Background: Within undergraduate science courses, instructors often assess student thinking using closed-ended question formats, such as multiple-choice (MC) and multiple-true-false (MTF), where students provide answers with respect to predetermined response options. While MC and MTF questions both consist of a question stem followed by a series of options, MC questions require students to select just one answer, whereas MTF questions enable students to evaluate each option as either true or false. We employed an experimental design in which identical questions were posed to students in either format and used Bayesian item response modeling to understand how responses in each format compared to inferred student thinking regarding the different options. Results: Our data support a quantitative model in which students approach each question with varying degrees of comprehension, which we label as mastery, partial mastery, and informed reasoning, rather than uniform random guessing. MTF responses more closely estimate the proportion of students inferred to have complete mastery of all the answer options as well as more accurately identify students holding misconceptions. The depth of instructional information elicited by MTF questions is demonstrated by the ability of MTF results to predict the MC results, but not vice-versa. We further discuss how MTF responses can be processed and interpreted by instructors. Conclusions: This research supports the hypothesis that students approach MC and MTF questions with varying levels of understanding and demonstrates that the MTF format has a greater capacity to characterize student thinking regarding the various response options.