Two incontrovertible facts about RCTs

“… the following are two incontrovertible facts about a randomized clinical trial:

1. over all randomizations the groups are balanced;

2. for a particular randomization they are unbalanced.

Now, no [statistically] ‘significant imbalance’ can cause 1 to be untrue and no lack of a significant balance can make 2 untrue. Therefore the only reason to employ such a test must be to examine the process of randomization itself. Thus a significant result should lead to the decision that the treatment groups have not been randomized…”

– Senn (1994,  p. 1716)

Senn, S. (1994). Testing for baseline balance in clinical trials. Statistics in Medicine, 13, 1715–1726.