Two-way ANOVA with repeated measures and random effect and assumptions violated I am trying to run a two-way ANOVA in JMP where I have the following variables-
Fixed effects:
1. Genotype (categorical)
2. Temperature (categorical)
Random effect:
1. Subject (animal)
I am using the same subject for different temperatures, violating the independent measures assumption of two-way ANOVAs. If I account for random effect of subject nested within temperature, does that satisfy the independent measures assumption?
I am satisfying equal variance assumption but violating normal distribution. Is it necessary to choose a non-parametric test if I'm violating normal distribution? 
Any help is greatly appreciated!



 A: For the violation of normality, I am assuming that you may have a large sample size since you are working with mice. The assumption of normality is sometimes hard to verify because some tests are too powerful for datasets with a large sample size. You can find more about this debate here: Normality assumption and sample size
Have a look at your distribution, if your sample size is low and the distribution doesn't seem to tend towards a normal distribution, you will have to find another statistical test that does not require the data to be normally distributed.
It seems to me that you have tested each mice in every temperature condition. If this is the case, then I do not think nesting individuals within temperature is the right thing to do. If you have tested some mice for a particular temperature, and then other mice for another temperature, then you may want to do that if you have some repeated measurements. You can read more about this issue here: Crossed vs nested random effects: how do they differ and how are they specified correctly in lme4?
A model of the type VO2 ~ genotype + temperature + temperature:genotype + (1|miceID) should work, then check the assumption of normality and decide whether or not you need to find an alternative to the ANOVA.
