I'm working on a project for a conservation plan. Part of the plan requires that areas added for conservation have less than one structure per five acres (these are pretty large, mostly undeveloped areas). I've done kernel density and and point density analyses before but always with many, many more points. In the past I've had problems if there are not enough points. Should I even be looking at density analysis options? Would Thiessen Polygons or a cost surface be a better option?
You could convert your points into a raster using the option count and perform a focal analysis on this raster. See ArcGis Help here and here. Choose a circular or square type corresponding to the size of 5 acres and use sum as statistic type. The result of this focal analysis will be a raster with the density of points per 5 acres.
I think that using point density would be fine (not Kernel). Use the buildings as input and set search radius to about 263.5 feet, which is the radius of a 5 acre circle (assuming you are using a circle-typed neighbourhood). Than if your units of choice are feet as well, than any value higher than 4.591e-06 will represnt an area (or a raster cell) in which density is higher than one building than 5 acers. You could use raster calculator to show only the areas that should be added to conservation, using the <= operator.
In a brief, point density tool counts the points within your serach radius defined neighbourhood (with no weights applied) and divide it by the neighbourhood area, namely 217800 squared feet. Hence the thershold mentioned above.