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!)
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$\begingroup$ it's a comparison of pre- and post-test data, using an 11-point numerical scale if that helps $\endgroup$– Ay-JayJan 7, 2013 at 18:56
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2$\begingroup$ sorry, probably could have explained that slightly better! I'm comparing participants pain score (which they rate on a scale of 0 to 10) before and after treatment to see if there has been an improvement/deterioration. Hope this helps! $\endgroup$– Ay-JayJan 7, 2013 at 19:03
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1$\begingroup$ This question is more interesting than I initially thought it would be. See here. You could always use just a sign test, but this test is less powerful. $\endgroup$– R SJan 7, 2013 at 19:13
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1$\begingroup$ Thank you for the reply. I do realise the sign test is less powerful, my question was largely to ensure I wasn't going about this completely wrong! If I can ask for your opinion, which would you suggest under the circumstances - the more powerful wilcoxon, or the sign test, as it is definitely appropriate, if not as powerful? And can you think of any sources I could use to back up my decision for my paper? Many thanks for this! $\endgroup$– Ay-JayJan 7, 2013 at 19:44
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4$\begingroup$ Well, you should not use the sign rank test. I would say that the sign test would be appropriate. I learned my nonparametrics out of Lehman. Using the rank test makes sense, because you have before and after treatment data. The one thing you need to take into account would be a control group, as time would probably play a factor in pain levels. $\endgroup$– R SJan 7, 2013 at 21:38
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2 Answers
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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.
answered Jan 8, 2013 at 13:20
Scortchi - Reinstate Monica♦Scortchi - Reinstate Monica
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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.
