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Theoretical and empirical distributions of the p value

Author

Listed:
  • J. S. Butler

    (University of Kentucky)

  • Peter Jones

    (University of Alabama at Birmingham)

Abstract

The use of p values in null hypothesis statistical tests (NHST) is controversial in the history of applied statistics, owing to a number of problems. They are: arbitrary levels of Type I error, failure to trade off Type I and Type II error, misunderstanding of p values, failure to report effect sizes, and overlooking better means of reporting estimates of policy impacts, such as effect sizes, interpreted confidence intervals, and conditional frequentist tests. This paper analyzes the theory of p values and summarizes the problems with NHST. Using a large data set of public school districts in the United States, we demonstrate empirically the unreliability of p values and hypothesis tests as predicted by the theory. We offer specific suggestions for reporting policy research.

Suggested Citation

  • J. S. Butler & Peter Jones, 2018. "Theoretical and empirical distributions of the p value," METRON, Springer;Sapienza Università di Roma, vol. 76(1), pages 1-30, April.
    • Handle: RePEc:spr:metron:v:76:y:2018:i:1:d:10.1007_s40300-017-0130-2
    DOI: 10.1007/s40300-017-0130-2
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    References listed on IDEAS

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    1. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    2. Sellke T. & Bayarri M. J. & Berger J. O., 2001. "Calibration of rho Values for Testing Precise Null Hypotheses," The American Statistician, American Statistical Association, vol. 55, pages 62-71, February.
    3. Poole, C., 1987. "Beyond the confidence interval," American Journal of Public Health, American Public Health Association, vol. 77(2), pages 195-199.
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