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I am asking for your help.

I have 3 variables that are divided into 4 groups (Quantitative variables).

I intend to check if there is any difference between the groups for each variable.

My difficulty in using ANOVA - it indicates that one of the group is different but it does not indicate which one of the group is different.

Can you please advise what kind of test to use in order to get an indication of which group is different in relation to the others. Should I use a T-TEST in the following way: checking one group in relation to the other 3 groups together (=as another one group)?

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  • $\begingroup$ With only four groups. I would start with graphical methods, like a side-by-side boxplot. There are other ideas for graphical anova, on CRAN there is a package granova for this. $\endgroup$ – kjetil b halvorsen Mar 30 '17 at 14:36
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You can use a randomization test of no difference in population means (null hypothesis) against a two tailed alternative, where the difference in sample means is the test statistic.

Then you can test that none of $k$=4 groups stochastically dominates one another.

The Kruskal-Wallis test can be applied to decide whether the population means on a dependent variable are the same across all levels of a factor.

Also, you can use the Friedman’s test. It is used to test for differences between the two snapshot data when the dependent variable being measured is ordinal (ranks). The null hypothesis that the distributions are the same across repeated measures was rejected.

See, for instance, here.

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