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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 <[email protected]>
To   [email protected]
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 <redacted>:

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




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