Hi all!
In a previous analysis, I've conducted a one-way anova with planned comparisons. As I've been advised to conduct some nonparametric tests instead, I'm looking for your help.
I used the Kruskall Wallis test, but now I'm struggling to find a nonparametric alternative for the planned comparisons. If I understand it correctly, the Mann-Whitney only allows me to compare separate groups (e.g. A vs B). However, I'd like to compare multiple groups at once (e.g. A+B vs C+D, or A+B+C vs D). Could anyone help me out how to do this?
Thank you very much in advance!
The Kruskal-Wallis test is a non-parametric analog to the one-way ANOVA F-test, and the Mann-Whitney U test is the non-parametric analog to the t-test. If I understand your question correctly, to test A+B vs C+D you should pool the groups A and B by giving them a single moniker, likewise for C and D. Then simply perform the Mann-Whitney U test on these two groups.
Dear Talia,
In the newer versions of SPSS you can do within-group analysis. For this, Go to Analysis ---> Non-parametric test ---> Independent samples
in the setting tab choose Kruskal-Wallis. In the end, click on result window, and on the right bottom side of the appeared window click on pair-wise comparison.
Thank you both for your responses!
Geoffrey S Johnson, I never thought it would be so simple, but your solution seems to work. Thank you for your suggestion!
Some of the approaches available may depend upon the software you are using.
What may be the most rigorous may to approach this problem is to use aligned-ranks anova, and then analyze the contrasts. This is relatively easy in R using the ARTtool and emmeans packages. I suspect this approach would be valid on more complex designs (e.g. 2-way anova) on the main effects. I'm not sure what would be valid with the interaction effects.
As far as I can tell, for a one-way anova, simply converting the dependent variable to ranks and then running a common anova followed by custom contrasts yields the exact same results as the aligned-ranks approach. This should be easy in any good statistics package. This might not be valid for more complex designs, though.
I'm not a big fan of combining multiple groups into a single group to do an analysis (as Geoffrey Johnson suggested). In the case of the one-way design, using the Mann-Whitney tests resulted in similar results to the anova-on-ranks or aligned-ranks-anova approaches. But the results were not exactly the same. I ran this comparison maybe 10 times with 3 contrasts each, and in one case the results differed enough to make a difference (like = 0.057 vs. p = 0.039).
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