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It's like the mean of every part increases, but the overall mean decrease; or the mean of a group is larger in every part but is smaller in all samples; or something like this.

I remember there is a name for this phenomenon like this (it may not be accurate) but my impression is very vague and I cannot remember it clearly.

gung - Reinstate Monica
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user900476
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  • [I think you mean Simpson’s paradox.](https://en.m.wikipedia.org/wiki/Simpson%27s_paradox) – Dave Jun 25 '21 at 19:09
  • @Dave Thank you very much, I still have a simple question. If group A has a larger mean in every part than group B but has a smaller mean overall, then which group is better? Assuming the larger the better. – user900476 Jun 25 '21 at 19:22
  • I suggest posting that as a separate question that includes either a drawing or a small data set (can be made up), because I do not totally follow what you mean. – Dave Jun 25 '21 at 19:32
  • It’s like [everything’s amazing now and nobody’s happy](https://youtu.be/nUBtKNzoKZ4) – Aksakal Jun 25 '21 at 19:44

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You are thinking of (one version of) Simpson's paradox. You can find many threads about it on the site.

gung - Reinstate Monica
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  • Thank you very much, I still have a simple question. If group A has a larger mean in every part than group B but has a smaller mean overall, then which group is better? Assuming the larger the better. – user900476 Jun 25 '21 at 19:22
  • @user900476, you need to read through some of the threads we have on the topic. I have a related answer [here](https://stats.stackexchange.com/a/78264/7290). – gung - Reinstate Monica Jun 25 '21 at 20:51