Before R. A. Fisher introduced randomized experimentation, the literature on empirical methods emphasized reducing heterogeneity of experimental units as the key to inference about the effects caused by treatments. To what extent is heterogeneity relevant to causal inference when ethical or practical constraints make random assignment infeasible?To what extent, if at all, do helmets reduce the risk of death reduce the risk of death in motorcycle crashes? Different crashes occur on different motorcycles, at different speeds, with different forces, on highways or country roads, in dense or light traffic, encountering deer or Hummers. One would like to compare two people, one with a helmet, the other without, on the same type of motorcycle, riding at the same speed, on the same road in the same traffic, crashing into the same object. Is this possible? Perhaps, it is when two people ride the same motorcycle, a driver and a passenger, one helmeted, the other not. Using data from the Fatality Analysis REporting System, Norvell and Cummings (2002) performed such a matched pair analysis using a conditional model with numerous pair parameters, estimating approximately a 40 percent reduction in risk associated with helmet use.
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