What sample size is needed for randomization to be meaningful? This study randomised 17 participants to 3 treatment arms. What sample size is needed for randomization to be meaningful? As an extreme example, randomly assigning 4 individuals to 2 treatment groups has a high chance that their characteristics are not balanced.
 A: In planning a study, the rules for randomization need to be
carefully studied. For example, suppose men and women are equally
available for assignment to two arms of a study, each of which is to have 50 subjects. If we assign 50
subjects completely at random to each arm of the study, 
there is probability about $0.20$ that
that one arm of the study will have 20 or fewer of one gender. [If there is a pool with equal numbers of men and women appropriate for the study and we randomize from the pool, the probability of the same degree of imbalance may be a little smaller.]
So, if it is really important to have 25 women in each arm of the study
we need to stratify the randomization so that exactly 50 women are chosen
with exactly half going into each arm of the study.
The difficulty is that if we also seek perfect balance as to age group, race,
severity of symptoms, religion, political party, and birth sign of the zodiac, then we soon have so many constraints
that there can be almost no randomness in the "randomization" procedure. It is important
to decide from the start which subject attributes really must be 
balanced in order for the study to be valid, and stratify only for those attributes. Then trust randomization to take care of any important attributes you didn't explicitly consider.
In practice, many factors are 'in line' to be considered when determining the sample size for a study. In that line, statistical power, size of effect that should be detected, budget, timeline, and availability of subjects may be ahead
of stratifying the randomization.  
