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

 From Kamarul Imran Musa To statalist@hsphsun2.harvard.edu Subject st: one way anova or kruskal wallis if sample size is less than 3 for each group Date Sun, 29 Aug 2010 10:53:34 +0800 (MYT)

```Dear all,

this is my first ever posting to statalist.

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

adjustment for ties 0.00
----------

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

Best regards

Dr Kamarul Imran Musa
MD MCommunityMed
Senior Medical Lecturer (Epidemiology and Biostatistics)
Department of Community Medicine
School of Medical Sciences
Universiti Sains Malaysia 16150 Kbg Kerian
Kelantan, MALAYSIA
office : +6097676628
Mobile : +60139302002

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