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

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