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I made an experiment where I measured the change of the impedance of a coil when I changed a environment parameter X times.

For each change I collected ~20 samples.

So I have a table with X lines that represent the number the change of the parameter and 20 columns that represent the repeat samples.

Now I would like to compare each line to the others and to find out if there is a significance difference between them.

Naturally I was thinking about T test. Unfortunately the measurement distribution is not normal, although the distribution is symmetric around the mean. ( I run Two-sample Kolmogorov-Smirnov test and found out that the test reject the hypothesis that the my sample arrived from normal distribution). You can find figure of the distribution here:

https://drive.google.com/open?id=1yp_Ufa4-N8kQD1twVCnHszL9RYLV-_3u

I know that if I had a higher number of samples I could average the sample groups till I will reach normal distribution and then use a T test, but I would like to avoid the idea to do the experiment again.

Now (Sorry about the long introduction... ) my questions are:

1) Do you know about a transformation that I can apply on my distribution so I will be able to use T test?

2) In case that there is no kind of transformation, which non parametric test would you suggest me to use?

Thanks a lot

Mosh