People’s intuitions about
randomness AND
probability: an empirical
study
Marie-Paule
Lecoutre
ERIS,
Université de Rouen
marie-paule.lecoutre@univ-rouen.fr
Katia Rovira
Laboratoire
Psy.Co, Université de Rouen
katia.rovira@univ-rouen.fr
Bruno Lecoutre
ERIS, C.N.R.S.
et Université de Rouen
bruno.lecoutre@univ-rouen.fr
Jacques
Poitevineau
ERIS, Université de
Paris 6 et Ministère de la Culture
poitevin@ccr.jussieu.fr
ABSTRACT
What people mean by randomness should be taken into
account when teaching statistical inference. This experiment explored
subjective beliefs about randomness and probability through two successive
tasks. Subjects were asked to categorize 16 familiar items: 8 real items from
everyday life experiences, and 8 stochastic items involving a repeatable
process. Three groups of subjects differing according to their background
knowledge of probability theory were compared. An important finding is that the
arguments used to judge if an event is random and those to judge if it is not
random appear to be of different natures. While the concept of probability has
been introduced to formalize randomness, a majority of individuals appeared to
consider probability as a primary concept.
Keywords: Statistics education research;
Probability; Randomness; Bayesian Inference
__________________________
Statistics Education Research
Journal, 5(1), 20-35, http://www.stat.auckland.ac.nz/serj
Ó International Association for Statistical Education (IASE/ISI), May, 2006
References
Albert, J.
(2002). Teaching introductory statistics from a Bayesian perspective. In
B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics.
[Online: www.stat.auckland.ac.nz/~iase/publications/1/ 3f1_albe.pdf]
Albert, J. (2003). College students’ conceptions of probability. The American Statistician 57, 37-45.
Barthélemy,
J.-P., & Guénoche, A. (1991). Trees
and proximity representations.
Bayarri, M. J., & Berger, J. O. (2004). The interplay of Bayesian and frequentist analysis. Statistical Science, 19, 58-80.
Berger, J. (2004). The case for objective Bayesian analysis. Bayesian Analysis, 1, 1-17.
Berry, D. (1997). Teaching elementary Bayesian statistics with real applications in science. The American Statistician, 51, 241-246.
Buneman, P. (1974). A note on the metric properties of trees. Journal of Combinatorial Theory (B), 17, 48-50.
D’Agostini, G.
(2000). Role and meaning of subjective probability: Some comments on
common misconceptions. In A. Mohammad-Djafari (Ed.), AIP conference proceedings,
Vol 568, Bayesian inference and maximum entropy methods in science and
engineering: 20th international workshop, Gif-sur-Yvette, France, July
8-13.
de Finetti,
B. (1974). Theory of probability
(Vol.1).
Falk, R. (1992). A closer look at the probabilities of
the notorious three prisoners. Cognition, 43, 197-223.
Falk, R., & Konold, C. (1997). Making sense of
randomness: Implicit encoding as a basis for judgment. Psychological Review, 104, 301-318.
Freeman, P. R. (1993). The role of p-values in analysing trial results. Statistics in Medicine, 12, 1443-1452.
Hawkins, A. S., & Kapadia, R. (1984). Children’s
conceptions of probability – A psychological and pedagogical review. Educational
Studies in Mathematics, 15, 349-377.
Jaynes, E. T. (2003). Probability
theory: The logic of science (Edited by G.L. Bretthorst).
Kac, M. (1983). Marginalia: What is random? American Scientist, 71, 405-406.
Kadane, J. B. (1996). Bayesian methods and ethics in a clinical trial
design.
Konold, C. (1991), Understanding students’ beliefs
about probability. In E. V. Glasersfeld (Ed.), Radical
constructivism in mathematics education (pp. 139-156).
Konold, C. (1995). Issues in assessing conceptual understanding in probability and statistics. Journal of Statistics Education, 3(1).
[Online: www.amstat.org/publications/jse/v3n1/konold.html]
Konold, C., Lohmeier, J., Pollatsek, A. Well,
A. D., Falk, R., & Lipson, A. (1991). Novices’ views on randomness. In
R. G. Underhill (Ed.), Proceedings of the thirteenth annual meeting of the
North American Chapter of the International Group for the Psychology of Mathematics
Education (pp. 167-173).
Laplace,
P.-S. (1951). A philosophical essay on
probability [English translation, original work published 1814: Essai philosophique sur les probabilités].
New York: Dover Publications.
Lecoutre, B. (2006). Training students and researchers in Bayesian methods for experimental data analysis. Journal of Data Science, 4, 207-232.
Lecoutre, B., & Derzko, G. (2001). Asserting the smallness of effects in ANOVA. Methods of Psychological Research, 6, 1-32.
[Online: www.mpr-online.de]
Lecoutre, B., Lecoutre, M.-P., & Grouin, J.-M.
(2001). A challenge for statistical instructors: Teaching Bayesian inference
without discarding the “official” significance tests. Bayesian Methods with
applications to science, policy and official statistics, 301-310.
Lecoutre, B., Lecoutre, M.-P., & Poitevineau J. (2001). Uses, abuses and misuses of significance tests in the scientific community: Won’t the Bayesian choice be unavoidable? International Statistical Review, 69, 399-417.
Lecoutre, M.-P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23, 557-568.
Loredo,
T. J. (1990). From
Moore, D. S.
(1997). Bayes for beginners? Some pedagogical questions. In S. Panchapakesan &
N. Balakrishnan (Eds.), Advances in statistical decision theory
(pp. 3-17).
Nickerson,
R. S. (2002). The production and perception of randomness. Psychological
Review, 109,
330-357.
Piaget, J.,
& Inhelder, B. (1951). La
genèse de l’idée de hasard chez l’enfant. [The origin of the idea of
chance in children]. Paris: Presses
Universitaires de France.
Pruzansky,
S., Tversky, A., & Carroll, J. D. (1982). Spatial versus tree representations of proximities
data. Psychometrika, 47, 3-24.
Robinson, D., & Foulds, L (1981). Comparison of phylogenetic trees. Mathematical Biosciences, 53, 131-147.
Sattath, S., & Tversky, A. (1977). Additive similarity trees. Psychometrika, 42, 319-345.
Savage, L. (1954). The foundations of statistical
inference.
Shaughnessy,
J. M. (1992). Research in probability and statistics: reflections and
directions. In D. A. Grouws (Ed.), Handbook of research on
mathematics and learning (pp. 465-494).
Steinberg,
H., & Von Harten, G. (1982). Learning from experience – Bayes’ theorem: A model for stochastic learning.
Proceedings of the First International Conference of Teaching Statistics, Volume 2, (pp. 701-714).
Thom, R.
(1986). Preface of P.S. Laplace, Essai
philosophique sur les probabilités
[Text of the 5th edition, 1825]. Bourgois: Paris.
Tryon, W. W. (2001). Evaluating statistical difference, equivalence, and indeterminacy using inferential confidence intervals: An integrate alternative method of conducting null hypothesis statistical tests. Psychological Methods, 6, 371-386.
Vranas, P. (2001). Single-case probabilities and content-neutral norms: A reply to Gigerenzer. Cognition, 81, 105-111.
Wagenaar, W. A. (1972). Generation of random sequences by human subjects: A critical survey of the literature. Psychological Bulletin, 77, 65-72.
Marie-Paule
Lecoutre
ERIS,
Laboratoire Psy.Co, E.A. 1780
Université
de Rouen, UFR Psychologie, Sociologie, Sciences de l’Education
76821
Mont-Saint-Aignan Cedex, France
http://www.univ-rouen.fr/LMRS/Persopage/Lecoutre/Eris