I thought p-values took into account small numbers in a trial and there would thus be a need for more robust results to attain stat sig results. And I thought the definition of stat sig means that results, whether they occur in a few patients or in a large number, reflect a pattern and are not just due to chance. I'll defer to others on here who are much more knowledgeable than me on statistical matters (admittedly not my forte) but that's my impression.
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