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I`m analyzing data for paper, and i used Kruskal-wallis test and Steel-dwass post-hoc test for data analysis. I found significant difference when using Kruskal-wallis test, but no significant differences when comparing each pairs of the data groups. Could anyone tell me what the reason is? And what should i do then?

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Check that the distribution of the data is skewed in the same direction. From what I remember it should be to use Kruskal-wallis tests. Also try Wilcoxon rank sum tests using Bonferroni correction on each pair.