I'm trying not to have a seizure among the bunch of numbers and data I have. My experiment data consists of three non-equal, non-parametric groups, and I need to compare those groups to state if there exists statistical difference between those groups. Which will be the best test I can use to achieve so? Group 1 data: n=12, mean=0.886, SD=0.74 | Group 2 data: n=16, mean= 0.554, SD= 0.39 | Group 3 data: n=13, mean= 0.79, SD= 0.68

Any help, suggestions or comments will be very helpful and appreciated!

  • $\begingroup$ Do you have all your data, or just the summaries you listed here? $\endgroup$
    – Matt Brems
    Commented Jan 30, 2016 at 23:01
  • $\begingroup$ I have all of my data if you need it $\endgroup$
    – Joe V.
    Commented Jan 30, 2016 at 23:17
  • $\begingroup$ I don't need the data; I was just making sure that you had it available and weren't solely relying on the summary statistics for your analysis. $\endgroup$
    – Matt Brems
    Commented Jan 30, 2016 at 23:18
  • $\begingroup$ Could you explain what a "non-parametric group" is and what you mean by a "statistical difference"? $\endgroup$
    – whuber
    Commented Jan 30, 2016 at 23:19
  • 1
    $\begingroup$ Data are neither parametric nor nonparametric; those are adjectives that apply to models or techniques. If you mean "not normally distributed" that's not at all the same thing as "nonparametric" and similarly "parametric" is not at all the same thing as "normally distributed" -- one can fit parametric non-normal models and correspondingly, one can happily use nonparametric procedures on data drawn from normal distributions. Please amend your post to more clearly express the actual situation. $\endgroup$
    – Glen_b
    Commented Jan 30, 2016 at 23:23

1 Answer 1


You should look at the Kruskal-Wallis one-way analysis of variance test. It is a nonparametric analog of the ANOVA F-test.

The Kruskal-Wallis test will assess the evidence against the null hypothesis that the populations are the same. If you find a statistically significant result (like via low p-value), then you might conclude that at least one of the population's distributions is greater than the others. The K-W test will not tell you which population is the one that is different (i.e. greater than or less than, roughly speaking) from the others.

If your goal is to also assess which population's distribution differs, you might look at Dunn's test (a nonparametric analog of Tukey's Honest Significant Difference test).

  • $\begingroup$ Whenever I try to use Krustal-Wallis on my samples using R, I get "Error en kruskal.test.default(LRNA, LISO) : 'x' and 'g' must have the same length" So, I think a Mann-Whitney will probably do the trick :) $\endgroup$
    – Joe V.
    Commented Jan 31, 2016 at 0:38
  • 1
    $\begingroup$ Mann-Whitney is inappropriate for more than two populations. I would advise you to Google the error and figure out what 'x' and 'g' are, then correct the issue. $\endgroup$
    – Matt Brems
    Commented Jan 31, 2016 at 0:51

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