Timeline for Normally distributed data but small sample size, use nonparametric test?
Current License: CC BY-SA 3.0
7 events
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| Aug 7, 2017 at 16:27 | comment | added | whuber♦ | @Michael Your comment could be misunderstood, because tests are not parametric or nonparametric: models are. A parametric model would, by definition, describe all possible distributions using a finite number of real parameters. Thus, it's not enough to suppose normality is a priori plausible: one must also be willing to test against a finite-dimensional space of alternative distributions--which includes specifying precisely which distributions those might be. | |
| Aug 5, 2017 at 12:28 | comment | added | Michael R. Chernick | Glen_b addressed the appropriateness of concluding normality with a small sample size. But suppose you have a good apriori reason to believe normality. Then a nonparametric test would have less power and would not overcome the small sample size issue. | |
| Aug 5, 2017 at 7:21 | comment | added | Katharine Davies | Thank you, Glen_b! That's what I was asking, is it out to ignore normality tests if they are unlikely to be right. | |
| Aug 5, 2017 at 3:11 | comment | added | Glen_b | ctd.. See Is normality testing essentially useless? -- in particular, I think this answer gets to the heart of the matter. The most important thing to start with is a clear statement of what you really wanted to find out (ignoring any issues of sample size or distribution shape to start with). | |
| Aug 5, 2017 at 3:06 | comment | added | Glen_b | Your opening sentence is incorrect. Failure to reject normality (especially at small sample size!) doesn't mean you do have normality, it means you didn't detect non-normality. Since power won't be great at low sample size, failure to detect it doesn't necessarily tell you much; it's a bit like tossing a coin twice, getting two tails and concluding that with this coin you're safe from the possibility of heads. On the other hand at large sample sizes, you can reject even fairly trivial deviations from normality, ones that won't affect your inference at all. ...ctd | |
| Aug 4, 2017 at 23:08 | comment | added | Dave2e | student t test is a possible option. | |
| Aug 4, 2017 at 23:03 | history | asked | Katharine Davies | CC BY-SA 3.0 |