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I am used to calling this thing "covariance matrix" and only very rarely see and here it being called "variance-covariance matrix". However, our tag here is called . It used to slightly annoy me all the time, so I have recently created a tag and voted to make it the synonym of the main tag. The voting has not finished yet$^*$, but in the meantime I see that my newly created tag is being used by other people.

This makes me wonder: shall we maybe have as the master tag, and as its synonym? I tried some google searches to establish the usus: "covariance matrix" search gives 3 mln results, and "variance-covariance matrix" only 400k (this is included in 3 mln too). On google scholar the numbers are 900k and 100k respectively. So it seems that "covariance matrix" is indeed a more common expression used over 80% of the times.

I am going to post two answers, please upvote the one with your preferred master tag.


$^*$The voting is likely to never finish; apart from me, only one single person (@gung) has taken part in it so far. Sad as it is, we will need a moderator to create this synonym one way or another.

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    $\begingroup$ My personal preference would actually be variance matrix, but I expect few people would go for that (and with a first-past-the-post system you don't want three options anyway, so I won't add it to the choices here). The corresponding searches are also smaller than either present option. Nevertheless it might be worth having as a synonym of whichever of these alternatives wins. $\endgroup$ – Glen_b -Reinstate Monica Oct 19 '15 at 16:51
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    $\begingroup$ Interesting, @Glen_b, I've never heard "variance matrix" before. Good idea to add it as another synonym. $\endgroup$ – amoeba says Reinstate Monica Oct 19 '15 at 18:53
  • $\begingroup$ @Scortchi, I based this entirely on the above by comment by Glen_b. I have never seen this exact term before. A search on google scholar finds lots of uses, but many of them are for "co-variance matrix"; still, by looking at the search results it does seem that some people refer to it simply as "variance matrix". No idea how widespread it is. Perhaps we should rather take if off from the wiki excerpt. $\endgroup$ – amoeba says Reinstate Monica Oct 22 '15 at 13:31
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    $\begingroup$ It's easy to find out approximately how widespread it is; search on "variance matrix" -"co-variance matrix". If I recall correctly it gets about a quarter the hits of "variance-covariance". $\endgroup$ – Glen_b -Reinstate Monica Oct 22 '15 at 13:49
  • $\begingroup$ This is interesting. I've never really consciously thought about this, but whenever I'm trying to find, what I call the covariance matrix of, say a matrix $X$, I write $Cov(X)$ instead of of $Var(X)$ as some do. $\endgroup$ – StatsStudent Oct 29 '15 at 23:22
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The master tag should be .

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  • $\begingroup$ I would upvote this option, but I cannot upvote my own answer. $\endgroup$ – amoeba says Reinstate Monica Oct 19 '15 at 13:44
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    $\begingroup$ When I teach, I refer to the "variance-covariance matrix", which I think is clearer. It isn't wholly unheard of; the R command is vcov(), eg. That said, most of the time I just say "covariance matrix", probably out of laziness ;-). Nb, as long as they're linked, so one is the synonym of the other, it won't really matter. $\endgroup$ – gung - Reinstate Monica Oct 19 '15 at 15:22
  • $\begingroup$ Interesting about the name of the R function, @gung, I didn't know. In Matlab it's cov(). In SciPy it's cov() too. $\endgroup$ – amoeba says Reinstate Monica Oct 19 '15 at 15:28
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    $\begingroup$ I agree with @gung that "variance-covariance" has added clarity. Over the years, one pedagogical point has brought me back to liking "covariance matrix" a bit more: "variance-covariance" suggests "variance" and "covariance" stand in contradistinction to one another, whereas really we should be thinking of "variance" as nothing more than a special type of covariance. (One of the many things where whuber's influence on this site has changed the way I perceptualise some key concepts, though I can't recall him making this exact comment in the context of the nomenclature of these matrices.) $\endgroup$ – Silverfish Oct 19 '15 at 20:14
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    $\begingroup$ @Silverfish, I am happy to agree that the term "variance-covariance matrix" has some extra clarity; if the tag in question were called [variance-covariance-matrix] I would be less annoyed by it (but arguably it's too long). But if we compare [covariance-matrix] and [variance-covariance], I find the first one clearer because of the word "matrix" in it. Apart from that, good point about some implied tension between "variance" & "covariance". $\endgroup$ – amoeba says Reinstate Monica Oct 19 '15 at 20:34
  • $\begingroup$ @amoeba, that's a good point. That's another reason to prefer this version. $\endgroup$ – gung - Reinstate Monica Oct 19 '15 at 22:49
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    $\begingroup$ I've done this now $\endgroup$ – Scortchi - Reinstate Monica Oct 22 '15 at 10:42
  • $\begingroup$ Thanks, @Scortchi. I think [variance-covariance] had a wiki excerpt, but [covariance-matrix] unfortunately doesn't and now I cannot access the old excerpt, because I always get a redirect to the new tag... Can you as a mod perhaps still see the old wiki somehow? Then you could copy it to the new tag. If not, I can suggest a new wiki excerpt. $\endgroup$ – amoeba says Reinstate Monica Oct 22 '15 at 10:50
  • $\begingroup$ @amoeba: I'm afraid I can't see the old wiki either ... $\endgroup$ – Scortchi - Reinstate Monica Oct 22 '15 at 12:30
  • $\begingroup$ @Scortchi: I made a wiki edit suggestion. But it's good to know for the future that one should better take care of the tag wikis before merging. $\endgroup$ – amoeba says Reinstate Monica Oct 22 '15 at 13:19
  • $\begingroup$ A covariance matrix equation can be derived from the variance equation, true, but it is not always trivial (as demonstrated here) and the purpose and usage is quite different. So I think that "variance-covariance" is an amalgame, while "covariance-matrix" is quite precise. Thus, "covariance-matrix" should be the master tag. $\endgroup$ – gaborous Oct 23 '15 at 17:47
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The master tag should be .

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