# Estimating proportion of region cropped by proportions in random samples

I have a series of quadrats placed randomly across aerial photography of a region. In each quadrat I have estimated the proportion of the quadrat under cropping and my goal is to estimate the proportion of the region cropped with a 95% confidence interval around that estimate.

The data are provided below, but include 1s and 0s, and the vast bulk of values is 0. My question is : Is my best option to estimate the mean to use the standard approach (i.e., mean = sum(x)/n; 95% CI = mean ± z(α/2) * σ(mean)) or is there are better approach / model for this sort of data.

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• (+1) If you still have access to the photography, consider implementing an adaptive cluster sampling technique. This consists of analyzing the neighborhoods of the quadrats with positive cropping proportions in a controlled way. It is possible, with relatively little additional effort, to obtain unbiased estimates and accurate CIs that are much better than what you get with this simple random sample. It is well explained in Steven Thompson's book. – whuber Aug 31 '15 at 1:53
• Thanks Gung. I've looked into adaptive cluster sampling but it would seem to work on defining some level of crop cover as a threshold for presence / absence, then estimating proportion of occupied quadrats based on that threshold. So I am confused at what it actually estimates - if I set that threshold at 0% (ie >0% crop cover means the cell is occupied while 0% means unoccupied), does that mean I wind up estimating the proportion of the region that has >0% crop cover, and if so is that the same as the proportion of the region under crop cover? – user87212 Sep 2 '15 at 3:33
• You can use adaptive sampling techniques to estimate the mean value, not just the proportion of cells that have some property. – whuber Sep 2 '15 at 14:08