Talk:Covariance/Draft

Definition

Peter - Please try again!

You have replaced a definition that was easily understood by most people, with one that can only be understood by mathematicians.

I know what covariance means, and I was once familiar with how it is calculated - and I find your definition absolutely incomprehensible. Just imagine how unhelpful it would be to (say) an economics student who needs to understand financial risk analysis - as a practical tool, not as an intellectual curiosity.

Nick Gardner 09:02, 25 January 2010 (UTC)

Nick, I understand your concern, and I am not surprised by your comment. I probably have gone too far in the attempt to avoid mathematical jargon. On the other hand, the definition no longer needs to explain everything since now the users can look at the page for more information. (Suggestions and comments for it are welcome, of course.) But I hope we can find a mutual satisfactory solution.

There is, however, a general problem behind this that will need to be addressed some time. It is the use of the r-template for quite different purposes.

• It was invented for and is mainly meant for the Related Articles subpage showing brief definitions.
• But it is also used in Glossary subpages (e.g., by you) and in Catalogs. Both these uses require other types of definitions and may, in addition, be context dependent. The Definition is not well-suited for this because it can be (and usually will be) changed without any regard to these uses.

--Peter Schmitt 01:10, 26 January 2010 (UTC)

Peter and Guido, the new definition and article seem to me to be much more useful for practical purposes, and I am now content.

What do you recommend using instead of the r-template ? Nick Gardner 06:22, 26 January 2010 (UTC)

Misleading phrase?

"And it is 0 if the two variables are not linearly correlated" — I bother that someone may conclude that, say, Cov(X,X²)=0 for every X just because their correlation is nonlinear. Boris Tsirelson 15:23, 26 January 2010 (UTC)

You are right. Though - taken literally - the statement is correct, it can easily be misunderstood. (Originally it had "independent" instead of "not linearly correlated".). --Peter Schmitt 23:35, 28 January 2010 (UTC)

Which space?

"used to compare two real random variables on the same sample space" — acceptable as is, but "...on the same probability space" would be more exact (since sometimes different probability measures on the same sample space are considered). Boris Tsirelson 18:12, 15 May 2010 (UTC)

I have made this explicit. (But my impression was that this is silently assumed in statistics. I may easily be wrong.) --Peter Schmitt 20:58, 17 May 2010 (UTC)

Notation

"Since the covariance cannot distinguish between random variables X and Y that have the same deviation" — maybe X₁ and X₂ are better than X, Y here (since X and Y are used to appear in Cov(X,Y)). Boris Tsirelson 18:22, 15 May 2010 (UTC)