
Sample Size Determination for Outcomes from Three-Level Trials 197
Owing to the invariance over product of N
3
N
2
N
1
property, the other sam-
ple sizes can be determined as follows:
N
2
=
f
1
(1 + 1/λ
1
) z
2
α,φ
N
3
N
(0)
1
∆
2
(1)
and
N
(0)
1
=
f
1
(1 + 1/λ
1
) z
2
α,φ
N
3
N
2
∆
2
(1)
which is the sample size of the first level units in the control arm per second
level data unit.
6.3.3.3 Summary
The sample size N
3
in (6.15) or in (6.16) required for a desired magnitude of
statistical power is not a function of ρ
2
and decreases with increasing N
(0)
1
,
N
2
, ∆
(1)
, and ρ
1
. Table 6.2 displays examples of statistical power for testing
the null hypothesis H
0
: δ
(1)
= 0, and shows that the statistical