I have a dataset that has two groups: mean_1 and mean_2. I want to find statistical significant difference between mean_1 and mean_2. The groups are paired but data is not normally distributed so I am using non-parametric tests like: Mann-Whitney U test or Wilxocon Sign-Ranked Test. As a result I get that there is a significant difference between two groups. But I also want to know how mean_1 is different from mean_2, i.e, which one is larger ? I learnt that there are few tests like Friedman's or Kruskal-Wallis test but I have only two groups to be tested whereas these tests are appropriate for more than 2 groups.
Please suggest which test will be valid in this scenario.
Jos Feys thanks! but these test do not help in finding which group is significantly different from the other group. the results only tell whether there is a difference or no.
Sorry, you do not need to rank the differences; just calculate the mean differences, which will indicate which is taller. If the mean of the differences is postive, score1 is taller.
Note that the Welch t-test is a very robust test.
https://en.wikipedia.org/wiki/Welch%27s_t-test
Only if the distributions really are very non-normal (e.g. heavily skewed) check the histograms) you can use the Wilcoxon signed ranks test
Jos Feys since the data is not normally distributed I would rather prefer using Wilxocon signed ranks test. Could you please share some links or examples in python with the methodology you described?
If you know or you can estimate the distributions of your data, you can calculate the exceedance probability as an alternative to t-tests. The discussion on exceedance probability can be found in Preprint Exceedance probability analysis: a practical and effective a...
Samiksha Samiksha, if you are using a nonparametric test such as the Mann-Whitney test, you could provide the mean rank for each group, which should definitely indicate which group is higher.
The following site should help:
https://statistics.laerd.com/spss-tutorials/mann-whitney-u-test-using-spss-statistics-2.php
Some researchers report the groups' medians, which I regard as more informative than reporting the mean ranks.
Robert Trevethan Thanks for looking into it. Any implementations or examples in python would be really helpful!
Samiksha Samiksha, I'm sorry, but I don't use Python. However, I suspect that it is not necessary to use Python to address your "issue" satisfactorily.
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