Feedback has a powerful influence on learning, but it is also expensive to provide. In large classes it may even be impossible for instructors to provide individualized feedback. Peer assessment is one way to provide personalized feedback that scales to large classes. Besides these obvious logistical benefits, it has been conjectured that students also learn from the practice of peer assessment. However, this has never been conclusively demonstrated. Using an online educational platform that we developed, we conducted an in-class matched-set, randomized crossover experiment with high power to detect small effects. We establish that peer assessment causes a small but significant gain in student achievement. Our study also demonstrates the potential of web-based platforms to facilitate the design of high-quality experiments to identify small effects that were previously not detectable.