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I have a group of individuals that is independent and identical distributed. Within each individual $i$, one may observe $N_i$ observations. The task is to test whether the within-individual observations are independent or not.

Currently I am considering runs test or rank von Neumann ratio, but I am not confident whether I should use them.

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Can you explain a little more about what is being observed for each individual? It’s difficult to say how this should be treated. Suppose that each individual has a set of characteristics. If each individual is randomly selected then one’s attributes should not be related to another’s other than by chance. The attributes of the individual, however, are most likely correlated (demographics, test scores, etc.)

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  • $\begingroup$ The observations could be, say, duration of absences from work within a year, scores of a series of exams etc. $\endgroup$ – skyindeer Apr 16 '18 at 16:03
  • $\begingroup$ Suppose one flips a coin in Europe and another person flips a coin in America. After this, both individuals win the lottery. If these individuals were chosen randomly, then both winning the lottery cannot be anything but chance. Conversely, one winning the lottery because the other didn’t would not be because of chance, thus making these two individuals not randomly chosen since there was a variable they shared that was not observed. (Ex:if two individuals have traits, say test scores, that are related, perhaps these folks came from the same area of the world but this wasn’t originally known.) $\endgroup$ – SFExplorer Apr 16 '18 at 16:13
  • $\begingroup$ For each individual person, their test scores may be related to their absence at work, but probably not correlated to winning the lottery unless it was rigged (something we have to make an assumption about.) $\endgroup$ – SFExplorer Apr 16 '18 at 16:16

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