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I'm trying to test if there are systematic differences in a balanced data.frame composed by 25 observations of 3 variables:

'data.frame':   25 obs. of  3 variables:
 $ sum: num  0 5228 7715 7715 7780 ...
 $ time: int  2012 2013 2014 2015 2016 2012 2013 2014 2015 2016 ...
 $ categories: Factor w/ 5 levels "I","II",..: 5 5 5 5 5 2 2 2 2 2 ...
  • $sum: a response numeric variabile representing surfaces extension, expressed in m²;

  • $time: a numeric variabile relative to temporal interval, with 5 years (2012-2016);

  • $categories: a nominal variable of 5 levels, I-V.

The question is:

Did sum values systematic change over time (from 2012 to 2015) in each level of categories?

I level: 2012 m² vs 2013 m² vs 2014 m² vs 2015 m² vs 2016 m²

II level: 2012 m² vs 2013 m² vs 2014 m² vs 2015 m² vs 2016 m²

III level: ...

IV level: ...

V level: ...

Because of the lack of normality assumption i'm performing kruskal wallis rank sum test in R (kruskal.test) for each level of $categories: (5 test).

When i run the 5 analysis i get the same pvalues for every single test (>0.05), even if sum values are different.

Am i performing kruskal wallis test correctly?

Can i accept the null hipotesis and adfirm that there are no significant differences in values among groups?

Are there any more suitable tests to perform? (cor test, wilcox.test or SIGN.test)

Thank you so much.

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