Nonparametric mixed-design ANOVA I have an experiment design with one "within subject" factor and one "between-subject" factor. So I have to use mixed-model ANOVA, but empirical distributions are not approximated by any good family. Thus I have to implement some nonparametric version of ANOVA. The only one is known to me is due to Brunner and Langer[1], with zero hypothesis on equivalence of marginal distrbutions. I would like to compare medians differences and report something related to them as effect size. As far as I understand,  after Brunner and Langer ANOVA I should use stochastic dominance posthoc test and the effect size related to it. Thus can't say anything about medians.
Is there any nonparametric version of ANOVA with hypothesis on median?
Could I make some posthoc test on median differences after Brunner and Langer ANOVA?
[1] Brunner E, Domhof S, Langer F (2002). Nonparametric Analysis of longitudinal Data in Factorial Experiments. John Wiley & Sons, New York.

Quantile regression has been mentioned.  Another viable option may be aligned ranks transformation anova (ART anova).  It's a nonparametric approach.  In some software implementations it can handle fixed and random effects and post-hoc tests.
