Table 1.

Empirical width and coverage [in brackets] of Wald (W) and Chebyshev (C) 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 (i) with numbers of groups m, number of individuals per group n_i, and continuous outcomes.

			m
			4	6	10	30	100
ni = 6	$\overline{\mathit{DE}}\left({\alpha }_1\right)$	W	3.70[0.88]	2.67[0.91]	2.03[0.93]	1.27[0.95]	0.73[0.95]
		C	8.04[1.00]	5.92[1.00]	4.54[1.00]	2.88[1.00]	1.66[1.00]
	$\overline{\mathit{IE}}({\alpha }_1,{\alpha }_0)$	W	1.89[0.80]	1.60[0.87]	1.26[0.91]	0.88[0.93]	0.42[0.95]
		C	3.92[0.94]	3.49[0.99]	2.82[1.00]	2.01[1.00]	0.96[1.00]
	$\overline{\mathit{TE}}({\alpha }_1,{\alpha }_0)$	W	3.79 [0.76]	2.31 [0.87]	2.32[0.91]	1.40[0.94]	0.74[0.96]
		C	7.57[0.93]	4.95[0.98]	5.14[1.00]	3.17[1.00]	1.69[1.00]
	$\overline{\mathit{OE}}({\alpha }_1,{\alpha }_0)$	W	2.54[0.77]	1.44[0.88]	1.69[0.90]	1.04[0.94]	0.51 [0.94]
		C	5.46[0.94]	3.21[1.00]	3.83[1.00]	2.37[1.00]	1.17[1.00]
ni = 1000	$\overline{\mathit{DE}}\left({\alpha }_1\right)$	W	0.86[0.66]	0.65[0.90]	0.50[0.90]	0.28[0.94]	0.15[0.95]
		C	1.75[0.74]	1.44[0.91]	1.12[0.99]	0.63[1.00]	0.34[1.00]
	$\overline{\mathit{IE}}({\alpha }_1,{\alpha }_0)$	W	0.12[0.80]	0.10[0.88]	0.11[0.91]	0.06[0.94]	0.03[0.95]
		C	0.24[0.95]	0.22[0.99]	0.25[1.00]	0.14[1.00]	0.08[1.00]
	$\overline{\mathit{TE}}({\alpha }_1,{\alpha }_0)$	W	1.21[0.66]	0.89[0.90]	0.69[0.97]	0.38[0.98]	0.20[0.99]
		C	2.35[0.69]	1.95[0.90]	1.56[0.99]	0.87[1.00]	0.46[1.00]
	$\overline{\mathit{OE}}({\alpha }_1,{\alpha }_0)$	W	0.68[0.66]	0.48[0.90]	0.39[0.92]	0.21[0.96]	0.11[0.97]
		C	1.31[0.66]	1.06[0.90]	0.88[0.99]	0.49[1.00]	0.26[1.00]