[Q] How to test effect of treatments in non normally distributed and differently shaped data?

Hi all,

I want to find out whether data differs across three treatments, my hypothesis is that it does.

Unfortunately the data collection process is very time and money consuming so I have a very small sample size for each treatment (but always bigger than 5) and different sample sizes across treatments. The data is not normally distributed (so I excluded parametric tests) and is not similarly shaped (so I excluded Kruskal Wallis, Mann Whitney and Moods Median test as they would not be testing my hypothesis but would rather be testing for mean ranks).

Does anyone have any idea of what test I could use to test my hypothesis given the data?

Thanks very much in advance!

submitted by /u/Ordep22
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Nevin Manimala

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