We report on an empirical study investigating the effectiveness and efficiency of spatial inference making with contiguous (value-by-area) cartograms, compared to informational equivalent choropleth maps, combined with graduated circles. We find significant differences in people's inference-making performance dependent on the map type. Overall, results suggest that the choropleth map with graduated circles is more effective and more efficient than the cartogram for the analysis of population census data. However, map effectiveness and efficiency also significantly depends on the inference task complexity, and more surprisingly, on the shape characteristics of the depicted enumeration units. For simple tasks, cartograms seem as effective and efficient as the more traditional mapping method. For complex inference questions, inference performance with cartograms is significantly dependent on whether regular or irregular zones are distorted. As we know still very little about the perception and cognition of cartograms, we hope to shed new light for this intriguing mapping method with this empirical study.