Admission practices at high-profile universities are often criticized for undermining academic merit. Popular tests for detecting such biases suffer from omitted characteristic bias. We develop a bounds-based test to circumvent this problem. We assume that students who are better qualified on observableswould, on average, appear academically stronger to admission officers based on unobservables. This assumption reveals the sign of differences in admission standards across demographic groups that are robust to omitted characteristics. Applying our methods to admissions data from a British university, we find higher admission standards for men and slightly higher ones for private school applicants, despite equal admission success probability across gender and school background.