Timeline for Can Kruskal-Wallis be used for discrete data?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Nov 25, 2020 at 1:08 | comment | added | Dave | 1) I do not follow what you mean about if the distributions are the same. 2) When the shapes are different, Wilcoxon MWU is not quite a test of median equality. | |
| Nov 24, 2020 at 23:22 | comment | added | emiru | @Dave, I do! And I do agree... I'd be grateful if you said more about why you think my edit is problematic. | |
| Nov 24, 2020 at 22:28 | comment | added | Dave | Fair point that the mean has to exist for my comment to be 100% correct, but do you see why, with the assumption of equal scale and shape, different medians is the same as different 75th percentiles or 11th percentiles (or mean, if it exists)? $\text{//}$ Your edit, the paragraph that mentions me, is problematic. | |
| Nov 24, 2020 at 14:38 | comment | added | emiru | @Dave as a separate point something like the Cauchy distribution doesn't even define a mean but it does have a median ... so in the general case it isn't true that a test of the mean will be a test of the median even if the distributions are the same. | |
| Nov 24, 2020 at 14:31 | history | edited | emiru | CC BY-SA 4.0 |
Added clarification RE why I don't think discreteness of data matters in real life but precision does. Clarification on difference between mean and median.
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| Nov 24, 2020 at 14:21 | comment | added | emiru | @Dave i think you're failing to distiniguish the difference between a continuous distribution and a non discrete value with limited precision. There is no such thing as an infinite precision measurement. The probability of your actual data having ties is certainly not zero, and the likelihood is governed by precision not whether its an integer or a float. | |
| Nov 23, 2020 at 22:40 | comment | added | Dave | @IsaBragantini I would call those distinct questions: 1) What exactly are the assumptions of the Wilcoxon MWU test? 2) How to test for a difference in means when there are many ties in the data? Cross Validated operates on a strict Q&A basis, where distinct questions get compartmented in distinct posts in order to organize discussions. Please feel free to post those two! (I suspect both are duplicates, so perhaps search around here.) | |
| Nov 23, 2020 at 22:26 | comment | added | Isa Bragantini | @Dave but what about the ties issue? Additionally, Wilcoxon doesn't assume equal variances? | |
| Nov 23, 2020 at 22:10 | comment | added | Dave | @IsaBragantini Much like a t-test is ANOVA with two groups, Wilcoxon (Mann-Whitney U) is KW with two groups. | |
| Nov 23, 2020 at 22:01 | comment | added | Isa Bragantini | There are a lot of ties in my data. Would a Wilcoxon test be better then? And I updated the questions to clarify a few things. | |
| Nov 23, 2020 at 21:53 | comment | added | Dave | If the distributions have identical shapes and scales, then the null hypothesis that the medians are equal is equivalent to a null that the means are equal. // Continuous distributions produce ties with probability $0$. | |
| Nov 23, 2020 at 21:48 | comment | added | emiru | On the assumption that continuous values are less likely to produce ties? That's about precision and range. Measuring height in $\mu m$ is discrete but less likely to produce ties than measuring heigh in metres to two decimal places. | |
| Nov 23, 2020 at 21:44 | comment | added | whuber♦ | There actually is something quite special about discrete data: the possibility of ties. Many rank-based nonparametric procedures, like the KW, will fall apart unless ties are properly accounted for and corrected. Extreme numbers of ties can render them powerless. | |
| Nov 23, 2020 at 21:41 | history | answered | emiru | CC BY-SA 4.0 |