Is the claim that 'variance kills' an ecological fallacy?

Over the past 15 years, a number of studies have reported positive correlations between estimated traffic crash rate and the dispersion of vehicle speeds. These correlations have on occasion been interpreted as supporting the view that slower and/or faster drivers have higher crash risks, or that speed variance itself is a causal factor for individual crash risk. This paper points out first that such positive correlations can be expected in situations where individual crash risk is either an increasing, or a decreasing, or a U-shaped function of speed, and so the correlations in themselves provide no evidence concerning the relation between speed and crash risk for individuals. Second, since such correlations can be expected in circumstances where individual risk is independent of speed variance, observation of these correlations provides no support for the hypothesis that increases in speed variance increase individual risk.