Recent research in introductory physics labs suggests that most students judge the quality of a measurement based on a comparison with theory. To probe this dimension of students' judgments based on authority, we sought to evaluate whether students' responses about evaluations of measurement depended on contextual cues. We asked students which measurement of the acceleration due to gravity was 'better:' (1) one given with uncertainty and found by 'you and your friend' or 'you and your research group' or (2) a textbook value with no reported uncertainty but more significant figures. By deliberately structuring multiple possible forms of authority (e.g., precision, expertise, equipment, theory) we intended to draw out nuances in how students draw upon authority in evaluating the quality of measurements. Our results suggest that contextual cues may influence students' judgments about measurement and the authority that they draw upon more than lab instruction aimed at developing students' experimentation skills.