AbstractRandom samples are assumed for the univariate two‐sample problem. Sometimes this assumption may be violated in that an observation in one “sample”, of sizem, is from a population different from that yielding the remainingm—1 observations (which are a random sample). Then, the interest is in whether this random sample of sizem—1 is from the same population as the other random sample. If such a violation occurs and can be recognized, and also the non‐conforming observation can be identified (without imposing conditional effects), then that observation could be removed and a two‐sample test applied to the remaining samples. Unfortunately, satisfactory procedures for such a removal do not seem to exist. An alternative approach is to use two‐sample tests whose significance levels remain the same when a non‐conforming observation occurs, and is removed, as for the case where the samples were both truly random. The equal‐tail median test is shown to have this property when the two “samples” are of the same size