# 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.

Modeling it as discrete would be rather odd; clearly, skill level exists on a continuum, and you are asking respondents to round to the nearest amount.

• Thanks for this explanation. Right, I won't consider it as discrete nor even as interval. What I understand here is that it seems to be very hard to measure somebody's skill and it's not just because of my study design if I can't use a discrete variable. Aug 21, 2018 at 15:48

To me it's still ordinal. Ordinal/discrete would describe the data, not the way the choice is presented to your audience.

• So from your point of view, student's marks, in philosophy for instance, are ordinal data rather than interval, right? I took philosophy as example because I guess the teacher doesn't add points from several exercices to get the final mark - as a math teacher would - but may just think " Yeah this is a Very Good work, I'll give it a 8/10 ". In that case I don't see the difference with my study. Aug 13, 2018 at 15:24
• It is at least ordinal. Whether it is interval data or not is debatable; I suspect it is not. Interval data is a subset of ordinal data. Aug 13, 2018 at 15:42
• Taking either of your examples (1 to 5, Not skilled to very skilled; or 1 out of 10 as a teacher's mark), I ask: Can comparisons between two values be done correctly with arithmetic? In the former, a 5 is probably not 5 times better or 4 units better than a 1-- they're many times better (or even infinitely better). But for a grade on a paper an 8 may be 4 units, or twice as a good, as a 4. A philosophy paper grade may be subjective but if the grading is consistent then the teacher should have some kind of rubric they use for quantifying the performance. Aug 13, 2018 at 16:17
• Thank you @ChrisUmphlett for this explanation. We both agree that, without some kind of rubric for the teacher, both examples are very similar. And you convinced me that both variables might be ordinal, because of what they measure. I guess I can forget statistical tests I'm used to and look for other methods that focus on ordinal data. Aug 21, 2018 at 15:38