Kruskal-Wallis test is not significant but some of the Mann-Whitney comparisons are significant I have a non-normalized dependent variable and an independent variable broken down into 4 groups. As such, I used the Kruskal–Wallis analysis to look for significant differences in the ranks of the groups.
The data look like the following:
\begin{array}{clc}\rm Group&\rm Size&\rm Means\\\hline
    0&n=24&31.79\\
 1&n=13&26.65\\
 2&n=8 &15.94\\
 3&n=10&30.30\\
 \rm Total& N=55\end{array}
I get an asymptotic significance of .103.
However, if I run a Mann–Whitney U on the same data, I see a clear significance between the 0 and 2 groups:
   0    24  18.81   451.50
   2    8   9.56    76.50
Total   32      

Mann-Whitney U  40.500
Wilcoxon W  76.500
Z   -2.416

Asymp. Sig. (2-tailed)  .016
Exact Sig. [2*(1-tailed Sig.)]  .013b

The only things I could come up with were that:


*

*I may be running into some kind of confounding error with the Mann–Whitney U test, and thus the significance is a mistake, or that 

*The large difference in between the sample sizes is what is causing me to see significance with the Mann–Whitney, but not the K–W since it has a bit more "power" to tease out what is significant and what isn't.


Any help or guidance would be appreciated.
 A: Perhaps not surprising that you got disparate results since (ahem): the Mann-Whitney rank sum test is not an appropriate post hoc pairwise test for the Kruskal-Wallis omnibus test.
The rank sum test:

*

*Ignores the rankings used to conduct the Kruskal-Wallis test


*Does not account for the pooled variance implied by the null hypothesis of the Kruskal-Wallis test.
A popular and appropriate post hoc pairwise test is Dunn's test, which does employ the same rankings as the Kruskal-Wallis, and does account for pooled variance implied by the null hypothesis of the Kruskal-Wallis test. Another less well-known post hoc test is the Conover-Iman test, which is strictly more powerful that Dunn's test (assuming the Kruskal-Wallis test rejects its null hypothesis).
Dunn's test is implemented for Stata in the dunntest package (within Stata type net describe dunntest, from(http://www.alexisdinno.com/stata)), and for R in the dunn.test package. The Conover-Iman test is implemented within Stata in the conovertest package (within Stata type net describe conovertest, from(http://www.alexisdinno.com/stata)), and for R in the conover.test package.
Being concerned that you found disparate results between the Kruskal-Wallis and rank sum tests is a little like being concerned that you found disparate results between ANOVA on transformed data, and unpaired t tests without pooled variance on untransformed data; I think you are asking the wrong question.
A: The Kruskal-Wallis test is the one that has a perfect multiplicity adjustment.  Looking for pairwise differences when K-W is insignificant is dangerous.  When you do want to look pairwise, heed the advice above to use a method that is consistent with K-W.  A model-based approach that generalizes K-W is the proportional odds ordinal logistic model, which can be used to test any contrast you want plus give the global likelihood ratio $\chi^2$ test that is related to the K-W test.
