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

#### NateLa

##### New Member
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.

Code:
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)

#### css

##### Member
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.

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#### NateLa

##### New Member
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).

Cheers,

#### katxt

##### 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.