,N and 10 ≤ N ≤ 100.