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I have a data set split into two time periods with the same subjects in each group. In the first 5 years they show above average performance. In the follow 5 years they perform averagely.

How do I statistically prove that this is mean reversion? So far I only have the graph described above to show the relationship. Thanks a lot for helping!

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    $\begingroup$ Can you say more about your situation, your data & your analysis? I don't really follow this, & I suspect it isn't answerable at present. $\endgroup$ Commented Jul 21, 2016 at 16:10

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Statistics can't prove anything, outside the rarefied world of theory. It is, after all, the science of reasoning under uncertainty, so the most you can hope for is finding evidence, not proof.

So, how can you find evidence of regression to the mean? Examine how the subjects were selected for your sample at time 1, and what the average performance among non-selected subjects was. Compare this average performance to the performance you obtained among your subjects at time 2. If your selected high performers ended up looking like typical performers at time 1, then you're likely seeing regression to the mean.

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