Table 3.

Empirical width and coverage [in brackets] of Wald (W), Chebyshev (C) and exact (E) 95% CIs of the direct effect $\overline{\mathit{DE}}\left({\alpha }_1\right)$, indirect effect $\overline{\mathit{IE}}({\alpha }_1,{\alpha }_0)$, total effect $\overline{\mathit{TE}}({\alpha }_1,{\alpha }_0)$ and overall effect $\overline{\mathit{OE}}({\alpha }_1,{\alpha }_0)$ for simulations under scenario (iii) with m groups, n_i = 1000 individuals per group, and binary outcomes.

		m
		4	6	10	30	100
$\overline{\mathit{DE}}\left({\alpha }_1\right)$	W	1.73[0.67]	1.33[0.90]	0.99[0.79]	0.55[0.98]	0.30[0.93]
	C	3.26[0.67]	2.89[0.90]	2.25[0.99]	1.26[1.00]	0.68[1.00]
	E	6.07[1.00]	4.96[1.00]	3.84[1.00]	2.22[1.00]	1.21[1.00]
$\overline{\mathit{IE}}({\alpha }_1,{\alpha }_0)$	W	1.22[0.67]	0.93[0.90]	0.70[0.99]	0.39[0.98]	0.21[0.99]
	C	2.31[0.67]	2.02[0.90]	1.59[0.99]	0.89[1.00]	0.48[1.00]
	E	3.84[1.00]	3.14[1.00]	2.43[1.00]	1.40[1.00]	0.77[1.00]
$\overline{\mathit{TE}}({\alpha }_1,{\alpha }_0)$	W	1.22[0.67]	0.96[0.90]	0.70[0.99]	0.39[0.98]	0.21[0.99]
	C	2.31[0.67]	2.08[0.90]	1.59[0.99]	0.90[1.00]	0.48[1.00]
	E	3.84[1.00]	3.14[1.00]	2.43[1.00]	1.40[1.00]	0.77[1.00]
$\overline{\mathit{OE}}({\alpha }_1,{\alpha }_0)$	W	0.03[0.85]	0.04[0.87]	0.02[0.92]	0.01[0.95]	0.01[0.96]
	C	0.06[0.98]	0.09[1.00]	0.05[1.00]	0.03[1.00]	0.02[1.00]
	E	3.84[1.00]	3.14[1.00]	2.43[1.00]	1.40[1.00]	0.77[1.00]