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After reading this answer, I found myself confused. Say I am looking for the percentage of people who are likely to vote for a particular candidate. I am sampling from a population which is known to have groups with non-independent answers, for example, a family (such as husband and wife who gives exactly same answers). Hence, I can expect my sample to contain some of these groups too. Now, in a strict sense, can I use random sampling here to obtain the percentage of votes expected?

I understand sampling is routinely used, but is it usable in a strict theoretical sense? Or are we only taking about the independence of the sampling process alone, and not the population?

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  • $\begingroup$ I edited the title to make it more informative. It could be made more elegant, but I am missing the right terminology. $\endgroup$ – Richard Hardy Feb 5 '16 at 20:15
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Yes, the sample mean from a correlated sample is still unbiased, because of the linearity of expectation.

https://en.wikipedia.org/wiki/Expected_value#Linearity

The variance, however, could be much larger than if you have an uncorrelated sample (assuming positive correlation).

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  • $\begingroup$ Any reference from basic stats books that I can read? $\endgroup$ – rahul Feb 5 '16 at 20:10
  • $\begingroup$ @linksys, could you expand your answer a little bit? One-liners are not very useful as answers (although could serve as comments). $\endgroup$ – Richard Hardy Feb 5 '16 at 20:11
  • $\begingroup$ @RichardHardy, I expanded my answer slightly. $\endgroup$ – linksys Feb 8 '16 at 15:38
  • $\begingroup$ @linksys, that's slightly better :) $\endgroup$ – Richard Hardy Feb 8 '16 at 15:45
  • $\begingroup$ About the variance, say we have a set of correlated random binary variables. Say I measure the output of each, and produce a set of black balls to represent Yes, and white balls to represent No in the measurement. Now, when I sample from this set of balls, shouldn't I get the same variance as that of the original correlated binary variables, even though the balls are not correlated? $\endgroup$ – rahul Feb 18 '16 at 17:36

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