In recent years, the number of smartphones with onboard Global Navigation Satellite System (GNSS) chipsets has been increasing. Although the navigation engines inside these phones use information from the GNSS chipsets as well as other sources of location such as network positioning, they are still vulnerable to GNSS spoofing. GNSS spoofing refers to the temperance of GNSS receivers using artificial GNSS signals to provide misleading positions, velocities, or time information. Failure to detect the presence of GNSS spoofing may result in the breach of integrity for systems using the navigation information from the GNSS receivers. There are several potential methods to detect GNSS spoofing for smartphones, including finding anomalies in the raw GNSS measurements and comparing the GNSS-based navigation solutions to inertial sensors. In this study, we explore the potential of utilizing the barometers inside smartphones to detect instances of GNSS spoofing. The advantages of using a barometer compared to other onboard GNSS-independent sensors include its potential to provide altitudes relative to the mean sea level, and its ability to provide high accuracy altitude rate data. In order to assess the capability of the barometers in GNSS spoofing detection, we assess the noise performances of both the barometers and the GNSS chipsets onboard smartphones under dynamic scenarios, and derive the thresholds for the discrepancy between the two sensors to establish acceptable levels of false detection. The novelty of this study lies in the improvement of the probability of false detection through local pressure corrections, carrier phase cycle slip mitigation, and filtering of both barometer and GNSS measurements using moving averaging and Kalman Filtering. Also, in the absence of local pressure corrections, the expected discrepancy bounds between the barometer, GNSS receiver, and truth due to spatial and temporal pressure variations are established as well. After the characterization of the thresholds, their performances are tested under real driving scenarios to simulate actual situations.