# Is this variable ordinal, interval data or discrete?

We asked people to evaluate their skills in different fields with this kind of question: " On a scale from 1 to 5, how would you qualify your skills in Field A, with 1 been 'Not skilled at all' and 5 been 'Very skilled'? " (I believe it's a kind of Osgood scale).

I guess if we asked people to chose between categories and then recoded those categories on a scale from 1 to 5, this variable would have been ordinal. But here we asked them a number directly and just told them what was the correspondence of the minimum and the maximum of the scale. So is this variable still ordinal? Or is it discrete or Interval data?

The aim here is to detect differences between skills in different fields (so between different questions) and I read that it may not be a good idea to use some statistical tests (e.g. the Wilcoxon Signed Rank Test) on ordinal data (Does it ever make sense to treat categorical data as continuous? & Is ordinal or interval data required for the Wilcoxon signed rank test?).

The only way it would be interval is if there is some reasonable way of quantifying a person's skill level, and you believe that the difference between the skill level of someone who put down $n$, versus someone who put down $n+1$, is constant, or close to constant, for every $n$. That is, the difference between someone who put down a 1 and someone who put down a 2 is roughly the same as the difference between someone who put down a 2 and someone who put down a 3, etc. Note that if respondents interpreted it as percentiles (1 is first 20 percentiles, 2 is 20 to 40 percentile, etc.), then interval would probably not be a good fit. It's ultimately up to you to decide whether you want to model the data as being such, based on what you know about the data, what you want, and how well different models get you what you want.