# Kruskal-Wallis output problem

#### Nich95

##### New Member
Hi everyone, I have some troubles understanding some result of my Kruskal-Wallis test:
I want to compare a variable across these 3 independent groups, and since its distribution is not normal, I run a non-parametric test. The test tells me to reject the null hypothesis (p=.000). The mean rank for each group is as follow: Gr1= 70.68; Gr2= 84.76; Gr3= 52.31

From the pairwise comparison, looking at the adjusted significance values, I see that Group 2 and 3 are significantly different (p=.000), while Group 1 and 3 (p=.078) and Group 1 and 2 (p.=.274) are not significantly different. But in the Homogeneous Sbubset table each group is placed under a different subset.

My questions are :
-Why are the two follow-up analyses giving me a different result? Which one do I trust?
-Am I doing right comparing the adjusted significance value with the "usual" .05 alpha, or should I compare it with an adjusted alpha of .0167 ?
-How do I interpret the fact that Gr 1 (the "middle one" in terms of mean rank) is not different from the other two groups, but gr2 and gr3 are different? (this is more a general question because a similar thing is happening in another analysis I run).

I hope everything is clear, I apologize if some terminology is not correct, it's my first time working with SPSS. Thank you for your time in advance #### Karabiner

##### TS Contributor
I want to compare a variable across these 3 independent groups, and since its distribution is not normal, I run a non-parametric test.
Who misinformed you that the dependent variable should be normally distributed?
Only the residuals from the analysis should be from a normally distributed
population, not the dependent variable itself. And even that assumption is unimportant
if the sample size is large enough.
-How do I interpret the fact that Gr 1 (the "middle one" in terms of mean rank) is not different from the other two groups, but gr2 and gr3 are different? (this is more a general question because a similar thing is happening in another analysis I run).
Why do you say it is not different? The mean ranks are different.
The associated p values are not < 0.05, that's all. If the groups
have different sample sizes, then the n's for the pairwise comparisons
differ, which could be one reason for seemingly contradictory
results.

With kind regards

Karabiner

#### Nich95

##### New Member
Only the residuals from the analysis should be from a normally distributed
population, not the dependent variable itself.
I don't know what this means, I read that non-parametric test are used when assumptions of other tests cannot be satisfied, and since the histogram graph it's very far from a normally distributed one I thought to use this family of tests.

Why do you say it is not different? The mean ranks are different.
So you are saying that to compare these groups I could only look at the mean rank without running any test?

If the groups
have different sample sizes
Group 1 and Group 2 have n=45, group 3 has n=47. Could this little difference explain it?

Thanks for your answer Karabiner!

#### Karabiner

##### TS Contributor
I don't know what this means, I read that non-parametric test are used when assumptions of other tests cannot be satisfied, and since the histogram graph it's very far from a normally distributed one I thought to use this family of tests.
Analysis of variance does not assume that the dependent variable is normally distributed.
It assumes that the prediction errors from the analysis are normally distributed (in the
population from which the sample was drawn). Alternatively: that the dependent variable
is normally distributed in each separate group. But if sample size is large enough (such as
yours) this assumption is no more necessary.
So you are saying that to compare these groups I could only look at the mean rank without running any test?
I just referred to the fact that you posted group differences, but claimed that groups
were the same. That a statistcial test is not significant does not mean the difference
is necessarily and exactely zero.
Group 1 and Group 2 have n=45, group 3 has n=47. Could this little difference explain it?
No.

With kind regards

Karabiner

#### Nich95

##### New Member
Ok thanks, I'll try running the ANOVA then!