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I would not be surprised if a lot of people here have a much better idea of the things I should be checking for than I do. Does anyone have any suggestions?
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I'd suggest pzhon, BruceZ, AAronBrown, or other stats guys have a look. But I don't know if they have time to spend on this kind of nonsense. The deviation observed for JJ would occur ~3% of the time by chance. I don't see anything extraordinary here.
Updated normal probability chart:
