Timeline for Comparison of two discrete distributions
Current License: CC BY-SA 3.0
8 events
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| Mar 25, 2018 at 7:32 | vote | accept | tquarton | ||
| Mar 24, 2018 at 2:29 | answer | added | JimB | timeline score: 4 | |
| Mar 24, 2018 at 1:50 | comment | added | JimB | By "size" I meant the value of any particular characterization of a difference (doesn't have to be a statistical moment). The Kolmogorov-Smirnov test statistic might not be a bad single-number summary statistic. Depends on what you need and the field of Statistics doesn't dictate your needs. That K-S statistic is estimating a quantity that doesn't change with sample size. But the P-value will tend to get smaller and smaller with increasing sample size. K-S statistic, fine. P-value, forget about it. But complex differences really need more than a single parameter for adequate description. | |
| Mar 24, 2018 at 0:30 | comment | added | tquarton | My intention is to generally characterize the differences more than just "size". If you look at the shape of the distributions, the typical statistical moments aren't telling as the distributions don't have statistically friendly shapes (at one point they are bi-modal and in another instance they have a single peak). I thought Kolmo-Smirnov would be the most appropriate for a general characterization, but maybe not. Thanks for taking the time to look at it. | |
| Mar 23, 2018 at 22:11 | comment | added | JimB |
The KolmogorovSmirnovTest returns a P-value which is close to zero for both. P-values are not of much use if you want to characterize the "size" of the difference between two distributions. A P-value just tells you the probability of seeing at least as extreme a sample difference in CDF's under the assumption that the samples are from the same distribution. That's usually not very interesting. You'd be better off to pick some summary statistics (mean, median, standard deviation, interquartile range, etc.) that have meaning to whatever subject matter you're dealing with and compare those.
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| Mar 23, 2018 at 22:06 | comment | added | JimB |
@anderstood The beginning/syntax part of the documentation doesn't list a KolmogorovSmirnovTest[data1, data2] option but that is given as one of the examples. Yes, that option should be made more explicit.
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| Mar 23, 2018 at 21:43 | comment | added | anderstood |
In the documentation for KolmogorovSmirnovTest, I don't see your usage: my understanding is that the second argument should be a distribution (e.g. LaplaceDistribution[1,2]). I don't see why you even get a result.
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| Mar 23, 2018 at 21:06 | history | asked | tquarton | CC BY-SA 3.0 |