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Permutation Statistical Methods

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A Primer of Permutation Statistical Methods

Abstract

This chapter presents two models of statistical inference: the conventional Neyman–Pearson population model that is taught in every introductory course and the Fisher–Pitman permutation model with which the reader is assumed to unfamiliar. The Fisher–Pitman model consists of three different permutation methods: exact permutation methods, Monte Carlo permutation methods, and moment-approximation permutation methods. The three methods are described and illustrated with example analyses.

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Notes

  1. 1.

    The Neyman–Pearson population model of statistical inference is named for Jerzy Neyman (1894–1981) and Egon Pearson (1895–1980).

  2. 2.

    The Fisher–Pitman permutation model of statistical inference is named for R.A. Fisher (1890–1962) and E.J.G. Pitman (1897–1993).

  3. 3.

    There are, of course, other models of statistical inference. A third model, the Bayesian inference model, is also very popular, especially in the decision-making sciences.

  4. 4.

    Some introductory textbooks denote the alternative hypothesis by H A.

  5. 5.

    In this book, an upper-case letter P indicates a cumulative probability value and a lower-case letter p indicates a point probability value.

  6. 6.

    Fisher’s exact test was independently developed by R.A. Fisher, Joseph Irwin, and Frank Yates in the early 1930s [13, 21, 40].

  7. 7.

    Emphasis in the original.

  8. 8.

    One petaflops indicates a quadrillion operations per second, or a 1 with 15 zeroes following it.

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Authors and Affiliations

  1. Department of Sociology, Colorado State University, Fort Collins, Colorado, USA

    Kenneth J. Berry

  2. Alexandria, Virginia, USA

    Janis E. Johnston

  3. Department of Statistics, Colorado State University, Fort Collins, Colorado, USA

    Paul W. Mielke Jr.

Authors
  1. Kenneth J. Berry
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  2. Janis E. Johnston
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  3. Paul W. Mielke Jr.
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Berry, K.J., Johnston, J.E., Mielke, P.W. (2019). Permutation Statistical Methods. In: A Primer of Permutation Statistical Methods. Springer, Cham. https://doi.org/10.1007/978-3-030-20933-9_3

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