We present Sunlight, a system that detects the causes of targeting phenomena on the web -- such as personalized advertisements, recommendations, or content -- at large scale and with solid statistical confidence. Today's web is growing increasingly complex and impenetrable as myriad of services collect, analyze, use, and exchange users' personal information. No one can tell who has what data, for what purposes they are using it, and how those uses affect the users. The few studies that exist reveal problematic effects -- such as discriminatory pricing and advertising -- but they are either too small-scale to generalize or lack formal assessments of confidence in the results, making them difficult to trust or interpret. Sunlight brings a principled and scalable methodology to personal data measurements by adapting well-established methods from statistics for the specific problem of targeting detection. Our methodology formally separates different operations into four key phases: scalable hypothesis generation, interpretable hypothesis formation, statistical significance testing, and multiple testing correction. Each phase bears instantiations from multiple mechanisms from statistics, each making different assumptions and tradeoffs. Sunlight offers a modular design that allows exploration of this vast design space. We explore a portion of this space, thoroughly evaluating the tradeoffs both analytically and experimentally. Our exploration reveals subtle tensions between scalability and confidence. Sunlight's default functioning strikes a balance to provide the first system that can diagnose targeting at fine granularity, at scale, and with solid statistical justification of its results.