Test if statistically significant differences between the means of groups exist

#1
Hello!
Currently, I'm writing my thesis and have some problems. I did a survey with a choice experiment and several statements, like e.g. I enjoy cooking with my friends. Participants had to rate on a 5 point likert scale (totally agree or disagree). With the help of a factor analysis, I found 6 factors.
Whereas, groups had been created based on the choices of particpants (latent class analysis). Now, I'd like to compare the groups based on the means of the factors. I thought of a ANOVA, but unfortunately, I don't fulfill the normal distribution criterion. Now, I wonder what kind of method I should use to compare the means of my factors?

I read something about friedman and kruskal, and chi-square-test but I really don't know which to use! :confused:

Please help me.
 

hlsmith

Not a robit
#2
Please provide an example of what your data will look like, in particular the outcome variable. Also, what is your sample size?