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Let's suppose there are Y options to choose from. I'd like to run an experiment with a sample of n participants (from a larger population), each will choose 1 option from the Y alternative according to his preference (can be thought of as elections, where each voter needs to pick the candidate for presidency).

How do I calculate the required sample size to know that the results that placed whoever/whatever is positioned in the 1st place (according to # of votes) are statistically significant?

Furthermore, I know things start to get really complicated when you enter rankings into the discussion, but if possible would also be curious to know if there's a way to calculate sample size needed to make the ranking of alternatives itself statistically significant. Anyway, the first part of the question is the one I'm particularly interested in.

Thank you!

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  • $\begingroup$ It's not clear what null and alternative you're dealing with when you say "to know that the results that placed whoever/whatever is positioned in the 1st place (according to # of votes) are statistically significant?" $\endgroup$ – Glen_b Oct 6 '14 at 12:59
  • $\begingroup$ Fair point. If I were polling a sample of the public before an election, what sample size do I need if the population is size N? $\endgroup$ – Optimesh Oct 6 '14 at 13:31
  • $\begingroup$ That depends on what exact questions you want to answer from your poll, and to what accuracy. But that's not related to statistical significance; it's related to widths of confidence intervals. $\endgroup$ – Glen_b Oct 6 '14 at 20:18

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