Comparing four distributions

[Pratap Pundir]

What are the well-accepted tests to compare distributions?
Essentially, I have data in the following form
obs_id, dependent_var, property_1, property_2, property_3, group_id
where obs_id is the observation id
group_id tells us which group (control, treatment 1, treatment 2, treatment 3) the observation belongs to.

I would like to test for each property whether the distributions are similar, so, e.g. if property_1 is age
I would like to see whether each group has a similar distribution of age or not.
I have come across Mann–Whitney–Wilcoxon, but not sure I understood the test or how to interpret its results. And it seems like, this allows comparing only 2 groups.

[Nick Cox]

You're correct. (Wilcoxon-)Mann-Whitney is for comparisons of two groups. Kruskal-Wallis and ANOVA are possibilities for three or more groups.

[Carlo Lazzaro]

Pratap:
why not interacting -property_n- with -group_id- as predictors of a given regression?