Say I have a raster with attribute values over some spatial area.
Also, say I have circular polygons of varying sizes contained within the raster's area.
What would be the proper method to test if the raster attribute values contained within a polygon are statistically different from raster attribute values in other polygons?
I first thought to put all raster cell values within polygons into a dataset and test their differences with a t-test, however, it doesn't seem proper to treat each raster cell as an "observation". The t-test would have far too many observations in each polygon and would give the test unwarranted statistical power.
Are there any proper methods for performing such a hypothesis test?