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I am working with monthly results of some variables, and I would linke to compare weather 6 years are statistically different or not, so my saple size per group (year) is bounded by 12. I ran Shapiro Wilk to test normality and every year passed the test, but, as the sample size is small, I am not convinced to use ANOVA rather than Kruskal Wallis.

Any advide will be appreciated! Thanks in advance!

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The only reason why your data passed the normality tests in the fact that you don't have enough data to achieve a significant results. In general, I would advice against the use of normality test altogether.

I would definitely try a non-parametric population comparison! But you can do it either way and you will see that differences are not that big.

Finally, check for seasonality patterns that may ruin the independence of your data. Without further information about your particular problem, I would say this is the main cause why your test could get ruined

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  • $\begingroup$ Thanks! I am actually comparing the performance of 27 working units through these 6 years, so, I am running tests for each unit separately, and for every unit, running Anova or KW gives the same result, except for 2. One of them is significant with Anova but is not with KW, and the other is upsidedown. So I am not sure to pick KW! haha $\endgroup$ – Francisca González Cohens Jun 19 '19 at 19:42
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    $\begingroup$ Well, "significant" depends on an arbitrary threshold,. Does that discrepancy between ANOVA and KW appear in a case where p-values are pretty close (above or below) your chosen threshold? Also, when running multiple comparisons, don't forget to use a correction like Tukey's or Bonferroni to adjust p-values $\endgroup$ – David Jun 20 '19 at 7:12

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