My problem is as follows:

I conducted a simple experiment to check for the effect of gender and gender pairing in the outcome of a game (the ultimatum game, I won't bother you with unnecessary details).

Important for my question to you, is just:

Each participant makes a monetary offer (decimal number between 0 and 10) to another participant and this offer is the dependent variable.

I have four groups:

Males who play with males

Males who play with females

Females who play with males

Females who play with females

Unfortunately the groups are not of equal sizes at all (17, 20, 11, 31), distribution is not normal, and the standard deviation is not the same across groups.

**Question 1**

I would like to build subgroups, such as:

female vs. male player

female vs. male opponent

mixed gender vs. same gender

--> Can I simply take the means/medians without accounting for the difference in group sizes?!

By first taking the means of each of the four conditions and only then the means of the wanted subgroups I get the weighted averages. But - it's only one number per condition and I cannot make statistical tests with that! (I would like to do a Wilcoxon Mann Whitney test e.g.).

**Question 2**

To compare the four groups I think I should use the Kruskal Wallis rank test.

--> Do you agree? If yes, is there a post-hoc method to compare the different subgroups? (I'm thinking of something that is like the Bonferroni method for ANOVA). Or can I simply use a Wilcoxon Mann Whitney then?

**Question 3**

I would like to run a regression (in order to be able to include other variables, such as age). Can I? Or would that lead nowhere, with all the assumptions that my data violate.

What do you think about the idea of creating a dummy variable that is:

0 if offer ≥X

1 if offer <X

and then running a probit regression?

--

I attach two pictures. They are both histograms of dependent variables that I would like to use in my regression. (one of them is the "offer" that I talked about above).

Thank you very much for your thoughts on these problems!

(...and for reading until here!)