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What statistical test should I use if I have three independent groups of interval data and would want to check whether their means are significantly different? I'd also note that the samples sizes of each group is different (N1= 50, N2= 10, N3=13).

Would it be wiser to compare one with another and then do the same for the other two other pairs? (G1=G2; G2=G3; G1=G3)?

I understand that one-way ANOVA and a Tukey's post-hoc would be the best option but does the difference in sample size pose a problem?

Thank you!

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    $\begingroup$ does the difference in sample size pose a problem? -- No $\endgroup$
    – Glen_b
    May 29, 2014 at 8:32
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    $\begingroup$ @Glen_b I think it might when the assumption of equal variances is not satisfied. This is the first reference I found from google theanalysisfactor.com/… $\endgroup$
    – JohnK
    Nov 24, 2014 at 0:35
  • $\begingroup$ @Glen_b I see your point. The OP's question indeed does not suggest that any of the assumptions are violated. $\endgroup$
    – JohnK
    Nov 24, 2014 at 9:20
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    $\begingroup$ @JohnK It is something that's worth mentioning -- I was just trying to explain my reasoning for commenting the way I did. $\endgroup$
    – Glen_b
    Nov 24, 2014 at 9:41

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Well, from what I know, using multiple comparison methods such as Fisher's LSD, Tukey's, Bonferroni comparison,etc would be sufficient. If you compare them by one by one using t-tests than your results will be erroneous unless your p-values or significance level is modified (this is known as the multiple comparison error). If you just want to know whether the mean of the three groups are not the same (H0: mu1=mu2=mu3=0, where mu1, mu2, mu3 denote the mean of each group), then ONE-way ANOVA is preferable. But, as sample sizes are small for some groups, using non-parametric methods such as the Kruskall-Wallis test might give better results.

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  • $\begingroup$ Thank you for the very helpful answer! Do I need other tests after the analysis with Kruskal-Wallis? $\endgroup$ May 29, 2014 at 8:14
  • $\begingroup$ It depends on what you want to know. If you want to know which groups have different means, then you have to implement multiple comparison methods. If you have a control group then using the Dunnet's method is preferred. If that's not the case there are several parametric and non-parametric methods you can use. $\endgroup$
    – Kenny
    May 29, 2014 at 9:04
  • $\begingroup$ I simply want to know which groups have different means. What specific multiple comparison method would you recommend? Can I use Tukey's? $\endgroup$ May 29, 2014 at 9:21
  • $\begingroup$ Yes, Tukey's method is useful, but in this case using multiple comparison based on the Kruskall-Wallis test would be more preferable (if the usual assumptions required for the one-way ANOVA are not met). $\endgroup$
    – Kenny
    May 30, 2014 at 9:49
  • $\begingroup$ Thank you Kenny for your answers! I'm gonna try this out and see where it leads me. $\endgroup$ Jun 2, 2014 at 9:03

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