Investigating Regression to the Mean in Before-and-After Speed Data Analysis

Abstract

Regression to the mean (RTM) in before-and-after speed data is a purely statistical phenomenon that makes random variation in repeated speed measurements from multiple time points before and after the introduction of an engineering treatment look like a genuine speed change brought about by the engineering treatment. This study shows that an observational before-and-after speed data analysis cannot collect speed measurements without measurement error and cannot be free from RTM bias. To obtain accurate estimates of the magnitude of the mean speed change brought about by an engineering treatment, RTM bias needs to be reduced. This study first uses a graphical method to illustrate the RTM phenomenon and then uses numerical examples (with aggregated speed data) to show how to reduce RTM bias in before-and-after speed data analysis. The numerical examples show that the estimated magnitude of the mean speed change that results from the introduction of an engineering treatment or the amount of uncertainty (measured by the estimated standard error and confidence interval) associated with the mean speed change can be misleading if RTM is not taken into account. The paper concludes with suggestions for more rigorous statistical methods, preferably suited for use with disaggregate speed data, that may help to reduce RTM bias in future speed data analysis.