# Can some variables be ordinal or interval/ratio, depending on the context?

I believe that some variables can be interval/ratio or ordinal based on the context. I'd like to know people's opinion on this. Let me explain:

Class variable with categories Freshman, Sophomore, Junior, Senior. Seems like an ordinal variable right? Well, a student's class standing is determined by credits. If you are looking at a population where students with 0-29, 30-59, 60-89, 90-119, 120+ credits are Freshman, Sophomore, Junior, Senior, and graduated, respectively, then the categories are equally spaced apart (by 30 credits). Then, you may be able to consider this class variable as a ratio variable that was simply poorly measured (It's like measuring people's height in feet without decimals or inches).

Do you think this is valid?

• There are many posts here relating to this topic more or less (e.g. this one). You might find this useful reading if you have access to it: Velleman, P & Wilkinson, L (1993). "Nominal, Ordinal, Interval, and Ratio Typologies Are Misleading". The American Statistician 47 (1): 65–72 Sep 23, 2013 at 6:51

Aren't we mixing terms here? Continuous should be contrasted with discrete. Ordinal should be contrasted to nominal, interval, and ratio.

• Those categories are far from definitive. Sep 23, 2013 at 3:42
• Agreed zbicyclist. fixed Sep 23, 2013 at 3:51
• (Though I should add that your underlying point was worth making) Sep 23, 2013 at 6:48

I think it's not. Variable is defined by its domain (and its properties) and it's quite deterministic. What you are after is mapping values from one domain to another, and then you may have mapping cross the boundaries of ordinal and continuous spaces.

• Applying terms like "nominal" and "interval" is intended to rule out certain forms of analysis. However, which analysis may be appropriate for a dataset is not entirely "deteministic" or obvious, because it depends on the purpose of the analysis, a conceptual understanding of its variables, and even the statistical relationships among those variables. This richer understanding of the typology of variables suggests that a more nuanced answer would be of greater help.
– whuber
Sep 29, 2013 at 18:56
• This question was edited since my answer the way it changed some semantic. And I completely agree. Sep 30, 2013 at 5:31

It's always been my impression that if you can make the case that the ordinal variable acts as if continuous, where the valued differences between groups are of known, comparable magnitudes, it should be fine. I've seen people argue that you can even do so if they're not of equal distances from each other, but I don't like that argument because the interpretation of model coefficients can't really apply well if there are different theoretical distances.

Otherwise, I think it can be useful, especially when what you're trying to ascertain in the direction of a relationship, or you're trying to compare magnitudes of a relationship across subgroups or clusters.

(And as a shameless plug, I asked a question yesterday or so about how we might be able to test if deviations from interval distances are significant enough to rule out the option for treating an ordinal variable as interval: Testing if treating a categorical variable as continuous is okay)