Prior research has shown that physics students often think about experimental procedures and data analysis very differently from experts. One key framework for analyzing student thinking has found that student thinking is more point-like, putting emphasis on the results of a single experimental trial, whereas set-like thinking relies on the results of many trials. Recent work, however, has found that students rarely fall into one of these two extremes, which may be a limitation of how student thinking is evaluated. Measurements of student thinking have focused on probing students' procedural knowledge by asking them, for example, what steps they might take next in an experiment. Two common refrains are to collect more data, or to improve the experiment and collect better data. In both of these cases, the underlying reasons behind student responses could be based in point-like or set-like thinking. In this study we use individual student interviews to investigate how advanced physics students believe the collection of more and better data will affect the results of a classical and a quantum mechanical experiment. The results inform future frameworks and assessments for characterizing students thinking between the extremes of point and set reasoning in both classical and quantum regimes.