Wikipedia:Articles for deletion/Normally distributed and uncorrelated does not imply independent

Normally distributed and uncorrelated does not imply independent

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Per WP:OR / WP:NOTESSAY, essentially. The whole thing boils down to "A Pearson's correlation coefficient of 0 does not mean variables are independent" (adding the normal distribution is a bit of a red herring). I do not see sources sufficient to establish that this very topic is anywhere close notable. It might be mentioned in a lot of places (e.g. ref 2) as a common student mistake, but not as an encyclopedic subject worthy of careful study.

If not kept, some cleanup is needed, as there are quite a few incoming links. A selective merge to the PCC article or the PCC section of correlation and dependence or might be workable. Tigraan^{Click here to contact me} 09:33, 2 July 2018 (UTC)[reply]

Merge and delete. Seems like some of the material here could be merged into Correlation and dependence, perhaps under 'Common misconceptions'. Much of it is very WP:TEXTBOOKy though. --RDBury (talk) 13:13, 2 July 2018 (UTC)[reply]

You seem to be missing the same point that the nominator missed: If this were to be merged into another article, it should be the articles on the normal distribution and the multivariate normal distribution. Nothing about the normal distribution need be included if they only point were to show that uncorrelatedness does not entail independence, but this article is explaining a fact about the normal distribution, not a fact about the relationship between independence and uncorrelatedness. Michael Hardy (talk) 00:36, 3 July 2018 (UTC)[reply]

Somewhere in Multivariate_normal_distribution#Joint_normality, then? Tigraan^{Click here to contact me} 07:33, 3 July 2018 (UTC)[reply]

Oppose deletion. This is an insightful article that highlights the difference between joint normality and marginal normality. And no, bringing in normality is not a red herring: the whole point is that while joint normality plus no correlation does imply independence (something that does not hold for non-normal distributions), marginal normality plus no correlation does not imply independence. The examples serve to illustrate how this can be. Loraof (talk) 15:00, 2 July 2018 (UTC)[reply]
Your point (repeated below by others) duly noted. However, that makes me doubt even more of the subject's notability; "PCC=0 is not independence" is certainly more interesting in the grand scheme of things^{[original research?]} than (joint normality + uncorrelated) <-> (joint normality + independence) (of course, my subjective judgement on that point is not worth zilch, what matters are the refs). We are not a repository of interesting mathematical facts. Tigraan^{Click here to contact me} 07:33, 3 July 2018 (UTC)[reply]

Note: This discussion has been included in the list of Mathematics-related deletion discussions. MarginalCost (talk) 16:38, 2 July 2018 (UTC)[reply]

Merge with another relevant article. The article is very nicely written and very helpful. I strongly oppose deletion. Goharshady (talk) 17:01, 2 July 2018 (UTC)[reply]
Keep. An important family of counterexamples, properly sourced. There are multiple textbook sources on exactly this topic [1] [2] [3] [4] [5]. —David Eppstein (talk) 17:21, 2 July 2018 (UTC)[reply]
I am not disputing this is well-sourced (as in WP:V), I am disputing the notability (as a standalone article) of that bit of math. I do not think multiple short mentions in specialized textbooks demonstrate notability, per the "in-depth" requirement of WP:GNG. You might well say that nothing else could be expected for a run-of-the-mill theorem and wishing for more is an impossible bar to pass, but is that not an indication of non-notability? Tigraan^{Click here to contact me} 07:33, 3 July 2018 (UTC)[reply]
Keep. Seems like a reasonable short encyclopedia article on some interesting mathematical objects. It would probably also be okay as a section of some other article, but it's hard to see a pressing need to merge. --2601:142:3:F83A:95A9:DA87:64C2:9A47 (talk) 18:01, 2 July 2018 (UTC)[reply]

Keep. Tigraan's statement about a "red herring" shows that Tigraan has no clue what this article is about. In a multivariate normal distribution, linear combinations of the components are independent if they are uncorrelated; this article shows that for each component to be normally distributed is not enough; rather, joint normality is needed. People should wait until they understand what an article says before nominating it for deletion. Michael Hardy (talk) 00:34, 3 July 2018 (UTC)[reply]
See above. Whether I have no clue what this article is about is hardly a rebuttal about my concerns of notability. Tigraan^{Click here to contact me} 07:33, 3 July 2018 (UTC)[reply]
Comment. This article makes a point about the nature of the normal distribution, not about the relationship between uncorrelatedness and independence. I wonder if it should be dumbed down somewhat to make that clearer. I would never have guessed that it could be misunderstood in the particular way in which the nominator and one of the other posters above have misunderstood it. Michael Hardy (talk) 00:57, 3 July 2018 (UTC)[reply]
Delete - This is not an encylopaedia topic, it's an essay or perhaps something for wikibooks. Anything relevant can be put into say Pearson coefficient. The merits of knowing this does not in of itself make it a notable or appropriate topic for an encyclopaedia. -mattbuck (Talk) 10:09, 3 July 2018 (UTC)[reply]

This material certainly does not belong at Pearson coefficient, and the suggestion that it could makes me more sympathetic to Michael Harry's comment than I was before. --2601:142:3:F83A:8985:D0DD:B024:F94C (talk) 11:54, 3 July 2018 (UTC)[reply]

delete. Not a named theorem, method or technique, not independently notable by any stretch. Just examples of Correlation and dependence, and not especially interesting ones being very contrived. There’s nothing special about the normal distribution in this, no evidence in the article that there is.--JohnBlackburne^words_deeds 12:00, 3 July 2018 (UTC)[reply]

Once again, I feel like this validates Michael Hardy's comments. You clearly have failed to understand what the article is about. --2601:142:3:F83A:611C:BD4F:C063:4BF2 (talk) 12:42, 3 July 2018 (UTC)[reply]