Let's say that N randomly chosen persons where asked a question where the answer could be in either of X categories. For example, 500 persons where asked which of the top 5 political parties they support the most. Each person can give only one answer.

How do I determine if the leading party which, for example, got 33 % is truly larger than the 2nd largest party that got 29 % (on a certain confidence level).

Calculations like these solve my question when there are only two choices, but how about my case when there are several? http://www.stat.wmich.edu/s216/book/node85.html

  • $\begingroup$ you can find here a continuation of this discussion: stats.stackexchange.com/questions/19537/… $\endgroup$
    – L_T
    Commented Dec 10, 2011 at 12:54
  • $\begingroup$ If the person can give only one answer then this is single choice, not multiple choice. $\endgroup$
    – Niksr
    Commented Oct 31, 2015 at 1:46

2 Answers 2


Find out if there's any difference at all through Pearson's Chi Square. If this turns out significant, then do a (set of) post-hoc test(s), e.g. Tukey's HSD.


You would need to use the "Simultaneous Score Intervals for Difference of Proportions" to solve your question. The reference is " Agresti et al. 2008. Simultaneous confidence interval for comparing binomial parameters. Biometrics 64, 1270-1275.

The corresponding R code is available in http://www.stat.ufl.edu/~aa/cda/software.html



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