“… 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.