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?
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8$\begingroup$ "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." $\endgroup$– whuber ♦Jun 30 at 12:21
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6$\begingroup$ 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. $\endgroup$– Nick CoxJun 30 at 14:54
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2$\begingroup$ 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. $\endgroup$– Scortchi - Reinstate Monica ♦Jun 30 at 16:51
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5$\begingroup$ 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. $\endgroup$– Scortchi - Reinstate Monica ♦Jun 30 at 19:19
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3$\begingroup$ @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. $\endgroup$– Scortchi - Reinstate Monica ♦Jul 1 at 11:56
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2 Answers
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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.
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$\begingroup$ 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. $\endgroup$– AadiJun 30 at 9:26
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3$\begingroup$ Second. In math I've never seen "Catergorial". I think in English that word is almost never used. $\endgroup$– High GPAJun 30 at 18:55
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$\begingroup$ Yeah but please don't use Google typo suggestions as evidence, however mild, for anything. $\endgroup$ Jul 1 at 11:53
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I second mkt's answer; this is a long comment rather than an answer. In math I've never seen "Categorial".
Also, I think in English that word is rarely used. The frequency is about 20 times less than the proper word "categorical"
I asked a question here and English experts will surely help us.
