The whole area of gene research is a speciality in itself, and the problem controlling false discovery dates of many thousands of statistical tests has a large literature also. The way that you ask the question suggests that you need to engage with the expertise in Lübeck university, get advice from a qualified person and study the topic yourself. A few answers on RG is not a substitute for engaging with local expertise as you carry out your analysis.

I'll add two things to the good advice you received from Ronán Michael Conroy. First, take a look at this (cheeky) poster by Craig Bennett:

• http://prefrontal.org/files/posters/Bennett-Salmon-2009.pdf

Second, read the classic article on MANOVA by Huberty & Morris (1989), and pay attention to what they say about the futility of following up a significant MANOVA with multiple ANOVAs.

Article Multivariate Analysis Versus Multiple Univariate Analyses

See also the more recent article by by Huang (2020).

Article MANOVA: A Procedure Whose Time Has Passed?

HTH.

Dear Bruce and Ronan,

thank you for your replies and suggested literature, I'll go with that. Indeed, I already reached out to a statistician on campus, however it might take a while until we can meet for counciling so the literature is a great way for me to prepare for that.

Kind regards

Thorben