Table 4.

Type I error rate (a) and power (b) for testing the null hypothesis Ho: δ = 0 based on 10000 simulations with characteristics similar to the WA EPT study. Binomial observations for 22 clusters in 5 times intervals are simulated from a linear model with μ = 0.09, a linearly decreasing time effect (−0.005 per time period), a random cluster effect (τ = 0.015) and random treatment effect (η = 0, 0.002, 0.008). Number of individuals per cluster per time period (n) is either constant (n = 305) or variable between clusters according to a lognormal distribution with mean log(171) and standard deviation 1.06 (giving a mean cluster size of 305).

(a) Type I error rate (nominal level = 0.05)
	$V_{\delta =0}^1(\widehat{\delta })$			$\frac{N}{N-1}{V}_{\delta =\widehat{\delta }}^1(\widehat{\delta })$			$V^2(\widehat{\delta })$
	Treatment standard deviation (η)
n	0	0.002	0.008	0	0.002	0.008	0	0.002	0.008
constant	0.05	0.05	0.05	0.06	0.06	0.06	0.07	0.07	0.08
variable	0.04	0.05	0.05	0.05	0.05	0.06	0.06	0.07	0.07
(b) Power (for the alternative Ha : δ = −0. 01)
	$V_{\delta =0}^1(\widehat{\delta })$			$\frac{N}{N-1}{V}_{\delta =\widehat{\delta }}^1(\widehat{\delta })$			$V^2(\widehat{\delta })$
	Treatment standard deviation (η)
n	0	0.002	0.008	0	0.002	0.008	0	0.002	0.008
constant	0.29	0.29	0.26	0.31	0.31	0.28	0.33	0.32	0.30
variable	0.18	0.17	0.08	0.20	0.18	0.09	0.22	0.20	0.12