The R script takes a shapefile consisting of polygons, finds each polygon's centroid, and writes 2 new shapefiles: one shapefile has all polygons flipped across their x axis, and the other has them all flipped across their y axis.

After this step, go into ArcGIS and define the projections as WGS 1984. Then you can run the python script.

The python script calculates the symmetric difference statistic using both sets of polygons, and prints symmetry.txt. If a polygon's symmetric difference cannot be calculated, it returns NA.