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I have surveyed two groups of people. They had option of answering one of three questions. Both groups picked one of the answers around 50 and 51 percent of time. How do I compare if this difference of 1 percent is significant? I would do margin of error and build confidence interval, but that's for the same group, right? I would like to conclude that one group is not different (in terms of picking certain anwer) from another statistically. Just forwarding me to a suitable method would be great.

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  • $\begingroup$ How have you sampled the two groups? Stratified random sampling? Or are they subdomains of the same sample stratum? $\endgroup$ – g3o2 Jun 18 '17 at 21:14
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Have you looked at this?

Basically you define a contingency table where you have you observed counts (O), where the entries are each group sample and their response.

Then the statistic is simple, you find the expected counts (E) under the hypothesis that there's an indipendent choice (simply multiply rows and cols totals), and calculate:

\begin{equation} \sum(O_i - E_i)^2/E_i = \chi^2 \end{equation}

Then you are looking at the Chi-Squared distribution to find your threshold of rejection.

I think that the example I linked could be transalted to your case.

Look closely at "Example: Political Affiliation and Opinion and Tax Reform".

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