Minimum sample sizes for estimating reliable Highway Safety Manual (HSM) calibration factors

The Highway Safety Manual (HSM) assists state and local agencies in improving highway safety by moving toward statistically proven quantitative analyses. The manual recommends using Empirical Bayes (EB) method with locally derived calibration factors to predict the agency's safety performance. It recommends deriving calibration factors using randomly selected 30 to 50 roadway sites that experienced a minimum of 100 crashes per year. Given the fact that the minimum sample size is a function of sample variance, this recommendation is clearly questionable as roadway characteristics of different roadway types are likely to have different levels of homogeneity. This research used Florida data to determine the minimum sample sizes to estimate reliable calibration factors for the following three facility types: rural two-lane roads, rural multilane highways, and urban and suburban arterials. The analysis was based on the data collected from more than 7,000 miles of segments and more than 1,000 intersections in Florida. The minimum sample size was determined such that there is a high probability that the calibration factor estimated from a sample is within 5% to 10% of the actual calibration factor calculated from the entire data set. For all the site subtypes, it was found that the minimum sample size of 30 to 50 sites, as recommended by the HSM, is insufficient to achieve the desired accuracy. Moreover, the sample sizes required for estimated calibration factors to lie within 5% of the actual calibration factors is almost double the sample sizes required for estimated calibration factors to lie within 10% of the actual calibration factors. The results also showed that the generalized one-size-fits-all approach of using a sample size of 30 to 50 sites is not appropriate as different facility types require different sample sizes depending on several factors, such as the extent of data variability, population size, crash experience, and so on, to estimate reliable calibration factors.