Timeline for importance of CLT in t-test and z-test
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| May 24, 2020 at 19:51 | vote | accept | Angadishop | ||
| May 24, 2020 at 19:51 | vote | accept | Angadishop | ||
| May 24, 2020 at 19:51 | |||||
| May 14, 2020 at 15:37 | comment | added | BruceET |
Just saw this. All good additions. (+1) About boxplot outliers in samples from normal populations. For $n=30,$ about 29% of samples have at least one outlier, average nr per sample 0.45; for $n=100,$ 52% and 0.92; for $n=500,$ 45% and 3.7. R code for 500 is nr.out = replicate(10^5, length(boxplot.stats(rnorm(500))$out)) followed by mean(nr.out>0) and mean(nr.out).
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| May 14, 2020 at 14:37 | history | edited | Dave | CC BY-SA 4.0 |
added 1 character in body
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| May 14, 2020 at 6:55 | comment | added | Stephan Kolassa | "if we don't know the underlying distribution, then it is always better to choose non-parametric approaches" - no, it isn't. Asymptotics may be good enough for parametric tests to be more powerful. Why would parametric statistics ever be preferred over nonparametric? | |
| May 14, 2020 at 2:54 | comment | added | Dave | That’s not what I meant, though that topic warrants a separate question that you may elect to post. Do a search first, though, as that topic very likely has come up on here, even if I don’t know the post offhand. | |
| May 14, 2020 at 2:47 | comment | added | Angadishop | gotcha!! so if we don't know the underlying distribution, then it is always better to choose non-parametric approaches like Wilcoxon. Please correct me if my understanding is wrong. | |
| May 14, 2020 at 2:34 | comment | added | Dave | That gets into issues about whether or not you’re “close enough” to the theoretical distribution, the idea of how fast the convergence is. Sure, the limit is normal, but maybe it’s not normal enough with the 65 observations you have, so you’d want to explore a method like Wilcoxon. But the major point you need to understand is that we only care about the distribution of the test statistic. The data coming from a norma distribution assures is of having a normal z-stat, but we can get super close for many other distributions. | |
| May 14, 2020 at 2:26 | comment | added | Angadishop | I am having hard-time to accept it (this was my understanding till yesterday) kindly look at this post and tell me if you still think the same | |
| May 14, 2020 at 2:19 | comment | added | Dave | That is incorrect. The z-stat (I’ve been calling it z-score, but I mean z-stat) will be very close to normally distributed if your data are drawn from a uniform distribution and you have a decent sample size...and that’s all that matters. As long as the test statistic is close enough to following the theoretical distribution, then you’re good. | |
| May 14, 2020 at 2:14 | comment | added | Angadishop | but one of the assumptions of t/z-test is data should be normally distributed or in other words it should be sampled from a distribution which is normally distributed. If my sample is from a uniform distribution, the mean of the sample may be normally distributed but the data isn't normally distributed. In such case I don't think we should be applying t/z-test. Kindly correct me if I am wrong. | |
| May 14, 2020 at 2:06 | comment | added | Dave | As I wrote in a comment to Bruce’s post, data cannot be normal; that terminology is mere slang. | |
| May 14, 2020 at 1:05 | comment | added | Angadishop | Thank you for answering my question. let's say that for some 'n' the z-score converges to normal because of CLT but, still my data is not normally distributed. In that case am I allowed to use z or t test? | |
| May 14, 2020 at 0:40 | history | answered | Dave | CC BY-SA 4.0 |