
Sample Size Determination for Outcomes from Three-Level Trials 207
TABLE 6.5
Sample size and power for detecting an effect δ
(r)
on slope differences in a
three-level random-slope model (6.22) with r
τ
= 0.1 when randomizations
occur at the third level (two-sided significance level α = 0.05)
λ
3
ρ
1
∆
(r)
N
1
N
2
N
(0)
3
Total N ϕ
(r)
1 0.1 0.3/4 5 8 67 5360 0.804
5 67 8 5360 0.804
0.3/8 9 8 161 23184 0.801
9 161 8 23184 0.801
0.2 0.3/4 5 8 63 5040 0.801
0.3/8 9 8 159 22896 0.802
0.1 0.4/4 5 8 38 3040 0.807
0.4/8 9 8 91 13104 0.803
0.2 0.4/4 5 8 36 2880 0.807
5 36 8 2880 0.807
0.4/8 9 8 89 12816 0.800
9 89 8 12816 0.800
1.5 0.1 0.3/4 5 8 56 5600 0.805
5 56 8 5600 0.805
0.3/8 9 8