A Constructivist View of the Statistical Quantification of Evidence

Christian Hennig

Download the full text in

PDF (508 kB)

> Citation
> Similar
> References
**> Add Comment**

## Abstract

Problem: 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

## Citation

Hennig 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 articles

## References

Albert J. (2009) Bayesian computation with R. Second edition. Springer, New York.

▸︎ Google︎ Scholar
Bayes T. (1763) An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London 53: 370–418.

▸︎ Google︎ Scholar
Berger J. O. (2003) Could Fisher, Jeffreys and Neyman have agreed on testing (with discussion)? Statistical Science 18 (1): 1–32.

▸︎ Google︎ Scholar
Bernardo J. M. & Smith A. F. M. (1994) Bayesian theory. Wiley, Chichester.

▸︎ Google︎ Scholar
Bernoulli J. (1713) Ars conjectandi, opus posthumum. Accedit Tractatus de seriebus infinitis, et epistola gallicé scripta de ludo pilae reticularis. Thurneysen, Basel.

▸︎ Google︎ Scholar
Box G. E. P. (1980) Sampling and Bayes inference in scientific modelling and robustness. Journal of the Royal Statistical Society Series A 143: 383–430.

▸︎ Google︎ Scholar
Davies P. L. (2008) Approximating data (with discussion). Journal of the Korean Statistical Society 37(3): 191–211.

▸︎ Google︎ Scholar
Dawid A. P. (1982) The well-calibrated Bayesian. Journal of the American Statistical Society 77: 605–610.

▸︎ Google︎ Scholar
Derksen T. (2007) 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

▸︎ Google︎ Scholar
Finetti B. de (1970) Teoria delle probabilità. Einaudi, Torino. English translation: Finetti B. de (1974) Theory of probability. Translated by A. F.M. Smith. Wiley, New York.

▸︎ Google︎ Scholar
Fisher R. A. (1935) The logic of inductive inference. Journal of the Royal Statistical Society, Series A 98: 39–54.

▸︎ Google︎ Scholar
Gillies D. (2000) Philosophical theories of probability. Routledge, London.

▸︎ Google︎ Scholar
Greenland S. & Mickey R. M. (1988) 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.

▸︎ Google︎ Scholar
Habermas J (1984) The theory of communicative action. Volume 1: Reason and the rationalization of society. Polity Press, Cambridge.

▸︎ Google︎ Scholar
Hand D. J. (1996) Statistics and the theory of measurement. Journal of the Royal Statistical Society Series A 159(3): 445–492.

▸︎ Google︎ Scholar
Hennig C. (2007) Falsification of propensity models by statistical tests and the goodness-of-fit paradox. Philosophia Mathematica 15: 166–192

▸︎ Google︎ Scholar
Hennig C. (2009) Mathematical models and reality – A constructivist perspective. Foundations of Science. Published online http://www.springerlink.com/content/c4504877l7317131 (paper version to follow).

▸︎ Google︎ Scholar
Hilbert D. (2004) David Hilbert’s lectures on the foundations of geometry, 1891–1902. Edited by M. Hallett & U. Majer Springer, Berlin.

▸︎ Google︎ Scholar
Howson C. & Urbach P. (2006) Scientific reasoning: the Bayesian approach. Open Court, Chicago.

▸︎ Google︎ Scholar
Kass R. E. & Wasserman L. (1996) The selection of prior distributions by formal rules. Journal of the American Statistical Association 91: 1343–1370.

▸︎ Google︎ Scholar
Kolmogorov A. N. (1933) Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer, Berlin.

▸︎ Google︎ Scholar
Lee P. M. (2009) Bayesian statistics. Third edition. Wiley, Chichester.

▸︎ Google︎ Scholar
Mayo D. G. & Kruse M. (2001) Principles of inference and their consequences. In: Cornfield D. & Williamson J. (eds.) Foundations of Bayesianism. Kluwer Academic Publishers, Dordrecht: 381–403.

▸︎ Google︎ Scholar
Mayo D. G. (1996) Error and the growth of experimental knowledge. University of Chicago Press, Chicago.

▸︎ Google︎ Scholar
Mises R. von (1928) Wahrscheinlichkeit, Statistik und Wahrheit, Springer, Berlin. English translation: Mises R. von (1981) Probability, statistics and truth. Dover, New York.

▸︎ Google︎ Scholar
Neyman J. & Pearson E. (1933) On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society London, Series A 231: 289–337.

▸︎ Google︎ Scholar
Paul O. (1968) Stimulants and coronaries. Postgraduate Medical Journal 44: 196–199.

▸︎ Google︎ Scholar
Searle J. R. (1997) 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.

▸︎ Google︎ Scholar
Sokal R. R. & Rohlf F. J. (1981) Biometry. Second edition. W. H. Freeman, San Francisco.

▸︎ Google︎ Scholar
Walley P. (1991) Statistical reasoning with imprecise probabilities. Chapman and Hall, London.

▸︎ Google︎ Scholar
## Comments: 0

To stay informed about comments to this publication and post comments yourself, please **log in** first.