Research-based assessment instruments (RBAIs) are ubiquitous throughout both
physics instruction and physics education research. The vast majority of
analyses involving student responses to RBAI questions have focused on whether
or not a student selects correct answers and using correctness to measure
growth. This approach often undervalues the rich information that may be
obtained by examining students' particular choices of incorrect answers. In the
present study, we aim to reveal some of this valuable information by
quantitatively determining the relative correctness of various incorrect
responses. To accomplish this, we propose an assumption that allow us to define
relative correctness: students who have a high understanding of Newtonian
physics are likely to answer more questions correctly and also more likely to
choose better incorrect responses, than students who have a low understanding.
Analyses using item response theory align with this assumption, and Bock's
nominal response model allows us to uniquely rank each incorrect response. We
present results from over 7,000 students' responses to the Force and Motion
Conceptual Evaluation