Generalized p Values and Random p Values When the Alternative to Uniformity Is a Mixture of a Beta(1,2) and Uniform



Combining p values methods and uniformity tests are closely related subjects in meta analysis. In this context it is also known that publication bias can seriously impair an overall decision. The recent concepts of generalized p values and of random p values emphasize that, when faced with a significant number of results that casts some doubt on the null hypothesis, the correct approach to the problem should be to combine evidence under the alternative hypothesis. Following previous research, we investigate generalized p values and random p values for testing uniformity when the alternative is a mixture of a Beta(1,2) and standard uniform random variables.


  1. 1.
    Brilhante, M.F., Mendonça, S., Pestana, D., Sequeira, F.: Using products and powers of  products to test uniformity. In: Luzar-Stiffler, V., et al. (eds.) Proceedings of the 32nd International Conference on Information Technology Interfaces, SRCE, Zagreb pp. 509–514 (2010)Google Scholar
  2. 2.
    Brilhante, M.F., Pestana, D., Sequeira, F.: Combining p-values and random p-values. In: Luzar-Stiffler, V., et al. (eds.) Proceedings of the 32nd International Conference on Information Technology Interfaces, pp. 515–520 (2010)Google Scholar
  3. 3.
    Dempster, A.P., Schatzoff, M.: Expected significance level as a sensibility index for test statistics. J. Am. Stat. Assoc. 60, 420–436 (1965)Google Scholar
  4. 4.
    Gomes, M.I., Pestana, D.D., Sequeira, F., Mendonça, S., Velosa, S.: Uniformity of offsprings from uniform and non-uniform parents. In: Luzar-Stiffler, V., et al. (eds.) Proceedings of the 31st International Conference on Information Technology Interfaces, pp. 243–248 (2009)Google Scholar
  5. 5.
    Iyer, H.K., Patterson, P.D.: In a recipe for constructing generalized pivotal quantities and generalized confidence intervals, Colorado State University Department of Statistics Technical Report 2002/10, (2002/2010)
  6. 6.
    Kulinskaya, E., Morgenthaler, S., Staudte, R.G.: Meta Analysis. A Guide to Calibrating and Combining Statistical Evidence. Wiley, Chichester (2008)Google Scholar
  7. 7.
    Pestana, D.: Combining p-values. In: Lovric, M. (ed.) International Encyclopedia of Statistical Science, pp. 1145–1147. Springer, Berlin (2011)Google Scholar
  8. 8.
    Royle, J.A., Dorazio, R.M., Link, W.A.: Analysis of multinomial models with unknown index using data augmentation. J. Comput. Grap. Stat. 16, 67–85 (2007)Google Scholar
  9. 9.
    Sackrowitz, H., Samuel-Cahn, E.: p-Values as Random Variables – Expected P Values. J. Am. Stat. Assoc. 53, 326–331 (1999)Google Scholar
  10. 10.
    Tsui, K., Weerahandi, S.: Generalized p-values in significance testing of hypotheses. J. Am. Stat. Assoc. 84, 602–607 (1989)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Universidade dos Açores (DM) and CEAULPonta DelgadaPortugal

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