Skip to main content
SpringerLink
Log in

Generalizations and Methodological Considerations for ANOVA

  • Chapter
  • First Online:
The Significance Test Controversy Revisited

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

  • 1282 Accesses

Abstract

This chapter generalizes the basic fiducial Bayesian procedures to the usual unstandardized and standardized ANOVA effect sizes indicators. Methodological aspects are discussed and appropriate alternatives to these indicators are introduced and illustrated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Baguley, T.: Standardized or simple effect size: What should be reported? Brit. J. Psychol. 100, 603–617 (2009)

    Article  Google Scholar 

  • Beauchamp, K.L., May, R.B.: Replication report: Interpretation of levels of significance by psychological researchers. Psychol. Rep. 14, 272 (1964)

    Article  Google Scholar 

  • Cohen, J.: Statistical Power Analysis for the Behavioral Sciences (revised edition). Academic Press, New York (1977)

    Google Scholar 

  • Geisser, S.: Bayesian estimation in multivariate analysis. Ann. Math. Statist. 36, 150–159 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  • Holender, D., Bertelson, P.: Selective preparation and time uncertainty. Acta Psychol. 39, 193–203 (1975)

    Article  Google Scholar 

  • Kelley, K.: Confidence intervals for standardized effect sizes: theory, application, and implementation. J. Stat. Softw. 20, 2–24 (2007)

    Google Scholar 

  • Lecoutre, B., Guigues, J.-L., Poitevineau, J.: Distribution of quadratic forms of multivariate Student variables. Appl. Stat.-J. Roy. St. C 41, 617–627 (1992)

    Google Scholar 

  • Lecoutre, B., Rouanet, H.: Deux structures statistiques fondamentales en analyse de la variance univariée et multivariée. Math. Sci. Hum. 75, 71–82 (1981)

    MATH  MathSciNet  Google Scholar 

  • Lecoutre, B.: Extensions de l’analyse de la variance: l’analyse bayésienne des comparaisons. Math. Sci. Hum. 75, 49–69 (1981)

    MATH  MathSciNet  Google Scholar 

  • Lecoutre, B.: Two useful distributions for Bayesian predictive procedures under normal models. J. Stat. Plan. Infer. 79, 93–105 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • Lecoutre, B., Derzko, G.: Asserting the smallness of effects in ANOVA. Methods Psychol. Res. 6, 1–32 (2001)

    Google Scholar 

  • Lecoutre, B.: Training students and researchers in Bayesian methods. J. Data Sci. 4, 207–232 (2006)

    Google Scholar 

  • Minturn, E.B., Lansky, L.M., Dember, W.N.: The interpretation of levels of significance by psychologists: A replication and extension. Paper presented at the meeting of the Eastern Psychological Association, Boston (1972)

    Google Scholar 

  • Nelson, N., Rosenthal, R., Rosnow, R.L.: Interpretation of significance levels and effect sizes by psychological researchers. Am. Psychol. 41, 1299–1301 (1986)

    Article  Google Scholar 

  • Oakes, M.: Statistical Inference: A Commentary for the Social and Behavioural Sciences. Wiley, New York (1986)

    Google Scholar 

  • Poitevineau, J., Lecoutre, B.: Interpretation of significance levels by psychological researchers: The. 05-cliff effect may be overstated. Psychon. B. Rev. 8, 847–850 (2001)

    Google Scholar 

  • Poitevineau, J., Lecoutre, B.: Implementing Bayesian predictive procedures: the K-prime and K-square distributions. Comput. Stat. Data An. 54, 723–730 (2010)

    Article  MathSciNet  Google Scholar 

  • Publication Manual of the American Psychological Association, 6th edn. American Psychological Association, Washington (2010)

    Google Scholar 

  • Rosenthal, R., Gaito, J.: The interpretation of levels of significance by psychological researchers. J. Psychol. 55, 33–38 (1963)

    Article  Google Scholar 

  • Rosenthal, R., Gaito, J.: Further evidence for the cliff effect in the interpretation of levels of significance. Psychol. Rep. 15, 570 (1964)

    Article  Google Scholar 

  • Rouanet, H., Lecoutre, B.: Specific inference in ANOVA: from significance tests to Bayesian procedures. Brit. J. Math. Stat. Psy. 36, 252–268 (1983)

    Article  MATH  Google Scholar 

  • Rouanet, H.: Bayesian procedures for assessing importance of effects. Psychol. Bull. 119, 149–158 (1996)

    Article  Google Scholar 

  • Scheffé, H.: A method for judging all contrasts in the analysis of variance. Biometrika 40, 87–104 (1953)

    MATH  MathSciNet  Google Scholar 

  • Schervish, M.J.: Bayesian analysis of linear models. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (eds.) Bayesian Statistics IV, pp. 419–434. Oxford University Press, Oxford (1992)

    Google Scholar 

  • Schervish, M.J.: Theory of statistics. Springer, New York (1995)

    Book  MATH  Google Scholar 

  • Steiger, J.H., Fouladi, R.T.: Noncentrality interval estimation and the evaluation of statistical models. In: Harlow, L.L., Mulaik, S.A., Steiger, J.H. (eds.) What If There Were No Significance Tests?, pp. 221–257. Erlbaum, Hillsdale (1997)

    Google Scholar 

  • Steiger, J.H.: Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychol. Methods 9, 164–182 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ERIS, Laboratoire de Mathématiques Raphaël Salem, UMR 6085, CNRS Université de Rouen, Saint-Étienne-du-Rouvray, France

    Bruno Lecoutre

  2. ERIS, IJLRA UMR-7190, CNRS, Université Pierre et Marie Curie, Paris, France

    Jacques Poitevineau

Authors
  1. Bruno Lecoutre
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacques Poitevineau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bruno Lecoutre .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 The Author(s)

About this chapter

Cite this chapter

Lecoutre, B., Poitevineau, J. (2014). Generalizations and Methodological Considerations for ANOVA. In: The Significance Test Controversy Revisited. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44046-9_9

Download citation

Publish with us

Policies and ethics

Search

Navigation