Timeline for Assumption of Normality - do the residuals need to be normally distributed for each independent variable (or each level of an IV)?
Current License: CC BY-SA 4.0
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| Oct 10, 2023 at 20:36 | vote | accept | Bennett K.N. | ||
| Oct 10, 2023 at 18:16 | comment | added | Stephan Kolassa | Plus, the nonparametric tests often peddled as "alternatives to ANOVA when your residuals are not normal" (think Wilcoxon) actually test a different hypothesis, i.e., answer a different question than the original parametric approach. I have to admit to some helpless exasperation at what amounts to "it's hard to answer question A, so we will simply answer question B and then pretend that we addressed question A all along". | |
| Oct 10, 2023 at 18:14 | comment | added | Stephan Kolassa | Actually, nothing that I could put my finger on right now. It very much depends on just what kind of non-iid we have... repeated measures is a different beast than having "real" time series in the data, and the models are of course very different. That said, I have done some handcrafted permutation tests in rather complex situations where the residuals were "not normal enough", and the results were disappointingly close to standard linear model/ANOVA-type p values, so by now I am a bit leery of running such complicated alternatives. | |
| Oct 10, 2023 at 17:34 | comment | added | Dave | @StephanKolassa I've seen plenty about the asymptotics for when $iid$ errors are not Gaussian. Do you have any references or thoughts about when the violation is of the $iid$ assumption? I know techniques like GLS and Newey-West exist to handle some of those situations. | |
| Oct 9, 2023 at 11:09 | history | edited | Dave | CC BY-SA 4.0 |
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| Oct 9, 2023 at 6:24 | comment | added | Stephan Kolassa | ... and often asymptotics kick in so your test statistics are "close enough" to the theoretical distribution even if these assumptions are somewhat violated. In the present example "who screams loudest", we know that residuals cannot be normally distributed, simply because there is a lower limit to sound volume, whereas the normal distribution is unbounded. Does this mean we should always run a nonparametric alternative? No. (No, you are not claiming this, but this is an argument I have seen far too often, like here.) | |
| Oct 9, 2023 at 2:24 | comment | added | Dave | I suspect this is a duplicate with an existing answer that is better than mine, but, offhand, I do not know one. // My answer and the comments here might be worth a read. | |
| Oct 9, 2023 at 2:20 | history | answered | Dave | CC BY-SA 4.0 |