Is ordinal or interval data required for the Wilcoxon signed rank test? Having looked at multiple online sources, I can't seem to get a straight answer. Could someone please clarify for me if ordinal data is sufficient to use for the WSRT and if not, is the sign test an appropriate alternative?
Finally, this is for my dissertation project at university and so if any references/literature could be included in answers it would be much appreciated as I need to justify my choice of test either way and so far have only found answers from websites (which I can't reference!)
 A: You can't use the signed rank test as a paired difference test for ordinal data, because you can't take differences of ordinal data.  If your scale were from A to K, & one patient's before and after scores were F and C, then what's F minus C equal to?†
The question really needs to be about the pain scale - is it reasonable to treat it as an interval scale, or can you transform it to an interval scale, so that going from '8' to '6' is the same reduction as going from '4' to '2'?  Just because you label it with numbers doesn't make that the case, & if it's not you need to use the sign test (which requires only the judgements that '8' is more than '6', & '4' is more than '2') instead.
The medical literature would be the place to start looking for more information.
† You could still use the signed-rank test if you're able to rank all the differences: F minus C may not have a numerical value but you know it's bigger than G minus D. But there could be a lot to compare & it's not often very practical.
A: According to the wikipedia page on Wilcoxon signed signed rank test, which could take ordinal data, it could still be applied to paired measurements like those in your case. I also found an examples using this test at this textbook.
However, with a closer look, in both examples, the magnitude of difference is assumed and require for computing the statistics. So It is not clear how, if possible to subtract e.g. 'Agree' from 'Strongly Agree' (quote @Scortchi
below). In contrast, a sign test signtest does not have this problem.
