## AbstractProblem: Evidence is quantified by statistical methods such as p-values and Bayesian posterior probabilities in a routine way despite the fact that there is no consensus about the meanings and implications of these approaches. A high level of confusion about these methods can be observed among students, researchers and even professional statisticians. How can a constructivist view of mathematical models and reality help to resolve the confusion? Method: Considerations about the foundations of statistics and probability are revisited with a constructivist attitude that explores which ways of thinking about the modelled phenomena are implied by different approaches to probability modelling. Results: The understanding of the implications of probability modelling for the quantification of evidence can be strongly improved by accepting that whether models are “true” or not cannot be checked from the data, and the use of the models should rather be justified and critically discussed in terms of their implications for the thinking and communication of researchers. Implications: Some useful questions that researchers can use as guidelines when deciding which approach and which model to choose are listed in the paper, along with some implications of using frequentist p-values or Bayesian posterior probability, which can help to address the questions. It is the – far too often ignored – responsibility of the researchers to decide which model is chosen and what the evidence suggests rather than letting the results decide themselves in an “objective way.” Key words: mathematical modelling, foundations of probability, p-values, frequentism, Bayesian subjectivism, objective Bayes, reality ## CitationHennig C. (2009) A constructivist view of the statistical quantification of evidence. Constructivist Foundations 5(1): 39-54. http://constructivist.info/5/1/039 Export article citation data: Plain Text · BibTex · EndNote · Reference Manager (RIS) ## Similar articlesMaturana H. R. (2012) Reflections on My Collaboration with Francisco Varela Vaz N. M. (2011) The Specificity of Immunologic Observations Riegler A. & Weber S. (2008) Non-dualizing from Now On? ## ReferencesBayesian computation with R. Second edition. Springer, New York.http://www.univie.ac.at/constructivism/journal/3/2/096.baecker Obey society and note your resistance. Constructivist Foundations 3(2): 96–97 Available at An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London 53: 370–418. Could Fisher, Jeffreys and Neyman have agreed on testing (with discussion)? Statistical Science 18 (1): 1–32. Bayesian theory. Wiley, Chichester. Ars conjectandi, opus posthumum. Accedit Tractatus de seriebus infinitis, et epistola gallicé scripta de ludo pilae reticularis. Thurneysen, Basel. Sampling and Bayes inference in scientific modelling and robustness. Journal of the Royal Statistical Society Series A 143: 383–430. Approximating data (with discussion). Journal of the Korean Statistical Society 37(3): 191–211. The well-calibrated Bayesian. Journal of the American Statistical Society 77: 605–610. Lucia de B. Reconstructie van een gerechtelijke dwaling. Uitgeverij Veen Magazines BV. For English information see http://www.luciadeb.nl/english/derksen-book-1.html Likelihood. Cambridge University Press. Theories of probability. Academic Press, New York. Teoria delle probabilità. Einaudi, Torino. English translation: Finetti B. de (1974) Theory of probability. Translated by A. F.M. Smith. Wiley, New York. The logic of inductive inference. Journal of the Royal Statistical Society, Series A 98: 39–54. On constructing a reality. In: Watzlawick P. (ed.) The invented reality. W. W. Norton, New York: 41–62. An invitation to social construction. Sage, Thousand Oaks CA. Philosophical theories of probability. Routledge, London. Radical constructivism. A way of knowing and learning. Falmer Press, London.http://www.univie.ac.at/constructivism/journal/1/2/061.glasersfeld A constructivist approach to experiential foundations of mathematical concepts revisited. Constructivist Foundations 1(2): 61–72. Available athttp://www.univie.ac.at/constructivism/journal/3/2/059.glasersfeld Who conceives of society? (With open peer commentaries.) Constructivist Foundations 3(2): 59–108. Available at Closed form and dually consistent methods for inference on strict collapsibility in 2 ╳ 2 ╳ K and 2 ╳ J ╳ K tables. Journal of the Royal Statistical Society. Series C (Applied Statistics) 37 (3): 335–343. The theory of communicative action. Volume 1: Reason and the rationalization of society. Polity Press, Cambridge. Statistics and the theory of measurement. Journal of the Royal Statistical Society Series A 159(3): 445–492. Falsification of propensity models by statistical tests and the goodness-of-fit paradox. Philosophia Mathematica 15: 166–192 Mathematical models and reality – A constructivist perspective. Foundations of Science. Published online http://www.springerlink.com/content/c4504877l7317131 (paper version to follow). David Hilbert’s lectures on the foundations of geometry, 1891–1902. Edited by M. Hallett & U. Majer Springer, Berlin. Scientific reasoning: the Bayesian approach. Open Court, Chicago. The selection of prior distributions by formal rules. Journal of the American Statistical Association 91: 1343–1370. Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer, Berlin.http://www.univie.ac.at/constructivism/journal/3/2/091.krippendorff Towards a Radically Social Constructivism. Constructivist Foundations 3(2): 91–94. Available at Bayesian statistics. Third edition. Wiley, Chichester. Social systems. Stanford University Press, Stanford. Model theory. Oxford University Press, Oxford. Principles of inference and their consequences. In: Cornfield D. & Williamson J. (eds.) Foundations of Bayesianism. Kluwer Academic Publishers, Dordrecht: 381–403. Error and the growth of experimental knowledge. University of Chicago Press, Chicago. Wahrscheinlichkeit, Statistik und Wahrheit, Springer, Berlin. English translation: Mises R. von (1981) Probability, statistics and truth. Dover, New York. On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society London, Series A 231: 289–337. Stimulants and coronaries. Postgraduate Medical Journal 44: 196–199.http://www.univie.ac.at/constructivism/journal/3/2/083.raskin The personal and social as mutually specifying. Constructivist Foundations 3(2): 83–84. Available at Rationality and realism – What is at stake? In: De George R. T. (ed.) Academic freedom and tenure: Ethical issues in academic ethics. Rowman & Littlefield, Lanham, Maryland: 197–220. Biometry. Second edition. W. H. Freeman, San Francisco. Statistical reasoning with imprecise probabilities. Chapman and Hall, London.## Comments: 0To stay informed about comments to this publication and post comments yourself, please | ||