I recently am analysing my results (behavioural, observation-based data), and I realised that my data are non-normal. No problem, this happens in behavioural data a lot, and I thought I just needed to do non-parametric tests instead. Turns out, my observational data are like multiple dependent variables (e.g. I recorded different courtship rituals of 1 individual in a 1h observational period/ continuous) against 1 independent variable (treatment/categorical). Hence, MANOVA seemed like the correct stats test to use.

Well, given that my data are all NON-NORMAL (in addition to no equal variances), I cannot use MANOVA. It violates most of its assumptions. I do not know of any non-parametric version of MANOVA either. The other issue comes with transformations as my data has a LOT of 0s. They are not due to measurement errors or outliers where I can dismiss them - they are true observations and are important to keep. I've tried log-transforming my data (i.e. log(y+1), so that 0 can be transformed into 0, increasing my constant to >1 etc), cube root transformation, square root transformations but my data is still non-normal.

Any idea how to overcome this non-normality issue? I need to do MANOVA, or something like that, in which I can compare multiple dependent, continuous variables against 1 categorical independent variable at one go.