Caveats for big data?

This stackexchange discussion has people saying that many (most?) significantly large real datasets deviate from normality in tests, making normality tests less useful.

dfrankow (talk) 17:37, 29 December 2014 (UTC)[reply]

How to choose?

Many methods of testing normality are proposed. Which one is best? Are there circumstances that favor one over another? If someone comes to this page to pick a test to use, how do they do it? dfrankow (talk) 17:34, 29 December 2014 (UTC)[reply]

Software?

I think it would be very helpful to show various statistical packages which implement the normality test, as I guess this is what most users would end up using with this. --Hailholyghost (talk) 15:59, 2 April 2019 (UTC)[reply]

The Applications section

[I'm new to editing or commenting on Wikipedia pages.] Concerning the Applications section of this article. As far as I can tell, the textbook cited (Portney and Watkins) doesn't mention using hypothesis tests for normality at all, and so is an inappropriate citation for the sentence. But more importantly, to my knowledge, it is not the general view of statisticians that normality tests should be used to assess the distribution of residuals from a linear model, at least as a blanket recommendation. In fairness, I guess it's true to say "One application of normality tests is to the residuals from a linear regression model". The next sentence --- "If they are not normally distributed, the residuals should not be used in Z tests or in any other tests derived from the normal distribution, such as t tests, F tests and chi-squared tests" --- A charitable view is that this as a gross simplification. In any case, not the way any statistician would sum up advice on the topic. The rest of the section --- "If the residuals are not normally distributed, then the dependent variable or at least one explanatory variable may have the wrong functional form, or important variables may be missing, etc." --- I guess is based on a strange assumption that all data in the world are conditionally normal, and you just need to find the other variables in the world that show this conditional normality? --SSM1974 (talk) 18:14, 12 August 2021 (UTC)[reply]