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We have

  • a normal-distribution tag with 3158 questions, no tag wiki, and the following tag wiki excerpt:

    The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is often used as a reference against which other distributions are compared.

  • a normality tag with 530 questions, no tag wiki and the following tag wiki excerpt:

    Refers to the normal distribution, the Gaussian continuous probability distribution.

There are 66 questions with both tags.

To be honest, I don't see the difference between the two tags. I would have understood something like "normality-testing", but not these two.

Is there any difference in the concepts at all? If so, maybe someone could make this clearer in the tag wiki excerpts, and ideally also indicate in each excerpt when the other tag should be used. However, I'm afraid that the two tags are so close to each other that people will continue to confuse them. Thus, I'd propose that "normality" simply be made a synonym of "normal-distribution".

Thoughts, anyone?

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I mentioned this once before, a long time ago, but can't find it now. There is [supposed to be] a distinction between them. [normal-distribution] is about the distribution itself, whereas [normality] is a property. For example,

How is the chi-squared distribution related to the normal distribution?

would be a question appropriate for the [normal-distribution] tag. On the other hand,

How important is the normality assumption for valid inference with a multiple regression model?

is a question appropriate for the [normality] tag.

That said, while better excerpts might be helpful, these are probably just too close together to ever be consistently used correctly by a large number of different users, many of whom are not steeped in how the site works and/or these kinds of nuances. I still think making them synonyms is a viable option.

Another option is to change the name of [normality] to [normality-assumption] and substantially rewrite the excerpts (and perhaps wikis). That might make it sufficiently clear to be workable going forward.

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    $\begingroup$ Yes, I did search for the two terms before posting the question, and I was a bit surprised at finding nothing. Thank you for not finding your own post on this, either - I find few things as embarrassing as posting a question and having it flagged as a duplicate of some easily found question within 30 seconds. $\endgroup$ – S. Kolassa - Reinstate Monica Mar 15 '18 at 12:36
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    $\begingroup$ I am usually a big supporter of synonymizing tags quite liberally, but in this case I have to say that I do see a meaningful difference. CC @StephanKolassa. [Normality] is supposed to be about normality testing and normality assumption of different procedures. Looking at the most upvoted Qs in [normality] tag, they are all about these topics. Are we sure there actually is much confusion between these two tags? $\endgroup$ – amoeba says Reinstate Monica Mar 15 '18 at 13:33
  • $\begingroup$ That said, I can see that the wiki excerpt for [normality] is unhelpful and even misleading. $\endgroup$ – amoeba says Reinstate Monica Mar 15 '18 at 13:35
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    $\begingroup$ @amoeba, we could change the name to [normality-assumption] & rewrite the excerpt. I'd have to go through the threads, but my impression is that when you get down into the mass of Q's w/ few votes & few views, it's a hash. I agree that the top ones are more coherent. $\endgroup$ – gung - Reinstate Monica Mar 15 '18 at 13:45
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    $\begingroup$ @amoeba: thanks for your perspective. Could you please post it as an answer so we can vote on it? I personally do see a difference along the lines you suggest, but as I wrote, I don't know whether we would be able to keep the tags distinct. Perhaps you would like to change the excerpts along the lines I suggested, including indications about when to use the "other" tag? $\endgroup$ – S. Kolassa - Reinstate Monica Mar 15 '18 at 15:15
  • $\begingroup$ @StephanKolassa I basically agree with gung's answer (+1) and in particular like his suggestion in the last paragraph (after the update). So I don't think I should post another answer. $\endgroup$ – amoeba says Reinstate Monica Mar 15 '18 at 20:52
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    $\begingroup$ @StephanKolassa I edited the excerpts (but I am sure one can come up with better formulations). I think renaming [normality] into [normality-assumption] makes total sense and should be done. After that we can still discuss whether to make it a synonym, but at the moment I am rather inclined to be against. $\endgroup$ – amoeba says Reinstate Monica Mar 15 '18 at 21:02
  • $\begingroup$ We definitely had some kind of a discussion on this along the lines you mention. $\endgroup$ – Glen_b Mar 15 '18 at 21:13
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    $\begingroup$ I see that this answer has been marked as accepted. Should we rename [normality] to [normality-assumption] now? The excerpts have already been edited. $\endgroup$ – amoeba says Reinstate Monica Mar 20 '18 at 9:22
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    $\begingroup$ [normality] should disappear in 24 hours, @amoeba. $\endgroup$ – gung - Reinstate Monica Mar 20 '18 at 13:26
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That makes sense to me. Even if someone could up with some way to distinguish these, I think there would be a ton of confusion about which to use where and a lot of error in their use. So I favor making one the synonym of the other.

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