Is randomising futile for small sample sizes?

Grossman and Mackenzie argue that, in some instances, observational studies may be superior to randomised control trials.  They argue that one situation in which randomisation is problematic is when there is a small sample size (pp. 527-528).  For instance, if there are four trial subjects, two male and two female, it makes sense to ensure that each group contains one male and one female.  If the groups are selected randomly, there is a 50 percent chance both males will end up in one group and both females in the other.

There are two mistakes with the argument above.  First, they make a simple technical error in their example; there is only a one in three chance, not a 50 percent chance, that both males will be in one group and both females in the other.  Second, and more importantly, to ensure each group has one male and one female assumes that sex is a relevant variable.  But sex may not be relevant, whereas other variables might be.  If weight is relevant and sex is not, for example, then balancing for sex will do no good.  Randomised control trials (at least well designed ones) avoid this shortcoming, since they do not assume which variables are relevant and which are not.  I am not convinced that, even for small sample sizes, randomised control trials are not best.

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