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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!

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  • $\begingroup$ Can you state clearly your biological question and provide a sample of your data (or simulated data with the same structure)? $\endgroup$
    – Nakx
    Jan 19, 2018 at 0:49
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    $\begingroup$ My biological question- How does a mouse with a protein deletion respond to lower temperatures via metabolic rate (VO2)? I have 2 genotypes of mice: control, and one with a protein deletion. I measure VO2 which is used to determine how well these mice are thermoregulating. I have 4 experimental temperatures and each subject (mouse) goes through all temperatures which are done on a separate day. I treat each temperature as a category (and I bin them. for example: 19-21 Celsius, 23-25, 27-30, and 33-35) and VO2 is the responding (continuous) variable. $\endgroup$
    – Carissa
    Jan 19, 2018 at 19:31
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    $\begingroup$ I am not sure why you want to nest individuals within temperatures. $\endgroup$
    – Nakx
    Jan 20, 2018 at 2:47

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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.

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  • $\begingroup$ I do not have a large sample size. I should mention that I have about 6-7 mice in each temperature category, for each genotype. I was not able to get ALL mice tested in each condition. For example, one mouse may have just been at 2 temperatures due to equipment issues, etc. So in that case, going by your advice, I should be nesting individuals within temperature. I will read those links and consult with my advisor. I will look more into my distribution as well and check out how the Q-Q Plots look! $\endgroup$
    – Carissa
    Jan 22, 2018 at 19:36
  • $\begingroup$ On this site there seems to be a general mistrust of pretesting for normality before ANOVA: stats.stackexchange.com/questions/300352/…, stats.stackexchange.com/questions/6350/…, stats.stackexchange.com/questions/5680/… $\endgroup$
    – kjetil b halvorsen ♦
    Aug 5, 2020 at 22:19

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