Appendix Table 3.

Minimum of mean RE for the different simulation designs with continuous outcomes

Cluster sizes n	# of clusters m	Range R	Distribution	ρ, Minimum[2] of mean RE[1]
				MD-corrected estimator	FG-corrected estimator
					d=0.1	d=0.75
5	12	n	Uniform	0, 0.91	0.16, 0.95	0.05, 0.93
			Unimodal	0, 0.95	0.16, 0.98	0.06, 0.96
			Bimodal	0, 0.88	0.16, 0.94	0.05, 0.91
			Positive Skewed	0, 0.92	0.14, 0.96	0.02, 0.94
			Negative Skewed	0.05, 0.92	0.21, 0.95	0.09, 0.93
		1.2n	Uniform	0, 0.86	0.18, 0.93	0.06, 0.89
			Unimodal	0, 0.93	0.18, 0.96	0.17, 0.95
			Bimodal	0.01, 0.83	0.18, 0.91	0.06, 0.86
			Positive Skewed	0, 0.89	0.14, 0.95	0.02, 0.92
			Negative Skewed	0.08, 0.88	0.24, 0.93	0.13, 0.90
		1.6n	Uniform	0.05, 0.75	0.23, 0.86	0.11, 0.79
			Unimodal	0.06, 0.88	0.23, 0.93	0.12, 0.90
			Bimodal	0.05, 0.69	0.23, 0.82	0.11, 0.74
			Positive Skewed	0, 0.80	0.15, 0.91	0.02, 0.85
		1.8n	Uniform	0.11, 0.67	0.28, 0.80	0.17, 0.72
			Unimodal	0.13, 0.84	0.28, 0.90	0.19, 0.86
			Bimodal	0.11, 0.59	0.28, 0.75	0.16, 0.65
			Positive Skewed	0, 0.75	0.16, 0.88	0.03, 0.82
	24	n	Uniform	0.11, 0.94	0.17, 0.95	0.13, 0.95
			Unimodal	0.11, 0.97	0.17, 0.97	0.13, 0.97
			Bimodal	0.11, 0.93	0.18, 0.94	0.13, 0.93
			Positive Skewed	0.09, 0.96	0.15, 0.96	0.11, 0.96
			Negative Skewed	0.14, 0.94	0.19, 0.95	0.16, 0.95
		1.2n	Uniform	0.12, 0.91	0.19, 0.93	0.14, 0.92
			Unimodal	0.13, 0.96	0.18, 0.96	0.14, 0.96
			Bimodal	0.12, 0.89	0.19, 0.91	0.14, 0.90
			Positive Skewed	0.09, 0.94	0.16, 0.95	0.11, 0.94
			Negative Skewed	0.18, 0.91	0.23, 0.92	0.20, 0.92
		1.6n	Uniform	0.17, 0.83	0.23, 0.85	0.19, 0.84
			Unimodal	0.17, 0.91	0.23, 0.92	0.19, 0.92
			Bimodal	0.16, 0.79	0.23, 0.82	0.18, 0.80
			Positive Skewed	0.10, 0.89	0.17, 0.91	0.12, 0.90
		1.8n	Uniform	0.23, 0.76	0.29, 0.79	0.25, 0.77
			Unimodal	0.24, 0.88	0.29, 0.89	0.25, 0.89
			Bimodal	0.22, 0.70	0.29, 0.75	0.24, 0.72
			Positive Skewed	0.10, 0.86	0.17, 0.88	0.12, 0.87

^[1]The mean RE among 1000 simulations is calculated for each ρ.

^[2]The minimum of mean RE including the corresponding ρ is identified across all the values of ρ.