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I created a poll on a sports forum asking people how they think their favorite NBA team did this off-season. The poll options were: Top 10, Middle 10, Bottom 10. I expect dozens of people to respond, which isn't a huge sample.

The hypothesis I'm testing (unbeknownst to the voters) is that there will be a "homerism" bias which makes the "Top 10" vote more likely. In terms of Bayesian methodology, I would like to compare two models, one has preference weighted uniformly across all three poll choices, and the other has the weight heavily biased towards the "Top 10" choice.

So, my question is how to create the prior and the likelihood functions for this type of problem. I don't need full details, but if you could point me in the right direction, I'd appreciate it.

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I think it would be difficult to draw meaningful results from a poll like this. You want to test for a bias in how fans view their team, but to do so you would need to control for:

  • Response bias: You only get the opinions of those who want to respond, which in a forum environment generally means those with a strong opinion
  • Distribution of fans: Successful teams might have more fans which could result in more votes for 'top 10' even if there is no perception bias.

Without being able to control for these (and probably other issues) I don't think you could be too confident in testing the hypothesis you are interested in.

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  • $\begingroup$ I agree with those points. Let's assume we do control for those things. I'm really here to learn how one would do the Bayesian analysis, not conduct a proper poll (although that is obviously also very important). $\endgroup$
    – thecity2
    Commented Aug 8, 2012 at 6:28
  • $\begingroup$ If you are still interested in an answer, I would suggest adding whatever you have come up with so far in terms of the prior. For a relatively simple situation like this if you are able to express in words the assumptions you are making before obtaining the data, then you are almost done in terms of coming up with the prior; you just need to turn the words into maths. It really depends on your assumptions, which aren't concretely stated in the question. $\endgroup$
    – Bogdanovist
    Commented Aug 15, 2012 at 23:13

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