Usability of value-by-alpha maps compared to area cartograms and proportional symbol maps

The value-by-alpha map is a recently proposed method for mapping bivariate spatial information. It is theoretically advantageous, but no thorough evaluations have yet been reported. Here we conducted a systematic evaluation of its usability in terms of effectiveness, efficiency and satisfaction. Major conclusions from this study are the following: (1) value-by-alpha maps are as effective and as efficient as area cartograms in bivariate mapping, but are generally less effective and efficient than bivariate proportional symbol maps, and (2) in terms of satisfaction, value-by-alpha maps are as popular as bivariate proportional symbol maps and are more popular than bivariate area cartograms.