# Summarizing several percentages of uneven size samples

We are comparing the prevalence of a trait across 40 depth bins in the ocean. The notable part is that the percentage of organisms with this trait is nearly the same (80%) across all depth bins, despite different total counts and diversity of entities. My question is how to summarize these percentages and show the low variability of this value across the depths. We are not as interested in a multiple comparison / null hypothesis test, as I have found those. It feels wrong to average and derive standard deviation for percentages. The total count of data points is around 480k, but N can be a couple orders of magnitude different between bins, so the ratio we are comparing could be 8/10 or 8000/10000.

You could view this as a meta-analysis problem. Each bin gives you an estimate of the prevalence (which you might want to transform) and its standard error. Using the standard inverse variance procedure for meta-analysis you would then get an overall estimate and also an estimate of its heterogeneity. You might be interested in the CRAN Task View on MetaAnalysis for some hints. I use metafor but your mileage may vary.