# Wilcoxon signed rank test - interpretation

I have 6 dependent variables that were measured on a 5 point Likert scale (treated as interval here). I want to test if their means differ significantly from the midpoint 3. As the normality assumption is violated, I conducted a Wilcoxon signed rank test. As far as I understood, it tests if the MEAN RANKS are different from each other or from a median.

How would I report my results? If the Wilcoxon test is significant, can I say 'The mean of Variable X differed significantly from the midpoint 3'? To me it doesn't make sense to state that the mean ranks differed, because I only want to prove that the means are significantly different from 3...

• Might be clearer and more accurate to say, 'The median of Variable X differed significantly from the midpoint 3 of the Likert scale." // If sign tests (above and below 3) are significant it might be easier to explain results to a non-statistical audience. Commented May 9, 2019 at 12:00
• Hi Bruce, thanks for your reply. However, I really wish to report the means in a table and then want to test if they are significantly different from 3. So it doesnt make sense to prove that the medians are different from 3, right?
– Mary
Commented May 9, 2019 at 12:14
• Means are meaningful for numerical data. Medians for ordinal. Likert data are ordinal, and I personally find efforts to treat them as numerical to verge on being delusional. // You can't "prove" anything, you can find null hypotheses to be "consistent with data" and report significance level. Commented May 9, 2019 at 12:31
• See the discussion here: Is my interpretation for Wilcoxon Signed Rank test correct? but replace all references to "pair differences" to "differences from 3". Commented May 9, 2019 at 14:07
• Have a look at logistic regression/the package 'ordinal' in R (function 'clm'). I believe that, with some amount of pain, you can use its outputs to construct confidence intervals for the proportion of your population that is in each Likert group category. (There may be easier ways to achieve the same thing, that's just one package I'm aware of). I think that could be a more informative way of describing your responses than what you are currently trying to do with a 'median'.
– Izy
Commented May 9, 2019 at 14:40