# Categorical or Categorial? Is there a difference between the two terms from a statistician's point of view?

I have heard about Categorical distribution and Categorical variables in statistics. But what is a Categorial variable? Can both Categorial and Categorical be used interchangeably? Are there specific cases in which we use either of these terms?

• "Categorial" is a common typographical error (especially among non-native English writers). Right up there in frequency is "binominal" (a technical term in other fields that is wholly absent in statistical literature) for "binomial."
– whuber
Jun 30 at 12:21
• Categorial is also used in philosophy, as witness Stephan Körner's book Categorial Frameworks. To the point, this is misquoted by Wikipedia as Categorical. But I agree: the term categorical is utterly standard in statistics for this meaning. Jun 30 at 14:54
• Categorial is uncommon, but still too common to be solely a typographic or an idiosyncratic error. (I've never seen historial or the like.) It must have some currency as a variant form of categorical in English; or in another language, in which perhaps analogues of categorical & categorial have more distinct senses. Jun 30 at 16:51
• Ah! .... kategorische in German corresponds to categorical in the sense of "absolute", "unconditional", or "unqualified"; kategorial to categorical in the sense we're here concerned with. So de.m.wikipedia.org/wiki/Kategoriale_Variable. In French there seems to be a similar distinction between catégorique & catégoriel - fr.wikipedia.org/wiki/Variable_cat%C3%A9gorielle. Jun 30 at 19:19
• @Aadi: Yes - categorial even sometimes makes it into published work - Gertheiss & Tutz (2010), "Sparse modeling of categorial variables", Ann. App. Stat., 4, 4. That's not a typo in the title - the authors are from Munich University & use categorial throughout the paper. Jul 1 at 11:56

I have literally never heard 'categorial' (without the second C) and assumed that this was a typo. But some googling does indicate that this word is used - in linguistics.

In statistics, as far as I know, we only use categorical.

As mild support for this claim, if one googles 'categorial statistics', Google assumes you've made a typo and returns only results for 'categorical statistics'.

Also, searching for 'categorial' on wikipedia returns no links, but the closest suggestion is 'categorial grammar' (again, about language/syntax). In contrast, searching for 'categorical' returns a bunch of suggestions including several articles about statistics (specifically categorical data), maths and logic.

EDIT: This excellent comment by Scortchi may have tracked down the origin of the confusion to German and French distinctions that are mostly absent in English.

• Thanks for the answer. I recently saw someone using 'Catergorial variables' while talking about Loss functions. Also, both words seem to be having the same meaning. 'Categorical' seem to be more prominent in the web.