Timeline for Why are parametric tests more powerful than non-parametric tests?
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| Jan 5, 2022 at 10:52 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Nov 16, 2021 at 11:19 | comment | added | Aksakal | @SextusEmpiricus this logic can be allowed to Bayesian approach: it only seems useful with small samples. Once the sample is big the prior doesn’t matter. The prior is always wrong in the same sense. So, on the other hand maybe it’s never useful because it’s always wrong and the bias it introduces | |
| Nov 16, 2021 at 10:32 | comment | added | Glen_b | I guess what I should do is offer a specific example or examples of something reasonably 'close to' normal where (say) a Wilcoxon-Mann-Whitney sometimes has better power than a t-test under a shift alternative. | |
| Nov 16, 2021 at 10:25 | comment | added | Glen_b | ctd... Can you be more specific about the circumstances? I'd be happy to fix my answer as needed. (If you specifically mean for the normal scores rank based test, no dispute there, that's really just a large sample result) | |
| Nov 16, 2021 at 10:24 | comment | added | Glen_b | Thanks for this. Where I was focused on A.R.E., sample size doesn't come into that -- but beyond that, the permutation test cases I have looked at the smallish-sample relative efficiency didn't typically shift all that far from the A.R.E. until you got down to fairly small n - in some cases small enough that you weren't doing tests at level $\alpha$ any longer; for those moving to the using the same actual significance levels tended to keep things pretty similar to the A.R.E. for a good while. It's definitely possible I've missed looking at some situation(s) you're referring to though. ...ctd | |
| Nov 16, 2021 at 8:08 | comment | added | Sextus Empiricus | ... This 'hardly at all' when it comes to the b-question (how much do you need to modify the situation) depends a lot on the sample size. And the advantage that a parametric test brings to the table is extra information about the distribution, which becomes less of an advantage for larger sample sizes (and more of a burden due to potential bias). But for smaller sample sizes the advantages will be relatively larger. | |
| Nov 16, 2021 at 8:07 | comment | added | Sextus Empiricus | If find this a very good answer because it explains more indepth the philosophy around the question and it's answer. But it sounds a bit pessimistic and one would come to believe that parametric tests are completely useless. But, could we say the following? ... | |
| Nov 16, 2021 at 7:35 | comment | added | Glen_b | Hmm, that (ii) is insufficently clear. Even for a nonparametric test, to compute a power you will generally be doing it under some specific parametric situation. | |
| Nov 16, 2021 at 7:28 | comment | added | Glen_b | It's more the combination of (i) a specific test statistic, (ii) the specific kind of alternative considered / the parametric distributional assumption (if any) and (iii) the remaining assumptions (like independence, for example), together that determine power. | |
| Nov 16, 2021 at 5:19 | comment | added | Nate | Thank you for contributing. It seems "the thing which gives power" has very little to do with the tests themselves, but instead the assumptions that come with them? For example, the assumed shape of a distribution. The area of overlap between two normally distributed samples of data I could compare the means of could be larger geometrically than if I assumed the data were non-normal; simple because of the shape of the distributions (less physical overlap based on non-normal assumption = more power to reject the null, no?). | |
| Nov 16, 2021 at 5:01 | vote | accept | Nate | ||
| Nov 16, 2021 at 4:07 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Nov 16, 2021 at 3:02 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Nov 16, 2021 at 2:10 | history | answered | Glen_b | CC BY-SA 4.0 |