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I performed the Kruskal-Wallis one-way ANOVA by ranks on five groups of data using Dataplot software. The software corrects for ties and uses Conover's procedure to do pairwise multiple comparisons.

The result of the test is $H=5.62$ and $p=.229$ so the results are not significant ($p$ is not less than $.05$). However, the pairwise multiple comparisons show that the group 1 data significantly differs ($p<.05$) from the group 2 data.

I report that there are no significant differences in the five groups (because $p=.229$).

My question is this: I am using box plots to graphically represent the results. Should I indicate that the group 1 data and the group 2 data significantly differ even though the H-test says that there are no significant differences in the five groups of data?

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    $\begingroup$ No, not unless you're prepared to defend why the significance of this one pairwise comparison (out of 10 such possible comparisons) is greater than would be expected by chance alone. $\endgroup$
    – guest
    Commented Mar 31, 2012 at 20:13
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    $\begingroup$ @guest, could you please turn your comment into an answer so I can accept it? $\endgroup$
    – JRN
    Commented Jul 2, 2012 at 4:56

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I'm turning guest's comment into an answer so that this question is not marked unanswered.

No, not unless you're prepared to defend why the significance of this one pairwise comparison (out of 10 such possible comparisons) is greater than would be expected by chance alone.

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