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From |
Nick Cox <n.j.cox@durham.ac.uk> |

To |
"'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: one way anova or kruskal wallis if sample size is less than 3 for each group |

Date |
Sun, 29 Aug 2010 16:12:52 +0100 |

Although it may be obvious, I'd add the comment that a graph is likely to show essentially all the structure in this data set. If you work through what Mann-Whitney U-tests actually mean when n = 2 or 3, your results are less surprising. Quantifying the underlying probabilities through use of Roger Newson's -somersd- may also be revealing. Bonferroni, (W.H.) Kruskal, Wallis, Mann and Whitney are all represented by vignettes in the Stata on-line documentation. Nick n.j.cox@durham.ac.uk Morten Hesse In principle, a problem for ANOVA is when variance and mean are correlated (i.e., typically that at higher mean scores, variance is also higher). The Bartlett test shows a trend towards different variances, which could indicate this. This is an instance where you may justify using Kruskal-Wallis. But what I would like to ask, is why you would even bother to run statistical tests on something that is so obviously different. If you can show a difference with 2-3 cases per cell, the difference is likely to be so obvious that nobody would bother to question it. You would not run statistical analyses to test whether 18-year old humans are taller than 3-year old children, simply because it is obvious that there will be a difference. However, if you still feel that you need to justify your restults through statistical analyses, I would recommend reporting the ANOVA, the Bonferroni post-hoc, and mention that you have tried the KW, and it gave significant results. Kamarul Imran Musa > I have a data with 5 groups (group) and a quantitative dependent > variable (score). Two groups have sample size of two and 4 groups > have sample size of 3. > > I run Kruskal-Wallis test and because the P-value is less than 0.05, > I do Mann-Whitney test. I am baffled that none of the p value from > Mann-Whitney test is less than 0.05. I also run one-way anova with > Bonferroni correction, and the results show p values of less than > 0.05. > > Can someone explain this and which test should I choose? > > Thank you very much > > > KRUSKAL WALLIS > > . kwallis score, by(group) > > Kruskal-Wallis equality-of-populations rank test > > +------------------------+ > | group | Obs | Rank Sum | > |-------+-----+----------| > | 1 | 2 | 29.00 | > | 2 | 2 | 3.00 | > | 3 | 3 | 12.00 | > | 4 | 3 | 21.00 | > | 5 | 3 | 41.00 | > |-------+-----+----------| > | 6 | 3 | 30.00 | > +------------------------+ > > chi-squared = 14.309 with 5 d.f. > probability = 0.0138 > > chi-squared with ties = 14.330 with 5 d.f. > probability = 0.0136 > > . ranksum score if group == 1 | group ==2, by(group) > > Two-sample Wilcoxon rank-sum (Mann-Whitney) test > > group | obs rank sum expected > -------------+--------------------------------- > 1 | 2 7 5 > 2 | 2 3 5 > -------------+--------------------------------- > combined | 4 10 10 > > unadjusted variance 1.67 > adjustment for ties 0.00 > ---------- > adjusted variance 1.67 > > Ho: score(group==1) = score(group==2) > z = 1.549 > Prob > |z| = 0.1213 > > *** other Mann-Whitney results not shown > > > ONE WAY ANOVA > > . oneway score group, bonferroni > > Analysis of Variance > Source SS df MS F Prob > F > ------------------------------------------------------------------------ > Between groups 43047.0833 5 8609.41667 106.20 0.0000 > Within groups 810.666667 10 81.0666667 > ------------------------------------------------------------------------ > Total 43857.75 15 2923.85 > > Bartlett's test for equal variances: chi2(5) = 9.2622 Prob>chi2 = 0.099 > > Comparison of score by group > (Bonferroni) > Row Mean-| > Col Mean | 1 2 3 4 5 > ---------+------------------------------------------------------- > 2 | -133 > | 0.000 > | > 3 | -125 8 > | 0.000 1.000 > | > 4 | -111.667 21.3333 13.3333 > | 0.000 0.400 1.000 > | > 5 | -8 125 117 103.667 > | 1.000 0.000 0.000 0.000 > | > 6 | -70 63 55 41.6667 -62 > | 0.000 0.000 0.000 0.003 0.000 > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: one way anova or kruskal wallis if sample size is less than 3 for each group***From:*Kamarul Imran Musa <drkamarul@kb.usm.my>

**Re: st: one way anova or kruskal wallis if sample size is less than 3 for each group***From:*Morten Hesse <mh@crf.au.dk>

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