Video dimensions are continuously increasing to provide more realistic and immersive experiences to global streaming and social media viewers. However, increments in video parameters such as spatial resolution and frame rate are inevitably associated with larger data volumes. Transmitting increasingly voluminous videos through limited bandwidth networks in a perceptually optimal way is a current challenge affecting billions of viewers. One recent practice adopted by video service providers is space-time resolution adaptation in conjunction with video compression. Consequently, it is important to understand how different levels of space-time subsampling and compression affect the perceptual quality of videos. Towards making progress in this direction, we constructed a large new resource, called the ETRI-LIVE Space-Time Subsampled Video Quality (ETRI-LIVE STSVQ) database, containing 437 videos generated by applying various levels of combined space-time subsampling and video compression on 15 diverse video contents. We also conducted a large-scale human study on the new dataset, collecting about 15,000 subjective judgments of video quality. We provide a rate-distortion analysis of the collected subjective scores, enabling us to investigate the perceptual impact of space-time subsampling at different bit rates. We also evaluated and compare the performance of leading video quality models on the new database. The new ETRI-LIVE STSVQ database is being made freely available at (https://live.ece.utexas.edu/research/ETRI-LIVE_STSVQ/index.html).