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Statistical Practice as Argumentation: A Sketch of a Theory of Applied Statistics

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Modelling and Prediction Honoring Seymour Geisser

Abstract

We have theories of statistics and we use statistical methods to solve subject matter problems. One might expect that the theories would affect how the methods are used, but they do so only superficially, because all statistical theories are quite incomplete as descriptions of and prescriptions for statistical practice. This paper sketches an extension of Bayesian theory that might address this incompleteness. The extension is based on five ideas:

  1. 1.

    The product of a statistical analysis is an argument — not an HPD region, posterior distribution, decision, or other data summary, but the entire argument, including premises and logical steps.

  2. 2.

    Arguments come in several logically distinct types, with an argument’s type being defined by the form of its conclusion. The paper catalogs the types of argument and identifies the main burden of each.

  3. 3.

    EDA and model-building activities establish a plausible, tractable baseline argument for a given problem and dataset.

  4. 4.

    Diagnostics and sensitivity analyses vary the premises of the baseline argument and display the resulting variation in the conclusion (as opposed to intermediate quantities).

  5. 5.

    An argument is strong to the extent that:

  • its premises are conclusions of strong arguments, or

  • the region of premises yielding the same conclusion is large.

A simple example demonstrates the mechanics of the extended theory. The example is then generalized to draw implications for statistical foundations, methods, and computing. This paper amounts to a research agenda, so it poses more problems than it solves.

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Author information

Authors and Affiliations

  1. Division of Biostatistics, University of Minnesota, USA

    James S. Hodges

Authors
  1. James S. Hodges
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Editors and Affiliations

  1. Institute of Statistics, National Chiao Tung University, 1001 Ta-Hseuh Road, Hsichu, Taiwan R.O.C

    Jack C. Lee

  2. Department of Statistics, University of California, Davis, 95616, Davis, CA, USA

    Wesley O. Johnson

  3. Graduate School of Business, University of Chicago, 1101 East 58th Street, 60637, Chicago, IL, USA

    Arnold Zellner

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Hodges, J.S. (1996). Statistical Practice as Argumentation: A Sketch of a Theory of Applied Statistics. In: Lee, J.C., Johnson, W.O., Zellner, A. (eds) Modelling and Prediction Honoring Seymour Geisser. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2414-3_2

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  • DOI: https://doi.org/10.1007/978-1-4612-2414-3_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7529-9

  • Online ISBN: 978-1-4612-2414-3

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