Hazard perception is a multi-faceted process that requires drivers to maintain an ongoing awareness of a complex driving environment. The majority of research studies, however, utilize behavioral responses to a limited number of discrete hazardous events (e.g., response to a braking lead vehicle, vehicle lane deviations, or pedestrians) to assess a driver's hazard perception ability. The current study uses a modification of SDT to expand these events, called fuzzy signal detection (fSDT) to account for the fuzzy nature of real-world driving hazards. Unlike traditional SDT, which requires a classification of any given scenario, as either containing a hazard or no hazard, fSDT allows for each scenario to be classified by it's potential to develop into a situation where a driver response is necessary to avoid a collision or near collision. The purpose of this study was to explore how performing a texting task impacts a driver's hazard perception ability while viewing real-world driving scenes using SDT metrics. The results showed that texting while driving increased perceived mental workload, reduced a driver's ability to discriminate hazards, and reduced a driver's likelihood to respond to a hazard, compared to driving only. What was found highlights the variability of the hazard perception process, suggesting that both sensitivity and response bias shifts occur when distracted. Additionally, the results indicate that these shifts are at least in part, moderated by the cognitive load the secondary task commands and by the current driving environment. These results also highlight the complexity in which distraction can impact both the allocation of cognitive resources as well as attentional selection.