How to compare two related ordinal variables?

Question

I would like to compare two measurements of a variable (anxiety) on the same subjects at different times. I was planning on using the paired samples t-test in SPSS, but I believe the variables are ordinal, since the questions were scaled 0,1,2,3. How can I compare them?

Expanding on @StasK 's comment: There could be a number of things you want to compare. I would start with a crosstabs of the two time points. Then you can define various changes that might be interesting: How many people get worse? How many people get a LOT worse? How many people get better? A lot better>? Stay the same? etc. And if you have additional info on the people, you can do a lot more interesting stuff. — Peter Flom, Aug 30 '12 at 17:29

score 5 · Answer 1 · edited Jul 16 '22 at 20:30

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Welcome to the site, ellen.

You can conduct contingency table analysis, and that can be done in two ways.

First, you can tabulate the category against the occasion, which would give you a 2x4 table with 3 degrees of freedom, and test for independence of the counts. The test will tell you whether the marginal distributions of the response have changed between the two occasions.

Second, you can tabulate the responses one against the other and perform the independence test that way -- although we can be pretty sure that the null of independence will be rejected. Based on this tabulation, you can also compute the polychoric correlation that would demonstrate how strongly the two measurements are related.

edited Jul 16 '22 at 20:30

answered Aug 30 '12 at 17:25

StasK

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For 2-way cross-classification, I would have thought of ordinal quasi-symmetry model (which account for pairing, unlike usual Pearson $\chi^2$). I also gave an example with R. In case the OP cannot access Psychometrika, John Uebersax provide a good overview of polychoric correlation. – chl Aug 30 '12 at 18:36
I thoughtI could correlate the variables using Spearman's rho. – ellen Aug 30 '12 at 18:40

score 1 · Answer 2 · edited Apr 13 '17 at 12:44

To @StasK, I think the contingency table doesn't work here since the samples are paired. The contingency table cannot account for the dependence between the paired samples.

The Wilcoxon signed-rank test compares the difference between two paired samples when the response variable is on ordinal scale, and thus fits your case the best. Note that the Wilcoxon signed-rank test does assume that the distribution of the difference between the two paired samples is symmetric. This assumption needs to be justified. If violated, the Sign test then needs to be used.

I answered a similar question here, in which there are links about the tests, and tutorials of how you could use SPSS for this purpose.

score 1 · Answer 3 · answered Aug 30 '12 at 17:17

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Since the data are not continuous and certainly not close to being normally distributed a nonparametric paired test seems to be the answer. My suggestion would be the Wilcoxon signed rank test.

answered Aug 30 '12 at 17:17

Michael R. Chernick

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How to compare two related ordinal variables?

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