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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 <drkamarul@kb.usm.my>
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 

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 




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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