TABLE 3.

Definition of Bias, Monte-Carlo Standard Error, 95% Confidence Interval, and the Type 1 Error Proportion (%)

Metric	Formula	Description
Bias	$\frac{1}{1000}\sum _{j=1}^{1000}({\widehat{\beta }}_j-0)$	The average difference between the null (ß=0) and its estimate across 1,000 replicates.
Monte-Carlo standard error (MCSE)	$\frac{S{D}_{\widehat{\beta }}}{\sqrt{1000}}$	An estimate of the standard deviation of the sampling distribution of the bias estimator.
95% CI	[bias±1.96 × MCSE]	95% confidence interval for the true bias.
Type 1 error proportion (%)	$\frac{\mathrm{Number}\mathrm{of}95\%\mathrm{CIs}\mathrm{exclude}0}{1000}\times 100\%$	Proportion of coefficient 95% CIs excluding 0