Sample size and power calculations are often based on a two-group
comparison. However, in some instances the group membership cannot be
ascertained until after the sample has been collected. In this situation,
the respective sizes of each group may not be the same as those prespeci-
ed due to binomial variability, which results in a di erence in power from
that expected. Here we suggest that investigators calculate an \expected
power" taking into account the binomial variability of the group member-
ship, and adjust the sample size accordingly when planning such studies.
We explore di erent scenarios where such an adjustment may or may not be
necessary for both continuous and binary responses. In general, the number
of additional subjects required depends only slightly on the values of the
(standardized) di erence in the two group means or proportions, but more
importantly on the respective sizes of the group membership. We present
tables with adjusted sample sizes for a variety of scenarios that can be read-
ily used by investigators at the study design stage. The proposed approach
is motivated by a genetic study of cerebral malaria and a sleep apnea stud