Kruskal-wallis Test  is a non-parametric method. It does not assume a normal distribution of the residuals. This is not like the analogous one-way analysis of variance(AVOVA). If you meet the assumptions, you can use Kruskal-Waillis

There are two common non-parametric tests that are analogous to two-way anova:  Friedman Test and Quade Test.  However, each is only for un-replicated block designs.  So, probably not what you want in this case.

Another approach is to use a robust method.  See the following link for an an example of two-way anova.  But it is not clear to me now far from parametric assumptions this kind of robust estimation allows.

http://rcompanion.org/rcompanion/d_08a.html

You might look at the Scheirer-Ray-Hare extension of the K-W test mentioned at the link below.  I am not familiar with it.

https://www.researchgate.net/post/Is_there_a_non-parametric_equivalent_of_a_2-way_ANOVA

Finally, you might want to use ordinal regression, especially if your "job satisfaction" is really a Likert response.  Ordinal regression as a generalized K-W test is mentioned at the link below.  I have used the ordinal package in R for this, and it is both powerful and relatively easy to use.  If use R, this would be my recommendation.

http://stats.stackexchange.com/questions/78365/what-is-the-non-parametric-equivalent-of-a-two-way-anova-that-can-include-intera

Thank you for the replies. They were very helpful.