Many online services, such as search engines, social media platforms, and digital marketplaces, are advertised as being available to any user, regardless of their age, gender, or other demographic factors. However, there are growing concerns that these services may systematically underserve some groups of users. In this paper, we present a framework for internally auditing such services for differences in user satisfaction across demographic groups, using search engines as a case study. We first explain the pitfalls of naïvely comparing the behavioral metrics that are commonly used to evaluate search engines. We then propose three methods for measuring latent differences in user satisfaction from observed differences in evaluation metrics. To develop these methods, we drew on ideas from the causal inference literature and the multilevel modeling literature. Our framework is broadly applicable to other online services, and provides general insight into interpreting their evaluation metrics.