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I have a follow up question to the answers given in the US Election results 2016: What went wrong with prediction models? question. I suspect there is some violation of an independence assumption among the samples taken in election polling.

Specifically, I think that poll results affect the sample population. I think that people have gotten a sophistication of sorts with polls and deliberately try to skew their results by working in concert with others through social media. For instance, if you are a part of a demographic that is polled, it is likely that you or someone you know is also being polled. It would not be a stretch to think that this demographic is loosely networked through social media and therefore able to have an effect on one another.

My question is this: What sort of statistical test can one employ to test for the independence of the samples in the sample population?

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    $\begingroup$ Obviously pools affect voters. But I do not think that there is any point in discussing if there is a conspiracy to bias the polls... Moreover the chance to get sampled to take part in a pool is so small that such conspiracy wouldn't work. $\endgroup$
    – Tim
    Commented Nov 10, 2016 at 18:02
  • $\begingroup$ Also for this to be on-topic you'd need to define precisely what kind of independence you are talking about. Samples to pools are drawn randomly so obviously it's not about dependence in sampling. $\endgroup$
    – Tim
    Commented Nov 10, 2016 at 18:10
  • $\begingroup$ "Independent and identically distributed" implies an element in the sequence is independent of the random variables that came before it. In this way, an IID sequence is different from a Markov sequence, where the probability distribution for the nth random variable is a function of the previous random variable in the sequence (for a first order Markov sequence). BTW I am not interested in discussing any conspiracy theories. The question simply asks how to test for the validity of an assumption of independence. $\endgroup$
    – grldsndrs
    Commented Nov 10, 2016 at 19:03
  • $\begingroup$ Perfect independence rather does not hold for most of the real-life problems. Also, there are time-trends in political preferences, so obviously there is some kind of auto-correlation and samples drawn in similar time period would be similar. Surely you can test for autocorrelation, but even without looking closely at the data I can tell you that it will be autocorrelated. $\endgroup$
    – Tim
    Commented Nov 10, 2016 at 21:14
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    $\begingroup$ Independence means that they aren't related. Non-independence means they are related, somehow. You need to specify how. Eg, the idea that responses are autocorrelated over time means that the people responding on day1 are more likely to say Clinton, & those on day3 are more likely to say Trump, although when averaged over you get 50-50. The idea that the errors are correlated is that if 1 poll is +2 points off towards Clinton, other polls will also tend to be +2 off towards Clinton. There are potentially infinite ways they can be non-independent. $\endgroup$
    – gung - Reinstate Monica
    Commented Nov 11, 2016 at 21:30

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