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I have movement information from 4 animals across different moon phases. I want to compare if their movement (eg. distance traveled per night) varied among different moon phases. However, I do not have equal number of data points from all 4 animals. For example, animal 1 has provided data for 4 nights and animal 2 has for more than 20 nights.

I tried a Kruskal Wallis test on my dataset with movement as the dependent variable and moon phase (categorical- 8 categories) as the independent variable. Now, I want to include animal ID in this analysis to account for the repeated measures issue (as not all animals have provided data for all the 8 moon phases).

Each of my moon phase categories have more or less equal data points but the animal IDs do not. Can I use a Friedman's test here? If not what is a better alternative for my situation?

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    $\begingroup$ It sounds like Friedman's test isn't going to work for your data set. You might look at Skillings-Mack test, but I doubt that will be satisfactory either. I would suggest a mixed effects model, perhaps with aligned ranks transformation anova (ART anova), which is a non-parametric approach. ... But with only four animals, it probably isn't very useful to treat Animal as a random effect. Also, I don't know how well ART anova deals with data that is this unbalanced ... (cont') $\endgroup$ Oct 4, 2022 at 14:54
  • $\begingroup$ (cont') ... You could construct a model where you treat Animal as a fixed effect. ... I imagine you can find a generalized linear model that will be appropriate for what you are measuring. $\endgroup$ Oct 4, 2022 at 14:54
  • $\begingroup$ @SalMangiafico Thank you for these answers. So from what I understand, you want me to try out the following GLMs 1. movement ~ moon phase+'Animal' 2. movement ~ moon phase and find a best fitting model from that. Is that correct? $\endgroup$ Oct 4, 2022 at 17:02
  • $\begingroup$ I think those are viable models. But first you'd have to decide what kind of link function for the generalized linear model would be appropriate for what you are measuring. I think that's probably your best bet. It still may be a little funky considering how unbalanced the observations are across Animals. Of course, if the effect of Animal doesn't matter, then you have a more balanced set of observations. $\endgroup$ Oct 4, 2022 at 17:39

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Answer from comments

It sounds like Friedman's test isn't going to work for your data set. You might look at Skillings-Mack test, but I doubt that will be satisfactory either.

Under different circumstances, I might suggest a mixed effects model, perhaps with aligned ranks transformation anova (ART anova). This is a non-parametric approach.

But with only four animals, it probably isn't very useful to treat Animal as a random effect. Also, I don't know how well ART anova deals with data that is this unbalanced.

You could construct a model where you treat Animal as a fixed effect.

I imagine you can find a generalized linear model that will be appropriate for what you are measuring. The first step here might be to decide what kind of link function for the generalized linear model would be appropriate for what you are measuring.

Any approach may be somewhat unsatisfactory considering the low number of Animals and how unbalanced the observations are across Animals. Of course, if the effect of Animal doesn't matter, then you have a more balanced set of observations.

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