Variables measured on an ordinal scale have an order but the distance between levels has not to be 'equal'. In case distances would be equal, does this imply the variable is measured on an interval scale?
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levels has not to be 'equal'
No. In Stevens typology of scale, a variable with equal intervals is still ordinal; the issue that would lead to calling it ordinal is usually that you don't know that it is equal, not that you definitely know it to be unequal. However if the differences in adjacent category values are 'equal', it is also interval scale.
Beware of attaching too much value to this particular typology. It can sometimes be helpful, but it's not an ideal taxonomy of variables (it's inadequate for describing many kinds of data) and people regularly treat it in an overly prescriptive way (often leading them into poor choice of analysis). Among a collection of other tools, it can be helpful to pull out now and again, but there are certainly times when you need to think outside its narrow framework.
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$\begingroup$ but not everything that is interval is also ordinal, right? because ordinal variables are qualitative. $\endgroup$ Jan 22 at 23:16
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$\begingroup$ The thing with interval is it has to be equal-intervals. With ordinal that requirement is absent. The point being made is that absence of a requirement is not the same thing as the requirement of its absence. You don't have to know the gaps to be unequal to treat the variable as ordinal. However, the nearer to equal, the less consequential it would be to treat them as equal (ceteris paribus) $\endgroup$– Glen_bJan 22 at 23:30