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 that are better-qualified on observables would, on average, appear academically stronger to admission-tutors based on unobservables. This assumption reveals the sign of differences in admission-standards across demographic groups which are robust to omitted characteristics. Applying our methods to admissions-data from a British university, we find higher admission standards for males and slightly higher ones for private-school applicants, despite equal admission success-probability across gender and school-background.