I have a data set from plant experiments with only 4 replicates. data are numbers of mites after different treatments. Because the datasets are small they are not normally distributed, so I use non parametric tests: Wilcoxon. First I did a pairwise comparison, without corrections which is not allowed normally, but I see the expected differences. then I did the same test with Bonferroni correction and don't see any significant differences anymore (alpha =0,1). Thirdly I did the same test again with BH correction and I see the differences again.

So my question is, am I allowed to apply the BH correction for analysing my data? Or Do I have to apply bonferroni correction and thus have to conclmude that there are no statistical differences and I should do more replications in future experiments?

Here my simplified data and the results of my 3 tests.

A B C D E F G H

111 47 0 102 1 0 0 12

88 31 0 152 0 0 0 2

216 35 0 102 0 1 1 75

169 30 1 75 0 3 6 46

Pairwise comparisons using Wilcoxon rank sum test

P value adjustment method: none

A B C D E F G

B 0.029 - - - - - -

C 0.027 0.027 - - - - -

D 0.309 0.029 0.026 - - - -

E 0.027 0.027 1.000 0.026 - - -

F 0.029 0.029 0.505 0.028 0.505 - -

G 0.029 0.029 0.505 0.028 0.505 1.000 -

H 0.029 0.886 0.027 0.041 0.027 0.059 0.059

Pairwise comparisons using Wilcoxon rank sum test

P value adjustment method: bonferroni

A B C D E F G

B 0.80 - - - - - -

C 0.74 0.74 - - - - -

D 1.00 0.82 0.72 - - - -

E 0.74 0.74 1.00 0.72 - - -

F 0.82 0.82 1.00 0.80 1.00 - -

G 0.82 0.82 1.00 0.80 1.00 1.00 -

H 0.80 1.00 0.74 1.00 0.74 1.00 1.00

Pairwise comparisons using Wilcoxon rank sum test

P value adjustment method: BH (Benjamini, Hochberg)

A B C D E F G

B 0.048 - - - - - -

C 0.048 0.048 - - - - -

D 0.413 0.048 0.048 - - - -

E 0.048 0.048 1.000 0.048 - - -

F 0.048 0.048 0.566 0.048 0.566 - -

G 0.048 0.048 0.566 0.048 0.566 1.000 -

H 0.048 0.954 0.048 0.064 0.048 0.083 0.083

Kind Regards

Joachim