The limit of usefulness of accident rate as a measure of accident proneness

Abstract

The liability to accident of a given automibile driver may be said to depend upon two sets of factors, those related to him such as aptitude as a driver and the distance he drives, and those unrelated to him, "which we may call luck." The best driver-testing system can predict the first but not the second set of factors, since they are determined by chance. Any group of drivers selected by this best possible testing system, then, would show a chance or Poissonian distribution of accidents. One mathematical property of the Poissonian distribution is that the variance is equal to the mean. If a sample of drivers is "separated into a number of classes, each of equal liability within itself, these classes will constitute" a series of "true Poissonian distributions." "The weighted means of these classes will be the mean of the whole sample. And the weighted mean of the variances within the classes will also… be equal to the mean of the whole sample. But this weighted mean variance will also be the variance from the regression line , which when added to the variance due to regression is identical with the variance of the whole sample." Knowing the variance due to regression when the best possible predictive instrument of accident liability is used, then, the validity of that best possible instrument can be estimated. (PsycInfo Database Record (c) 2025 APA, all rights reserved)