Highway Safety Manual Calibration: Estimating the Minimum Required Sample Size

Crash frequency has been identified by many experts as one of the most important safety measures, and the Highway Safety Manual (HSM) encompasses the most commonly accepted predictive models for predicting the crash frequency on specific road segments and intersections. The HSM recommends that the models be calibrated using data from a jurisdiction where the models will be applied. One of the most common start-up issues with the calibration process is how to estimate the required sample size to achieve a specific level of precision, which can be a function of the variance of the calibration factor. The published research has indicated great variance in sample size requirements, and some of the sample size requirements are so large that they may deter state departments of transportation (DOT) from conducting calibration studies. In this study, an equation is derived to estimate the sample size based on the coefficient of variation of the calibration factor and the coefficient of variation of the observed crashes. Using this equation, a framework is proposed for state and local agencies to estimate the required sample size for calibration based on their desired level of precision. Using two recent calibration studies, South Carolina and North Carolina, it is shown that the proposed framework leads to more accurate estimates of sample size compared with current HSM recommendations. Whereas the minimum sample size requirement published in the HSM is based on the summation of the observed crashes, this paper demonstrates that the summation of the observed crashes may result in calibration factors that are less likely to be equally precise and the coefficient of the variation of the observed crashes can be considered instead.