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

 From Morten Hesse To 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 10:45:05 +0200

```Hi
```
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 instant where you may justify using Kruskall-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.
```Best regards
Morten

Citat af Kamarul Imran Musa <drkamarul@kb.usm.my>:

```
```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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