[dmwood]

As noted, ordinary maps may suffer (for example, in epidemiology)from the impact of a very non-uniform population density. A disease cluster then MAY be a cluster, or it may be ordinary disease rates in a highly populated area. In my limited experience a cartogram is a deliberate distortion of the SHAPE of a map region in order to make some property (say, population DENSITY) constant everywhere in the new region. Then anomalies jump out. Done with care, one can do careful statistics within the cartogram and then back-transform to get statistics for the original map area.