I'm a 5th semester statistics major doing an internship at a government agency. My department is performing a research on how well citizens evaluate services provided by the agency.

People can evaluate the questionnaire in six different ways: 1, 2, 3, 4, 5, or 6. The response variable is therefore ordinal, with 6 different categories. The values are discrete, and follow no particular probability distribution as far as I'm aware.

To illustrate, here's a question and how a small sample looks like

How do you evaluate the accuracy of the information provived by the agency?

{5, 3, 2, 6, 1, 2, 4, 3, 6, 3, 2, 1, 2, 4, 5, 3}

My ideas on how to do statistical inference in this situation

What first striked me is that we have to use nonparametric inference methods. My first thought was about Wilcoxon's Signed Rank test, but that requires data to be symmetric and that's not the case.

Then I thought about the Sign Test, but that requires data to be continuous, and that's not the case either.

Now I'm thinking about Bootstrap methods, but as far as I know, bootstrap is used for small samples and now I'm not so sure about any particular inference method, so I'm here looking for suggestions from people with more knowledge and experience.

You might think they wouldn't leave this something this important to the intern. My boss is an economist who has literally said he never cared much about statistics, then left the problem for me to handle.

  • $\begingroup$ Are you going to be modelling anything? I.e. fit any covariates to try to estimate the parameters for different groups and such? If so, then I think The proportional odds cumulative logit model is a good start for ordinal data. Maybe you can just fit a model with just an intercept and that'll tell you the odds someone belongs to X level or below. $\endgroup$ – Huy Pham Nov 24 '18 at 12:11
  • $\begingroup$ I won't be modelling anything in the sense that you're talking about, but I need inference on the mean, and I want to do confidence intervals and hypothesis tests. I actually already did bootstrapped mean, CI and HT. Thank you for the suggestion anyway, I'll take a look at it tomorrow. $\endgroup$ – Victor S. Nov 25 '18 at 13:31

A very quick and easy approach is to create a boxplot for the questionnaire and then check for any outliers. Is a non parametric approach with interpretable results.

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