Die Falsifikation Statistischer Hypothesen

  • Max Albert

The falsification of statistical hypotheses


It is widely held that falsification of statistical hypotheses is impossible. This view is supported by an analysis of the most important theories of statistical testing: these theories are not compatible with falsificationism. On the other hand, falsificationism yields a basically viable solution to the problems of explanation, prediction and theory testing in a deterministic context. The present paper shows how to introduce the falsificationist solution into the realm of statistics. This is done mainly by applying the concept of empirical content to statistical hypotheses. It is shown that empirical content is a substitute for ‘power’ as defined by Neyman and Pearson. Since the empirical content of a hypothesis is independent of alternative hypotheses, the proposed theory of statistical testing allows for tests of isolated hypotheses.

Key words

Wissenschaftstheorie Statistik Falsifikationismus Testtheorie Hypothesentests Signifikanztests Neyman-Pearson-Theorie 


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  1. Albert, Hans: 1987,Kritik der reinen Erkenntnislehre, Tübingen: Mohr (Siebeck).Google Scholar
  2. Albert, Hans: 1989, ‚Die Möglichkeit der Erkenntnis‘, in Salamun, Kurt (ed.),Karl R. Popper und die Philosophie des Kritischen Rationalismus, Amsterdam: Rodopi 1989, 3–18.Google Scholar
  3. Andersson, Gunnar: 1984, ‘How to Accept Fallible Test Statements: Popper's Criticist Solution’, in Andersson, Gunnar (ed.),Rationality in Science and Politics, Dordrecht: Reidel, 1984, 47–68.Google Scholar
  4. Armstrong, David: 1983,What is a Law of Nature?, Cambridge: Cambridge University Press.Google Scholar
  5. Baird, Davis: 1983, ‘The Fisher/Pearson, Chi-squared Controversy: A Turning Point for Inductive Inference,British Journal for the Philosophy of Science 34, 105–118.Google Scholar
  6. Basu, Dev: 1988, ‘Statistical Information and Likelihood’, in: Gosh, J. K. (ed.),Statistical Information and Likelihood. A Collection of Critical Essays by Dr. D. Basu, New York: Springer 1988, 20–42.Google Scholar
  7. Berger, James O., Berry, Donald A.: 1988, ‘The Relevance of Stopping Rules in Statistical Inference (with discussion)’, in Gupta, Shanti S. and Berger, James O. (eds.),Statistical Decision Theory and Related Topics IV, Vol. I, New York: Springer 1988, 29–72.Google Scholar
  8. Bowley, Arthur L.: 1948,Elements of Statistics, 6th ed., London: Staples Press.Google Scholar
  9. Bowley, Arthur L. and Connor, L. R.: 1923, ‘Tests of Correspondence Between Statistical Grouping and Formulae’,Economica 3, 1923, 1–9.Google Scholar
  10. Cramér, Harald: 1946,Mathematical Methods of Statistics, Princeton: Princeton University Press.Google Scholar
  11. Casella, George: 1988, ‘Conditionally Acceptable Frequentist Solutions (with discussion)’, in Gupta, Shanti S. and Berger, James O. (eds.),Statistical Decision Theory and Related Topics IV, Vol. I, New York: Springer 1988, 73–117.Google Scholar
  12. Fine, Terence: 1973,Theories of Probability, New York: Academic Press.Google Scholar
  13. Fisher, Ronald A.: 1929, ‘Tests of Significance in Harmonic Analysis’,Proceedings of the Royal Society of London A125, 54–59.Google Scholar
  14. Fisher, Ronald A.: 1959,Statistical Methods and Scientific Inferences, 2nd rev. ed., Edinburgh: Oliver and Boyd.Google Scholar
  15. Fisher, Ronald A.: 1970,Statistical Methods for Research Workers, 14th rev. and enl. ed., New York: Hafner.Google Scholar
  16. Gadenne, Volker: 1990, ‚Unvollständige Erklärungen‘, in Sukale, M. (ed.),Sprache, Theorie und Wirklichkeit, Frankfurt/M.: Lang 1990, 263–287.Google Scholar
  17. Giere, Ronald N.: 1973, ‘Objective Single-case Probabilities and the Foundations of Statistics’, in Suppes, Patricket al. (eds.),Logic, Methodology and Philosophy of Science IV, Amsterdam/London: North-Holland 1973, 467–483.Google Scholar
  18. Giere, Ronald N.: 1977, ‘Testing Versus Information Models of Statistical Inference’, in Colodny, Robert G. (ed.),Logic, Laws & Life, Pittsburgh: University of Pittsburg Press 1977, 19–70.Google Scholar
  19. Gigerenzer, Gerd; Swijtink, Zenc; Porter, Theodore; Daston, Lorraine; Beatty, John; Krüger, Lorenz: 1989,The Empire of Chance, Cambridge: Cambridge University Press.Google Scholar
  20. Gillies, Donald A.: 1971, ‘A Falsifying Rule for Probability Statements’,British Journal for the Philosophy of Science 22, 231–261.Google Scholar
  21. Gillies, Donald A.: 1973,An Objective Theory of Probability, London: Methuen.Google Scholar
  22. Hacking, Ian: 1965,Logic of Statistical Inference, Cambridge: Cambridge University Press (Seitenangaben nach: 1st paperback ed. 1976).Google Scholar
  23. Hacking, Ian: 1973, ‘Propensities, Statistics and Inductive Logic’, in Suppes, Patricket al. (eds.),Logic, Methodology and Philosophy of Science IV, Amsterdam/London: North-Holland 1973, 485–500.Google Scholar
  24. Hacking, Ian: 1980, ‘The Theory of Probable Inference: Neyman, Peirce and Braithwaite’, in Mellor, David H. (ed.),Science, Belief and Behaviour, Cambridge: Cambridge University Press 1980, 141–160.Google Scholar
  25. Hempel, Carl G. and Oppenheim, Paul: 1948, ‘Studies in the Logic of Explanation’, repr. in: Pitt, Joseph C. (ed.),Theories of Explanation, Oxford: Oxford University Press 1988, 9–46.Google Scholar
  26. Hempel, Carl G.: 1977,Aspekte wissenschaftlicher Erklärung, Berlin: De Gruyter.Google Scholar
  27. Horn, Susan D.: 1977, ‘Goodness-of-fit Tests for Discrete Data: A Review and an Application to a Health Impairment Scale,Biometrics 33, 237–248.Google Scholar
  28. Kimball, A. W.: 1957, ‘Errors of the Third Kind in Statistical Consulting’,Journal of the American Statistical Association 52, 133–142.Google Scholar
  29. Lancaster, H. O.: 1969,The Chi-squared Distribution, New York: Wiley.Google Scholar
  30. Lehmann, Erich, L.: 1959,Testing Statistical Hypotheses, New York: Wiley.Google Scholar
  31. Mayo, Deborah G.: 1982, ‘On After-trial Criticisms of Neyman-Pearson Theory of Statistics’, inPSA 1982, Vol. I, 145–158.Google Scholar
  32. Neyman, Jerzy: 1929, ‘Contributions à la théorie de vraisemblance des hypothèses statistiques’,Revue Trimestrielle Statistique de la République Polonaise 6, 1–28.Google Scholar
  33. Neyman, Jerzy: 1952,Lectures and Conferences on Mathematical Statistics, Graduate School of the U.S. Department of Agriculture.Google Scholar
  34. Neyman, Jerzy: 1957, ‘“Inductive Behaviour” as a Basic Concept in the Philosophy of Science’,Revue l'Institute International de Statistique 25, 7–22.Google Scholar
  35. Neyman, Jerzy: 1965, ‘Behavioristic Points of View on Mathematical Statistics’, inOn Political Economy and Econometrics — Essays in Honor of Oskar Lange, Oxford: Pergamon Press 1965, 99–115.Google Scholar
  36. Neyman, Jerzy und Pearon, Egon S.: 1930, ‘On the Problem of Two Samples’, repr. in Neyman, Jerzy and Pearson, Egon S.:Joint Statistical Papers, Cambridge: Cambridge University Press, 1967, 140–185.Google Scholar
  37. Neyman, Jerzy und Pearson, Egon S.: 1933, ‘On the Problem of the Most Efficient Tests of Statistical Hypotheses’, repr. in Neyman, Jerzy and Pearson, Egon S.:Joint Statistical Papers, Cambridge: Cambridge University Press, 1967, 140–185.Google Scholar
  38. Popper, Karl R.: 1973,Objektive Erkenntnis, Hamburg: Hoffmann und Campe.Google Scholar
  39. Popper, Karl R.: 1984,Logik der Forschung, 8. weiter verb. und verm. Aufl., Tübingen: Mohr (Siebeck).Google Scholar
  40. Readhead, Michael L. G.: 1974, ‘On Neyman's Paradox and the Theory of Statistical Tests’,British Journal for the Philosophy of Science 25, 265–271.Google Scholar
  41. Spielman, Stephen: 1974, ‘The Logic of Tests of Significance’,Philosophy of Science 41, 211–226.Google Scholar
  42. Stegmüller, Wolfgang: 1973,Jenseits von Popper und Carnap: Die logischen Grundlagen des statistischen Schließens, broschierte Studienausgabe, Berlin: Springer.Google Scholar
  43. Wald, Abraham: 1950,Statistical Decision Functions, New York: Wiley.Google Scholar
  44. White, Douglas J.: 1976,Fundamentals of Decision Theory, Amsterdam: North-Holland.Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Max Albert
    • 1
  1. 1.Fakultät für Wirtschaftswissenschaften u. StatistikUniversität KonstanzKonstanzGermany

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