# Thread: evaluating Kruskal-Wallis test results

1. ## evaluating Kruskal-Wallis test results

Using an online statistical tool I evaluated 5 group of students' (self-identified ethnic groups with na= 105; nb= 50; nc= 44; nd= 43; ne= 33.) answer to Likert like question. The computer gave me the following answer:
H=10.4
Df=4
P= 0.0398

Am I correct in saying that the median for the groups are statistically different?
Do I have to perform a Mann-whitney test on each combination?

Thank you.

2. ## Re: evaluating Kruskal-Wallis test results

Hi,
if I understand correctly you had data like 105 a-s 50 b-s etc and the research question was whether you have about the same number of a-s, b-s ... with the alternative being that there is a systematic effect leading to more a-s, say, then would come from just random variation? If I am correct you probably should have used a chi-squared test instead of KW.

regards

3. ## Re: evaluating Kruskal-Wallis test results

Thank you! The survey asked students to respond to questions e.g. “In my opinion, the economic system in the US leads to an unfair distribution of income” by indicating their opinion in a Likert scale. The 5 groups are their self-identified ethnic groups. If P= 0.0398 than does that signify that the median for the groups are statistically different? Do I have to perform a Mann-whitney test on each combination?

4. ## Re: evaluating Kruskal-Wallis test results

The p-value indicates that at least one group significantly differs from the others. Usually, a follow-up test would be the Dunn test. Sometimes, some softwares perform MW test on a paiwise basis, with some sort of p-value correction (e.g., Bonferroni).
As for the "median" issue, like MW test, KW is not a test of equality of medians. A broad interpretation can be thinking about the test as a means to assess if at least one group scores higher than the other ones. Since the test is based on ranks, maybe thinking of it in terms of mean ranks among groups would be also appropriate.

Hope this helps

5. ## Re: evaluating Kruskal-Wallis test results

Thanks. I will explore the Dunn test.

6. ## Re: evaluating Kruskal-Wallis test results

Btw,
did you try a simple ANOVA? Only the residuals need be normal, so giving it a try could be worth it.

regards

7. ## Re: evaluating Kruskal-Wallis test results

The post-hoc test for the K-W test is:

Thus, with an alpha per-comparison rate of 0.05 and k = 5, the critical value of z from the standard normal distribution would be 2.80703.

8. ## Re: evaluating Kruskal-Wallis test results

Thank you, will try

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