Timeline for What is the difference between "scale parameter" and the variance?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 5, 2020 at 0:54 | vote | accept | Katikarnata | ||
| May 3, 2020 at 18:18 | comment | added | Dave | “The nonparametric test should be almost as good as the parametric.” | |
| May 3, 2020 at 17:58 | comment | added | Nick Cox | @Dave I think a non- is missing in your comment. | |
| May 3, 2020 at 15:18 | comment | added | Dave | @Katikarnata When I took nonparametric methods, the professor’s comment was that a good parametric test should be almost as good as the parametric test when the parametric test’s assumptions are met and beat the heck out it when those assumptions are violated. But that comment is a concession that the nonparametric method would be worse if the assumptions are met, even if only slightly worse. | |
| May 3, 2020 at 15:13 | comment | added | Katikarnata | That's it! Thank you. So, now I understand this test is "more general" (based on ranks), which - in case of the normal distribution, "converges" (I know it's bad word, but in layman's terms) to comparing variances. I run a simulation and sampled from the normal distribution. Now the outcomes agree, but sometimes it's on the border line, for example: [AB = 5490, p-value = 0.03153 vs. F = 0.36666, p-value = 0.000001059] and most of the time AB "judged" more liberally. But I believe it's the nature of a non-parametric test, which is usually "weaker", not making distributional assumptions, right? | |
| May 3, 2020 at 14:51 | comment | added | Dave | @Katikarnata I think I see what you mean in the Ansari-Bradley documentation. It’s the “notes”, right? Notice the mention of normality. Then the scale parameter is standard deviation which has a known relationship to variance. | |
| May 3, 2020 at 14:41 | comment | added | Katikarnata | Thank you very much. Yes, I saw this definition, which told me why it's called "scale" (it scales the "width" of the distribution). When the dispersion grows, the scale does too, so the variance should too. So, I thought the two properties of a distribution should agree. But in the example that I linked, the Ansari-Bradley test of scales shows no difference, while the test of variances shows difference at very low p-value. From this I concluded those measures aren't the same, but in documentations it is mentioned, that the A-B test verifies equality of variances. That's why I'm so confused! | |
| May 3, 2020 at 14:37 | history | answered | Dave | CC BY-SA 4.0 |