Kruskal-Wallis Test

[Baris Oruc]

I will assign the following test result for my research but I can not be sure about the accuracy of interpretation. Can anybody help me?


H₀ : there is no difference in total consumption between treatment groups
H₁ : there is difference in total consumption between treatment groups

Treatment Group	Obs	Rank Sum
0	34	1395.50
1	32	1543.00
2	34	2111.50

Chi-squared = 9.248 with 2 d.f.
Probability = 0.0098
Chi-squared with ties = 9.982 with 2 d.f.
Probability = 0.0068

The calculated value of the Kruskal-Wallis test is less than the critical chi-square value. Thus, the null hypothesis has rejected and stated that there is a significant difference in total consumption between treatment groups.

[Carlo Lazzaro]

Baris:
welcome to the list.
Kruskal-Wallis test outcome says that you can reject the null hypothesis at any level below 0.68% that the total consumption is the same across the compared population.

[Marcos Almeida]

Just adding to Carlo's insightful advice: there is at least one treatment group with a significantly different rank sum. Probably, well, almost surely, group 3. In other cases, when the difference is not so visible, a post-hoc test will unveil the group(s) involved.

[Nick Cox]

These tests remain popular in many quarters although it is hard to see why. I can't see your data, but it's mostly my experience that

(a) such tests lead nowhere interesting or useful; at most your conclusion is a yes or no result and a P-value. If the limit of your curiosity is just whether or not groups are the same, so be it, but that would be surprising. How much? is more often a much more interesting and useful question.

(b) a linear model (often with a logarithmic link) will give pretty similar P-values and allow all sorts of extra statements that are positive or interesting. If not, there are plenty of other things to try.

(c) even if your data are (perceived to be) awkward in some sense, which is why you reach for Kruskal-Wallis, various kinds of simple graph will show the awkwardness directly and also any broad contrasts or fine structure.

You have 100 observations any way, so need not be too paranoid about the risks of very small samples.

If you post the data I can try to convince you directly. Conversely, if somebody is telling you to do this as part of some course or assignment, then sympathies. See FAQ Advice #12 on how to post data.