# Comparing proportions of plants that died (two-way analysis with interest in interaction effect)

I want to compare the proportions of plants in an experiment that had died by the end of the growth period. I am not interested in how long it took for them to die, although I suspect some people will not like it if this isn't considered in the statistical tests.

Seeds were planted in one of two soils (soil treatments) and were supplied with one of three amendments (amendment treatments). 22 individual seed replicates were established under each treatment combination (e.g., Soil A with Amendment C). As to be expected, not all seeds germinated/emerged, however the majority did. Thus, throughout the experiment, there was an 'unbalanced design' or 'missing data' (?) for subsequent analyses related to growth variables and death.

One question I wish to explore is, "Are the death rates consistent between amendment treatments, and is this affected by soil type?". Hence I wish to include an interaction term.

I believe I have found a valid statistical test but would like others' opinions please.

Would a binomial (e.g., logistic) regression apply here? That is, per each seedling (remember, these numbers are different per treatment groups due to differing emergence rates), can I treat death as a yes/no determination and compare the numbers using a binomial regression.

For those who are interested, using R, I have constructed this model already with the following code: glm(DIED ~ SOIL * AMENDMENT, data = X, family=binomial). I then ran this through Anova {car}.
"DIED" is scored as 0 for no, and 1 for yes. The data for this code are restricted to seeds that did emergence (no NA scored for death)

• On the surface, my first inclination would be to consider a binomial model, as you suggest. The missingness would concern me though, since I imagine it's probably not MCAR, but instead likely to relate to P(DIED| predictors) Jan 9, 2022 at 3:06
• I think that's the first step: determine if seed emergence was affected by the the soil and amendment treatments. It's normal for there to be less than 100% germination, but, when possible, it's helpful if plants are established before the application of treatment. Since seeds were established under treatment conditions, I would include emergence as a separate dependent variable. Other than that, having some imbalance in the counts of plants at the beginning of the experiment shouldn't cause any major trouble in the results. Jan 9, 2022 at 13:35
• Thanks for the advice. You are both suggesting that the test is invalid(?) if the treatments also accounted fro the missing data (different germination rates). ANOVAs suggest germination to be significantly affected by treatments. Do you think it alright to continue using the binomial model as proposed and note the limitation/issue? I am always given advice that "its up to you to decide how accurate you want to be" which is rather annoying as stats novice. I think a more complicated model (e.g., including time) would be too complicated for the current application and time frame... Jan 10, 2022 at 23:28
• If you care only about whether the plant was alive or dead at the end of the experiment, then there's no reason to try to take into account plant health over time. It is common in agricultural experiments to look at, e.g., crop yield at the end of the experiment. That being said, it is sometimes of interest to plot e.g. plant survival over time as a matter of interest for your audience, if you recorded that data. ... I would analyze plant emergence as a separate dependent variable. ... And then I would use the binomial for model you propose for alive / dead at the end of the experiment... Jan 11, 2022 at 1:37
• How many plants are you talking about ? Like for full emergence in a soil/amendment combination, and then in the worst case for emergence in a soil/amendment combination ? Jan 11, 2022 at 1:39