0.2820.160−0.440, 0.227 Fieller's theoremN/A−0.012, 0.267N/A−0.201, 0.336N/A−0.610, 0.280 Bootstrapd0.071−0.023, 0.2570.138−0.221, 0.3220.997−2.041, 1.868 Bayesian0.1190.072−0.013, 0.2730.0550.169−0.232, 0.390−0.1000.456−1.012, 0.554Abbreviations: CI, confidence interval; IV, instrumental variable; N/A, not applicable; SE, standard error.a The simulated data sets consisted of 10,000 persons with data on G and Y and 2,000 persons with data on G and X. The true effect of X on Y was set to 0.1, and a confounding variable U had the effect of 0.2 on both X and Y.b Theoretical F values were obtained using the following equation: F = R2 (nX − 1)/(1 − R2).c For the second-stage regression (of sequential regression), robust SEs are reported.d Bootstrapping was conducted using 1,000 replications, with samples of size nX and nY randomly selected (with replacement) from the original samples of size nX and nY.
