Table 1

Empirical type I errors for testing the null of no difference in group mean across three groups in equation (7) from the F-test based on 1000 Monte Carlo simulated samples from the ANOVA in equation (6) under (A) no violation of normality and homoscedasticity, (B) violation of normality and (C) violation of homoscedasticity for sample size n=10, 100 and 1000 with nominal type I error α=0.05 and α=0.01

	n=10		n=100		n=1000
	α=0.01	α=0.05	α=0.01	α=0.05	α=0.01	α=0.05
No violation
Normality and homoscedasticity	0.007	0.043	0.014	0.057	0.01	0.051
Violation of normality
χ² distribution	0.005	0.031	0.011	0.053	0.006	0.054
Weibull distribution	0.009	0.037	0.009	0.053	0.01	0.054
Violation of homoscedasticity
Scenario (i), k=1	0.019	0.056	0.013	0.061	0.032	0.073
Scenario (i), k=10	0.025	0.061	0.014	0.063	0.034	0.076
Scenario (i), k=20	0.025	0.059	0.013	0.063	0.034	0.077
Scenario (ii), k=1	0.012	0.043	0.01	0.054	0.016	0.059
Scenario (ii), k=10	0.018	0.05	0.012	0.06	0.022	0.066
Scenario (ii), k=20	0.017	0.051	0.012	0.057	0.022	0.065

ANOVA, analysis of variance.