Poisson regression or ANOVA, repeated measures or independent?

Question

I have been trying to figure out the best way to approach analysis of my data for a while now and I'm struggling to understand if a Poisson regression is correct and, embarrassingly, I'm not sure if my data are independent observations.

I have two data sets:

Firstly,

I have data from rows sown with 100 seeds each (n=6) with counts of seedlings recorded at different stages of seedling development (germinated, emerged etc, 6 stages). The same seeds/seedling were tracked over time. I want to know which stages have significantly different counts of seeds/seedlings. Are these independent observations as they are different outcome variables (germinated, emerged etc)? Note: each time point can only be equal to or less than the preceding time point. Should this be approached with a GLM with Poisson distribution or can it be a simple one-way ANOVA or a repeated measures ANOVA?

My second data set has data from 10 seeds per pot (n=6 pots) for two species, under 3 different treatments. There are four outcome variables (germinated, ungerminated etc) with the seeds proportioned into one of the four outcome variables (if 80% germinate, for example, then 10% could be ungerminated and 10% dead). This means quite a lot of 0's in some cases. I have performed a Poisson regression in R to find significant differences between treatments for each outcome variable and it makes sense but I want to check that this is the best approach and meets the correct assumptions but, I'm confused..

Answer 1

Welcome to this site, Scott! It's a bit hard from your description to tease out what exactly is going on in your two studies. You may need to revise your question and provide more specifics.

Your first study seems to involve different time points, although you don't share how many. Are we talking about 3 time points or 20 time points, say? Also, you mention that counts are recorded at each time point but you don't explain what those counts represent (e.g., are they counts of seeds that germinated?), what entities they are recorded for and, most importantly, whether those entities are kept the same at each time point or they are different from one time point to another? Also, what do you mean by replicate rows?

Your research question for the first study needs to be stated more carefully: "I want to know which time points are significantly different (i.e. significantly less than the preceding time point).". I suspect what you really mean is that you want to know whether the expected/average value of your count outcome variable at time point $t$ is less than that at time point $t-1$? (It's clear that the time points themselves are different from each other by virtue of how you chose them.)

If you measure the same entity over time with respect to a variable of interest, you can reasonably expect temporal correlation among the recorded values of that variable for that entity. As an example, if you track the same seed over time and at each time point you record whether or not that seed germinated, the germination status values (yes or no) will likely be correlated over time.

Your second study needs more clarifications also. How many treatments are we talking about? Etc.