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The quality assessment of impaired stereoscopic video is a key element in designing and deploying advanced immersive media distribution platforms. A widely accepted quality metric to measure impairments of stereoscopic video is, however, still to be developed. As a step toward finding a solution to this problem, this paper proposes a full reference stereoscopic video quality metric to measure the perceptual quality of compressed stereoscopic video. A comprehensive set of subjective experiments is performed with 14 different stereoscopic video sequences, which are encoded using both the H.264 and high efficiency video coding compliant video codecs, to develop a subjective test results database of 116 test stimuli. The subjective results are analyzed using statistical techniques to uncover different patterns of subjective scoring for symmetrically and asymmetrically encoded stereoscopic video. The subjective result database is subsequently used for training and validating a simple but effective stereoscopic video quality metric considering heuristics of binocular vision. The proposed metric performs significantly better than state-of-the-art stereoscopic image and video quality metrics in predicting the subjective scores. The proposed metric and the subjective result database will be made publicly available, and it is expected that the proposed metric and the subjective assessments will have important uses in advanced 3D media delivery systems.