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Introduction Understanding driver behavior is important for traffic safety and operation, especially at intersections where different traffic movements conflict. While most driver-behavior studies are based on simulation, this paper documents the analysis of driver-behavior at signalized intersections with the SHRP 2 Naturalistic Driving Study (NDS) data. This study analyzes the different influencing factors on the operation (speed control) and observation of right-turn drivers. Method A total of 300 NDS trips at six signalized intersections were used, including the NDS time-series sensor data, the forward videos and driver face videos. Different factors of drivers, vehicles, roads and environments were studied for their influence on driver behavior. An influencing index function was developed and the index was calculated for each influencing factor to quantitatively describe its influencing level. The influencing index was applied to prioritize the factors, which facilitates development and selection of safety countermeasures to improve intersection safety. Drivers' speed control was analyzed under different conditions with consideration of the prioritized influencing factors. Results Vehicle type, traffic signal status, conflicting traffic, conflicting pedestrian and driver age group were identified as the five major influencing factors on driver observation. Conclusions This research revealed that drivers have high acceleration and low observation frequency under Right-Turn-On-Red (RTOR), which constituted potential danger for other roadway users, especially for pedestrians. Practical applications As speed has a direct influence on crash rates and severities, the revealed speed patterns of the different situations also benefit selection of safety countermeasures at signalized intersections. [ABSTRACT FROM AUTHOR]