
Sample Size Determination for Outcomes from Two-Level Trials 169
The corresponding statistical power can be expressed as
ϕ
xz(2)
= Φ
(
∆
XZ(2)
r
N
(0,0)
2
N
1
.
4f − Φ
−1
(1 − α/2)
)
.
where ∆
XZ(2)
=
δ
XZ(2)
σ
. Accordingly, the corresponding required sample
size is [16]:
N
(0,0)
2
=
4fz
2
α,φ
N
1
∆
2
XZ(2)
. (5.26)
It is notable that when Equations (5.5) and (5.26) are compared, it is
clear that N
(0,0)
2
= 2N
(0)
2
, where N
(0)
2
is the required sample size for the
control arm (X = 0) for testing H
0
: δ
(2)
= 0 in model (5.3). If follows that
the total number of measurements, that is, 4N
(0,0)
2
N
1
required for testing
H
0
: δ
XZ(2)
= 0 in model (5.25) is four times larger than the total number