
212 Sample Size Calculations for Clustered and Longitudinal Outcomes
1) levels, respectively. Comparisons of sample sizes across different levels of
randomizations are discussed in Section 6.3.4.
6.5.1 Randomization at the Third Level
For trials with m = 3, we define the intervention assignment indicator for
treatment X as X
ijk
= 0 if the ith level 3 unit is not assigned to receive X
and X
ijk
= 1 if assigned to receive X; therefore X
ijk
= X
i
for all j and k.
Likewise, we define the assignment indicator for treatment Z as Z
ijk
= 0 if the
ith level 3 unit is not assigned to receive Z and Z
ijk
= 1 if assigned to receive
Z; therefore Z
ijk
= Z
i
for all j and k. Here, ...