Appropriate statistical test for lesion distribution


I have 2D image data of lesions in independent samples of diseased tissue. I would like to know whether the total lesion area is greater in one half compared to the other half of the tissue (call the halves A and B; they can be distinguished clearly). I identify lesions and calculate their total area in both halves as well as their grand total. Since the grand total varies with each sample, I calculate the proportion in each half relative to the grand total.

What is the appropriate statistical test to assess whether the proportion of lesion area in A differs from that in B? I first thought an unpaired two-tailed t-test of proportions A and proportions B across all samples would be suitable. Then I worried that this is not valid, as the two proportions calculated from a single sample are not independent. Perhaps a one-sample t-test is more appropriate, comparing the proportion of lesion area in A against the hypothetical proportion of 0.5, which is expected if there is no difference in distribution?

Thanks for your help.
You could estimate the proportion of “A” with a beta-distribution and test if that is equal to 0.5. That is a distribution where the values are from zero to one. It is sometimes called “beta regression”.

An other possibility is to simply estimate a “usual model” but estimate with weighted least squares. If I remember correctly Maartenbuis wrote some good comments about that here at talkstats some time ago, but I can't find the posts.