Most of what we understand about data sensitivity is through user self-report (e.g., surveys); this paper is the first to use behavioral data to determine content sensitivity, via the clues that users give as to what information they consider private or sensitive through their use of privacy enhancing product features. We perform a large-scale analysis of user anonymity choices during their activity on Quora, a popular question-and-answer site. We identify categories of questions for which users are more likely to exercise anonymity and explore several machine learning approaches towards predicting whether a particular answer will be written anonymously. Our findings validate the viability of the proposed approach towards an automatic assessment of data sensitivity, show that data sensitivity is a nuanced measure that should be viewed on a continuum rather than as a binary concept, and advance the idea that machine learning over behavioral data can be effectively used in order to develop product features that can help keep users safe.