Evidence from social psychology suggests that agents process information about their own ability in a biased manner. This evidence has motivated exciting research in behavioral economics, but also garnered critics who point out that it is potentially consistent with standard Bayesian updating. We implement a direct experimental test. We study a large sample of 656 undergraduate students, tracking the evolution of their beliefs about their own relative performance on an IQ test as they receive noisy feedback from a known data-generating process. Our design lets us repeatedly measure the complete relevant belief distribution incentive-compatibly. We find that subjects (1) place approximately full weight on their priors, but (2) are asymmetric, over-weighting positive feedback relative to negative, and (3) conservative, updating too little in response to both positive and negative signals. These biases are substantially less pronounced in a placebo experiment where ego is not at stake. We also find that (4) a substantial portion of subjects are averse to receiving information about their ability, and that (5) less confident subjects are more likely to be averse. We unify these phenomena by showing that they all arise naturally in a simple model of optimally biased Bayesian information processing.