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I ran a survey containing a multiple choice question (i.e. you can only select 1 of 5 options; the options are considered nominal variables). This survey was completed by 2 different groups (no repeats). There were 1600 responses from the first group, and 600 responses from the second group.

I would like to show that there is no significant difference in how the two groups answered the multiple choice question. For instance, the number of people in Group 1 who selected options 1, 2, 3, 4 and 5 was not significantly different from Group 2.

What statistical test should I use?

Thanks!

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You have two alternatives if you are looking at a difference in proportion of people rather than number. Proportion makes more sense in your case.

  1. Using 5 two sample tests of proportions; given your high sample size, it seems Ok to assume normality of the underlying distribution. Null hypothesis is both the groups have the same proportion.
  2. Go for a MANOVA test on all the 5 proportions together.
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    $\begingroup$ For the 5 tests of proportions, would adjusting alpha to reduce Type I error apply (e.g. something like Bonferroni's correction)? $\endgroup$ – Jane Wayne Nov 30 '17 at 22:09
  • $\begingroup$ For the MANOVA, I think he'd have to use one-way MANOVA with the independent variable being the 2 groups, and dependent variables being the 5 choices, right? If he does detect a statistically significant difference, what would be the follow-up procedures (post-hoc testing)? I've done post-hoc testing for 1-way ANOVA using Tukey's HSD, and I'm wondering in the case of p < alpha, what would be the post-hoc testing procedures for 1-way MANOVA. $\endgroup$ – Jane Wayne Nov 30 '17 at 22:12
  • $\begingroup$ @JaneWayne: You are right about the Bonferroni's correction. For the Post-hoc testing in ANOVA, I use post-hoc testing to find possible pairs that differ significantly when there are more than 2 groups. In this case, I don't think that is required as there are only two groups. $\endgroup$ – kasa Dec 1 '17 at 0:23
  • $\begingroup$ Thanks for the replies, I was wondering if it were still possible to use a one-way MANOVA if the dependent variable (the 5 choices) were not continuous (i.e. a nominal variable). $\endgroup$ – Dodo_13 Dec 1 '17 at 16:14
  • $\begingroup$ @Dodo_13 Here the variable under consideration is the proportion of people who opt for a particular choice. This is a continuous variable. If you feel that answer is satisfactory, please accept it $\endgroup$ – kasa Dec 1 '17 at 16:49

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