Table 1.

Empirical rejection probabilities (sizes) in the null case. The nominal significance level is set at 0.05. Each entry is based on 5000 Monte Carlo replicates.

Simulation	β	M	λ	Test
				TF	TCM	F-test	Kruskal-Wallis
A	0	25	2	0.041	0.075	0.089	0.085
		25	10	0.057	0.077	0.107	0.096
		50	2	0.034	0.065	0.074	0.069
		50	10	0.052	0.089	0.099	0.095
		100	2	0.031	0.061	0.069	0.064
		100	10	0.050	0.094	0.096	0.094
A	1	25	2	0.037	0.071	0.081	0.075
		50	2	0.032	0.064	0.070	0.069
		100	2	0.024	0.058	0.070	0.063

Simulation	β	M	a	Test
				TF	TCM	F-test	Kruskal-Wallis
B	0	25	Φ−1 (⅓)	0.043	0.054	0.058	0.055
		25	0	0.040	0.046	0.052	0.052
		25	Φ−1 (⅔)	0.044	0.049	0.053	0.052
B	0	50	Φ−1 (⅓)	0.037	0.042	0.047	0.044
		50	0	0.045	0.053	0.053	0.053
		50	Φ−1 (⅔)	0.042	0.047	0.051	0.050
B	0	100	Φ−1 (⅓)	0.038	0.045	0.049	0.046
		100	0	0.038	0.047	0.047	0.047
		100	Φ−1 (⅔)	0.044	0.049	0.050	0.051
B	1	25	0	0.044	0.050	0.051	0.055
		50	0	0.045	0.052	0.052	0.053
		100	0	0.037	0.044	0.046	0.045

Model A: Cluster sizes from Poisson-distribution; Y from a random intercept normal model.

Model B: Cluster sizes either 5 or 10 at proportions controlled by parameter a; Y with random intercept normal model and with errors from a t₁₀-distribution (ν₁ = ν₂ = 10).

Φ(·) is the cumulative distribution function of the standard normal distribution.