What is the appropriate ANOVA model for the following experimental design: the effect of four different concentrations of compound X on microorganisms? Each X concentration has three jars and three replicates are collected from each pot. Samples are drawn weekly for 18 weeks.
Since you used different concentrations (levels) of the same variable X, ultimately, it is a study of the impact of one parameter on the response y (microorganisms). I think one-way ANOVA is appropriate in your case.
I refer to the following refs (examples):
ANOVA (general):
https://www.mathworks.com/help/stats/anova.html
One-Way ANOVA:
https://www.mathworks.com/help/stats/one-way-anova.html
You would actually need a rather complex model.
One aspect is that you have repeated measures, in that you are taking samples from the same experimental units across 18 weeks.
Another aspect is that you have three samples from each jar, so usually you would use a model that includes sample within jar (nested effects).
You might be able to simply things depending on what you need to know.
It may be that the effect of jar isn't meaningful, so that you can treat three samples from three jars as nine simple samples.
It may be that you you don't need to account for the 18 weeks of samples, but only look at the final week for your statistics. In this case, you could still plot and present the data over 18 weeks, which may be of interest, but not have to run statistics over the 18 weeks. Again, it depends on what you want to know.
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