FIGURE 2.

Sample size calculated to detect a mean difference of ${\mu }_1-{\mu }_0=0.375-0.275$ with 90% power at a two-sided 5% significance level using the $n_{\text{IPRW}}$, $n_{\text{known}}$, $n_{\text{approx}}$ and $n_{\text{standard}}$ formulas. The correlation $\left(\rho \right)$ between the weighting variable $\left(X_i\right)$ and the outcome $\left(Y_i\right)$ is varied on the x-axis. The probability of the outcome being observed at each $x_i$ value and intervention group is as displayed for $P\left(R_i=1\mid X_i=x_i,Z_i=1\right)=\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{i}\mathrm{t}\left({\beta }_{01}+{\beta }_{11}{x}_i\right)$ and $P\left(R_i=1\mid X_i=x_i,Z_i=0\right)=\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{i}\mathrm{t}\left({\beta }_{00}+{\beta }_{10}{x}_i\right)$. $n_{\mathrm{I}\mathrm{P}\mathrm{R}\mathrm{W}}$ is approximated by Gauss-Hermite quadrature with 100 quadrature points.