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I am running an ecological/environmental experiment in a salt marsh with 5 experimental treatments and 3 replicate soil samples taken from each treatment. I have been taking measurements from these treatments across three seasons, giving me three timepoints for my experimental variables. I want to run a mixed effect model with my target experimental variable (gaseous nitrogen removal from each treatment) and season (spring, summer, fall) as fixed effects and replication as a random effect. Given that I have so few replicates, I would like to opt for a non-parametric test because I think a sample size of 3 is too small to adequately evaluate the assumptions for parametric tests. Am I on the right track with this thinking? If so, what test is recommended for non-parametric mixed effect models?

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  • $\begingroup$ Why do you want to declare the replicates as random effects? If I understand correctly, each combination of treatment and season (5 * 3 = 15 combinations) will be a cluster with three measurements. It may be easier to average the three replicates. $\endgroup$
    – dipetkov
    Commented Oct 11, 2023 at 0:08
  • $\begingroup$ @dipetkov the decision to declare replicates as random effect is based off of several papers I have read that perform the same kind of experimental design and experimental variables using this type of random effect assignment. I guess they are accounting for the high variability between replicates that is commonly seen in salt marsh samples. $\endgroup$
    – Emma
    Commented Oct 11, 2023 at 15:00
  • $\begingroup$ It makes sense to utilize methods that are commonly used in your field. Then why look at non-parametric methods? Another option -- somewhat in the opposite direction of what you are considering -- is to do Bayesian analysis. This would allow you to incorporate knowledge from related studies via the priors. Using (moderately) informative priors could work well with a small dataset. $\endgroup$
    – dipetkov
    Commented Oct 11, 2023 at 15:15
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    $\begingroup$ @dipetkov I want to go the non-parametric route because my sample size is smaller than those other papers. Granted, those papers still have samples sizes of 5-10 which isn't huge but it grants more confidence for testing their normality assumptions. One of my thesis committee members also recommended that I look into nonparametric tests for GLMM. $\endgroup$
    – Emma
    Commented Oct 11, 2023 at 15:40

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