Bayesian Estimation for Inequality Constrained Analysis of Variance

  • Irene KlugkistEmail author
  • Joris Mulder
Part of the Statistics for Social and Behavioral Sciences book series (SSBS)


In Chapter 2, several examples of research questions in the analysis of variance (ANOVA) context were presented. The model parameters of an ANOVA are two or more population means and the common and unknown residual variance. In the examples, the hypotheses or research questions of interest impose inequality constraints on the means. For instance, for the four-group ANOVA in the Dissociative Identity Disorder (DID) data from Huntjens et al.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bernardo, J.M., Smith, A.F.M.: Bayesian Theory. Chichester, Wiley (1994)zbMATHCrossRefGoogle Scholar
  2. [2]
    Box, G.E.P., Tiao, G.C.: Bayesian Inference in Statistical Analysis. Reading, MA, Addison-Wesley (1973)zbMATHGoogle Scholar
  3. [3]
    Cowles, M.K., Carlin, B.P.: Markov chain Monte Carlo convergence diagnostics: A comparative review. Journal of the American Statistical Association, 91, 883–904 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Everitt, B.: Statistics for Psychologists: An Intermediate Course. Mahwah, NJ, Lawrence Erlbaum Associates (2001)Google Scholar
  5. [5]
    Gelfand, A.E., Smith, A.F.M., Lee, T.: Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. Journal of the American Statistical Association, 87, 523–532 (1992)CrossRefMathSciNetGoogle Scholar
  6. [6]
    Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis (2nd ed.). London, Chapman & Hall (2004)zbMATHGoogle Scholar
  7. [7]
    Gelman, A., Rubin, D.B.: Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457–511 (1992)CrossRefGoogle Scholar
  8. [8]
    Gill, J.: Bayesian Methods. A Social and Behavioral Sciences Approach. London, Chapman & Hall (2002)zbMATHGoogle Scholar
  9. [9]
    Howson, C., Urbach, P.: Scientific Reasoning: The Bayesian Approach (2nd ed.). Chicago, Open Court Publishing Company (1993)Google Scholar
  10. [10]
    Huntjens, R.J.C., Peters, M.L., Woertman, L., Bovenschen, L.M., Martin, R.C., Postma, A.: Inter-identity amnesia in dissociative identity disorder: A simulated memory impairment? Psychological Medicine, 36, 857–863 (2006)CrossRefGoogle Scholar
  11. [11]
    Jeffreys, H.: Theory of Probability (3rd ed.). Oxford, Oxford University Press (1961)zbMATHGoogle Scholar
  12. [12]
    Kass, R.E., Wasserman, L.: The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91, 1343–1370 (1996)zbMATHCrossRefGoogle Scholar
  13. [13]
    Klugkist, I., Laudy, O., Hoijtink, H.: Inequality constrained analysis of variance: A Bayesian approach. Psychological Methods, 10, 477–493 (2005)CrossRefGoogle Scholar
  14. [14]
    Lee, P.M.: Bayesian Statistics: An Introduction. London, Arnold (1997)zbMATHGoogle Scholar
  15. [15]
    Lindley, D.V.: Bayesian Statistics, A Review. Philadelphia, SIAM (1972)Google Scholar
  16. [16]
    Raiffa, H., Schlaifer, R.: Applied Statistical Decision Theory. Boston, Graduate School of Business Administration, Harvard University (1961)Google Scholar
  17. [17]
    Rutherford, A.: Introducing ANOVA and ANCOVA; a GLM approach. London, Sage (2001)zbMATHGoogle Scholar
  18. [18]
    Smith, A.F.M., Roberts, G.O.: Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, B, 55, 3–23 (1993)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Methodology and StatisticsUtrecht UniversityUtrechtThe Netherlands

Personalised recommendations