Uncertainty is an important concept in physics laboratory instruction.
However, little work has examined how students reason about uncertainty beyond
the introductory (intro) level. In this work we aimed to compare intro and
beyond-intro students' ideas about uncertainty. We administered a survey to
students at 10 different universities with questions probing procedural
reasoning about measurement, student-identified sources of uncertainty, and
predictive reasoning about data distributions. We found that intro and
beyond-intro students answered similarly on questions where intro students
already exhibited expert-level reasoning, such as in comparing two data sets
with the same mean but different spreads, identifying limitations in an
experimental setup, and predicting how a data distribution would change if more
data were collected. For other questions, beyond-intro students generally
exhibited more expert-like reasoning than intro students, such as when
determining whether two sets of data agree, identifying principles of
measurement that contribute to spread, and predicting how a data distribution
would change if better data were collected. Neither differences in student
populations, lab courses taken, nor research experience were able to fully
explain the variability between intro and beyond-intro student responses. These
results call for further research to better understand how students' ideas
about uncertainty develop beyond the intro level.Comment: 19 pages, 12 figure