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Some weeks ago, I used 5 different microphones to record the same sound. The idea was to compare what differences existed between these recordings. To do that I wanted to use some sort of test to check for significant differences in the audio features that I am interested (amplitude, fundamental frequency, etc.).

All the audio features from the recorded audios do not follow a normal distribution. For this reason, I should use nonparametric tests. Furthermore, since all the microphones recorded the same sound I should use some sort of repeated measures test. However, I am not sure what test I should use. I have only used repeated ANOVA before, but according to my knowledge that would not be correct for this case, as it is a parametric test.

Could you recommend me some non parametric test for repeated measures in order to control for differences? (it would be great that it was also implemented in R).

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Friedman test maybe?

(microphones<-matrix(c(1:10,2:11,3:12,4:13,5:14), nrow=10)) # 5 microphones, 10 features
      [,1] [,2] [,3] [,4] [,5]
 [1,]    1    2    3    4    5
 [2,]    2    3    4    5    6
 [3,]    3    4    5    6    7
 [4,]    4    5    6    7    8
 [5,]    5    6    7    8    9
 [6,]    6    7    8    9   10
 [7,]    7    8    9   10   11
 [8,]    8    9   10   11   12
 [9,]    9   10   11   12   13
[10,]   10   11   12   13   14


friedman.test(microphones)

    Friedman rank sum test

data:  microphones
Friedman chi-squared = 40, df = 4, p-value = 4.328e-08
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