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I have survey data from students from two Universities. One of the questions in the survey had 4 response categories and students were allowed to check only one (categorical variable).

I want to make a table that shows the odds ratio and 95% CI for OR with University arranged in columns and all 4 possible answers in rows. I also want to see if there is a statistical difference between ORs in rows.

Is it possible? If so, how should I do it?

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I think you misunderstand exactly what an odds ratio is. To see why it's probably not the best way to answer your question requires a tangent into exactly what odds and odds ratios are. The simple answer is that an odds ratio is a ratio of ratios which isn't really as complex as most make it sound.

To begin, you must first understand what odds are. It's simply the odds of success to the odds of failure. This is similar to but distinct from probability. So an odds of 1 means a 50-50 chance of success. An odds of 2 would mean you expect 2 successful outcomes for every unsuccessful one. An odds of .5 would mean half a success for every failure or, put differently, 1 success for every 2 failures.

With this in mind, an odds ratio tells you how much you can expect the odds of your outcome (your dependent variable) to change for a 1 unit increase in your independent variable. So, an odds ratio of 2 for your independent variable would mean the odds of success double for every one unit increase of your independent variable. From this, you should now wonder what the original or base odds were because doubling a small number is not the same as doubling a large number. Unfortunately, most never consider the baseline odds when interpreting odds ratios which is most unfortunate.

Now that you hopefully have an understanding of odds and odds ratios you should be able to see that they are most useful for understanding dichotomous outcomes - things that can be quantified as success vs. failure. This could be something like pass vs. fail, dead vs. alive, incarcerated vs. not incarcerated.

From your description it sounds like the outcome you're interested in is categorical but not dichotomous which makes it somewhat less intuitive for study using odds ratios.

It is still possible though. If there's an ordering of the categorical variable then you can generate odds ratios which predict the odds of being in a higher category vs. a lower category. If the categories are not rank-able then you can pick a base or reference category and compare the odds of being in any other category vs. that one. However, these approaches aren't very intuitive and there's probably an easier way to understand the relationship between university and your outcome, perhaps a contingency table.

In any case it would help to know more about your data and research question.

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  • $\begingroup$ My 4 response categories are not rankable. I assumed that ORs are not the best thing to do, but my supervisor is asking for it. She saw it in an article dealing with similar questions, but there, response categories were indeed rankable (levels of education). I know how to get ORs in 2 x 2 tables, but it's of no use. I've already made contingency tables and compared column properties (and noted statistical difference between columns). Is there anything else I could have done? $\endgroup$ – Lee Mar 24 '12 at 12:38
  • $\begingroup$ I know SPSS will do multinomial unordered logit regression. I don't routinely use SPSS for that sort of task though so I can't provide you with sample code. You would just run your mlogit model with your 4 category variable as the outcome and university as the predictor and report the resultant odds ratios. Pick a sensible reference category because the odds ratios reported will be relative to that category. The reference category should also have a healthy number of responses. $\endgroup$ – Will Mar 24 '12 at 18:57
  • $\begingroup$ Assuming you choose category 1 as the base or reference then the reported odds ratios will tell you the effect that university has on being in category 2 vs 1, category 3 vs 1, and category 4 vs 1. As you can see this probably isn't as intuitive as a simple contingency table. The contingency table on the other hand is not useful when you wish to partial out the effect of multiple predictors on your outcome. Try to persuade your supervisor that fancier sounding statistics don't always provide more insightful answers. $\endgroup$ – Will Mar 24 '12 at 19:03
  • $\begingroup$ Thank you so much. I'll try out both your advice. Hopefully the second one (persuading my supervisor) will work. :) $\endgroup$ – Lee Mar 24 '12 at 20:45

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