Statistics
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aas...20920920m&link_type=abstract
2007 AAS/AAPT Joint Meeting, American Astronomical Society Meeting 209, #209.20; Bulletin of the American Astronomical Society,
Statistics
Scientific paper
Equilibrium properties of macroscopic (large N) systems are highly predictable as N approaches and exceeds Avogadro’s number. Theories of statistical physics depend on these results. Typical pedagogical devices used in statistical physics textbooks to introduce entropy (S) and multiplicity [S = k ln(w), where w is the system multiplicity] include flipping coins and/or other equivalent binary events, repeated n times. Prior to instruction, our students usually give reasonable answers about the probabilities, but not the uncertainties of the predicted outcomes of such events. However, they reliably predict that the uncertainty in a measured quantity (e.g., the amount of rainfall) decreases as the number of measurements increases. Typical textbook presentations presume that students will either have or develop the insight that the relative uncertainty of binary outcomes will similarly decrease as the number of events increases. That is at odds with our findings among students in two successive statistical mechanics classes. Many of our students had previously completed mathematics courses in statistics, as well as a physics laboratory course that included analysis of statistical properties of distributions of dart scores as the number (n) of throws (one-dimensional target) increased. There was a wide divergence of predictions about how the standard deviation of the distribution of dart scores should change, or not, as n increases. We find that student predictions about statistics of coin flips, dart scores, and rainfall amounts as functions of n are inconsistent at best.
Supported in part by NSF Grant #PHY-0406764.
Bucy B. R.
Mountcastle Donald B.
Thompson Richard Jule Jr.
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