A KW test will not tell you if there is any effect of the interaction of the independent variables (factors) on your dependent variable. You could try a data transformation and repeat the test for normality and homoscedasticity. If anova's assumptions don't hold, you could try with a GLM.

Ey Cristina qué rápida! muchas gracias! Que tipo de GLM y con qué software lo corres generalmente?

The Kruskal-Wallis test is one-way, as Cristina pointed out. For the interaction, you will need tha ARTool. See:

https://depts.washington.edu/acelab/proj/art/

If you have a between x within design (with repeated measures), you might want to use the f1.ld.f1 test from the nparLD R package.

I'll second the recommendation of Jos Feys . For a non-parametric two-way design, ART anova is the most flexible, respected option. In R, it has methods for effect size, post hoc tests, and it's relatively easy to get a pseudo r-squared value.

I agree with Cristina, the simplest procedure would be to try with GLM models. on the other hand, thank you very much for the ARTool approach, very interesting.

Thank all of you for your help! I sincerely appreciate it

BTW, in this context GLM stands for "generalized linear model", not "general linear model", as GLM means in SAS-speak.

Jose Miguel Sandoval-Gil The GLM carries two important functions: the family, and the link function. The selection of these depends on the type of your data (counts, proportions, continuous...). I use R and Rstudio to run it. I'm sharing with you some links with theoretical and practical information in order to thelp to research:

https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/glm

Article Generalized Linear Models

https://link.springer.com/book/10.1007/978-1-4419-0118-7

BTW, thank all for the information. I didn't familiarized with ARTool, so I will explore the package and funtions in R.

I want to highlight a possible problem with the recommendation of ART (aligned rank transformation) given by Jos and Sal:

A statistical interaction denotes a non-additive combination of effects. To judge (non-)additivity one has to have a quantitative effect measure. Using ranks (rank order statistics) just removes any quantitative information and therefore makes it impossible to study interaction (there are cases where interaction is mapped in ART, but it is really difficult to get the correct interpretation in such cases, or to recognize when this is the case at all).

Note that (monotone but non-linear) transformations do change the additivity of effects. Multiplicative effects in Y are additive in log(Y), so one may find an interaction when analyzing Y bit no interaction when analyzing log(Y). Here, other (distributional and functional) assumptions of the statistical model become much more relevant than in simpler cases (where interaction plays no role). Being ignorant about the scale on which interaction (non-additivity) happens is very dangerous and can lead to very misleading or wrong conclusions.

Maybe you can use Scheirer–Ray–Hare Test. It is a nonparametric test used for a two-way factorial design. For info: https://rcompanion.org/handbook/F_14.html

Muchas gracias Marta!!! saludos