Abstract
Every measurement in science, every experimental decision, result and information drawn from it has to cope with something that has long been named by the term “error”. In fact, errors describe our limitations when it comes to experimental science and science looks back on a long tradition to cope with them. The widely known way to cope with them in nowadays classrooms and introductory laboratories is the so-called traditional “approach to error treatment” dated back by many to the ideas of Gauss. However, this is not exactly true, and as one digs deeper into the history of errors (or: uncertainty) one finds not only surprising stories about the treatment of data and uncertainty but also a lot to learn from for our today’s teaching. The treatment of error did not just appear out of the blue but evolved along side with the history of experimental science, a growing insight into data and sensitivity for its trustworthiness. Virtues that today’s learners are hoped to develop just the same.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
While the Bayesian includes all available information about the considered matter, the frequentist approach analyses frequencies in data sets. The chance of a coin to show head can be said to be 50/50. From a Bayesian point of view this information could originate in the inspection of the coin to appear fair and even so that no side could be favored over the other. From a frequentist point of view however, this statement would originate in the execution of a series of 100 tosses that produce about as many heads as tails. Until today, these totally different views on probability have not been reconciled mathematically.
References
Allie, S., Buffler, A., Campbell, B., & Lubben, F. (1998). First year physics students’ perceptions of the quality of experimental measurements. International Journal of Science Education, 20(4), 447–459.
Bernoulli, D. (1778/1961). The most probable choice between several discrepant observations and the formation therefrom of the most likely induction. Biometrika, 48, 3–13.
Bessel, F. W. (1838). Untersuchungen über die Wahrscheinlichkeit der Beobachtungsfehler. Astronomische Nachrichten, 15, 379–404.
BIPM. (1995/2008). Guide to the expression of uncertainty in measurement (GUM). Geneva: International Organization for Standardization.
Buffler, A., Allie, S., & Lubben, F. (2008). Teaching measurement and uncertainty the GUM way. The Physics Teacher, 46, 539–544.
Coulomb, C. (1785). Premier Mémoire sur l’Electricité et le Magnétisme. Mémoires de l’Académie Royale des Sciences, (1788), 569–577.
De Moivre, A. (1756). The doctrine of chances. Or: A method of calculating the pobabilities of events in play. London: A. Millar.
Fischer, P. (1845). Lehrbuch der höheren Geodäsie, Band 1. Darmstadt: Leske.
Galilei, G. (1632). Dialogo sopra i due massimi sistemi del mondo. Florenz.
Gauss, C. F. (1809). Theoria motus corporum coelestium in sectionibus conicis solem ambientium. Hamburg: Perthes & Besser.
Gauss, C. F. (1821). Theoria combinationis observationum erroribus minimis obnoxiae, pars prior. Göttingen: Dieterich.
Hagen, G. (1837). Grundzüge der Wahrscheinlichkeitsrechnung. Berlin: Dümmler.
Heering, P. (1992). On Coulomb’s inverse square law. American Journal of Physics, 60, 988–994.
Heinicke, S., Riess, F. (2012). Missing links in the experimental work. In L. Maurines & A. Redfors (Eds.), ESERA 2011 Proceedings.
Kepler, J. (1609). Astronomia Nova. Heidelberg: Voegelin.
Koestler, A. (1961). The watershed, a biography of Johannes Kepler. London: Heinemann.
Lambert, J. H. (1760). Photometria, sive de Mensura et Gradibus Luminis, Colorum et Umbrae. Augsburg: Christoph Peter Detleffsen for the widow of Eberhard Klett.
Laplace, P. S. (1776). Recherches sur l′intégration des équations différentielles aux différences finies. Laplace Werke, t. 8. Paris, p. 69–197.
Lippmann, R. (2003). Students’ understanding of measurement and uncertainty in the physics laboratory. Ph.D. thesis: University of Maryland.
Robison, J. (1822). A system of mechanical philosophy. Edinburgh: John Murray.
Séré, M.-G., Journeaux, R., & Larcher, C. (1993). Learning the statistical analysis of measurement error. International Journal of Science Education, 15, 427–438.
Simpson, T. (1756). A letter to the honourable George Earl of Macclesfield. Philosophical Transactions of the Royal Society of London, 49(1), 82–93.
Stigler, S. (1986/2003). The history of statistics. The Measurement of Uncertainty before 1900. Cambridge and London: Harvard University Press.
Tomlinson, J., Dyson, P., & Garratt, J. (2001). Student misconceptions of the language of error. University Chemistry Education, 5(1), 1–8.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Heinicke, S. How to Cope with Gauss’s Errors? Motivation for Teaching Data and Uncertainty Analysis from a History of Science Perspective. Interchange 45, 217–233 (2014). https://doi.org/10.1007/s10780-015-9227-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10780-015-9227-9