Statistical Test for 85th and 15th Percentile Speeds with Asymptotic Distribution of Sample Quantiles

The 85th and 15th percentiles are two parameters that are commonly used in traffic engineering and traffic safety. For example, 85th percentile speeds are used to set speed limits and to evaluate the effectiveness of safety countermeasures, and 15th percentile speeds are used to establish typical walking speeds for traffic signal timing. But the lack of a simple statistical test for percentiles has led some researchers to omit statistical analysis or apply nonideal approaches, such as averaging the 85th percentiles or using the binomial proportion test. This paper presents a statistical test for the 85th and 15th percentiles that is based on Crammer's theory of the asymptotic distribution of sample quantiles. This test is simpler to apply than the double bootstrapping or quantile regression methods. To illustrate its practical use, this quantile test is applied to three sample case studies: sequential warning lights at nighttime work zones, residential speed limits, and pedestrian signal timing.