z-test or beta regression for assessing differences between groups of averaged proportions?

If I'd like to test the hypothesis that there is no difference in mean seagrass cover between two months, over all years, what test/analysis is best to use? My thoughts move to a z-test because I'm testing differences between two samples and the sample size is >30. On the other-hand I've recently learned beta regression can be for data confined between 0->1 with a categorical predictor (in my case, month). So, dumb question I know, but what's the correct line of thinking here?

I found this discussion "T test not for proportion" helpful, but I'm still not sure my data meets the z-test assumptions. If a distribution of average values comes close to a normal distribution and my data consist of average seagrass cover values per site (n=47 sites), and per month, would this meet the assumptions for a z-test? Or because I'm dealing with proportions, rather than continuous data, using a categorical factor as a predictor, I should actually stick to regression techniques? I hope to also understand the advantages of both (if the data works for both). I'm working in R.

years <- c(2010, 2021)
month <- c("March", "July")
site <- seq(1:47)
ave_seagrass <- runif(188, min=0.0, max=1)

df <- data.frame(ave_seagrass, site, years, month)
Hi NateLa,
From your question, I assume that you are talking about a z-test to compare two independent means. If that is the case, I would not use it and I would stick to beta regression. As I see it, the fact that you are working with a bounded distribution makes it incompatible with the normality assumption (even if it looks like one). Note, though, that beta regression assumes that no 0 or 1 values are not present in your distribution (if they are, you should probably introduce the correction suggested in the original article of Ferrari & Cribari-Neto (https://www.tandfonline.com/doi/abs/10.1080/0266476042000214501) .

In any case, please note that I am not a professional statistician, so my opinion has a limited value.

PS: this article may be helpful, https://personal.utdallas.edu/~dxs093000/papers/beta32.pdf
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Thank you for helping me think this through! Thankfully I don’t have any 1’s, but I do have an over abundance of 0’s (might be looking at a zero-infated beta regression, which I have no idea how to do, but gotta start somewhere).



Well-Known Member
If you are unhappy about the suggestions offered in your other thread on this topic, a matched pairs permutation test may well solve your problems.