Skip to main content
SpringerLink
Log in

Rank tests for the 2×2 split plot design

  • Publication
  • Published:
Metrika Aims and scope Submit manuscript

Summary

In the 2×2 split plot design there are given rank tests for the classical hypotheses of the main effects and interaction.

The asymptotic normality of the proposed teststatistics is proved and their consistency is investigated. For testing the main effects these methods cannot be extended on the generala×b split plot design Counter-examples are given.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Brunner, E., andN. Neumann: Rank Tests for Correlated Random Variables. Biom. J.24, 1982, 373–389.

    Article  MathSciNet  MATH  Google Scholar 

  • Conover, W.J., andR.L. Iman: On some Alternative Procedures Using Ranks for the Analysis of Experimental Designs. Commun. Statist.A5 (14), 1976, 1349–1368.

    Article  Google Scholar 

  • —: Rank Transformations as a Bridge Between Parametric and Nonparametric Statistics. Amer. Statist.35, 1981, 124–129.

    MATH  Google Scholar 

  • Fligner, M.A.: Comment to Conover/Iman [1981]. Amer. Statist.35, 1981, 131–132.

    Google Scholar 

  • Hilgers, R.: Ein asymptotisch verteilungsfreier Wechselwirkungstest in zweifaktoriellen vollständigen Zufallsplänen. Dissertation Dortmund 1979.

  • Iman, R.L.: A Power Study of a Rank Transform for the Two-Way Classification Model when Interaction May Be Present. Canadian J. of Statist. C: Appl.2 (2), 1974, 227–239.

    Article  MATH  Google Scholar 

  • Kirk, R.E.: Experimental Design: Procedures for the Behavioral, Sciences. Belmont, CA, 1968.

  • Koch, G.G.: Some Aspects of the Statistical Analysis of ‘Split Plot’ Experiments in Completely Randomized Layouts. JASA64, 1969, 485–506.

    MathSciNet  MATH  Google Scholar 

  • —: The Use of Non-Parametric Methods in the Statistical Analysis of a Complex Split Plot Experiment. Biometrics26, 1970, 105–128.

    Article  Google Scholar 

  • Koch, G.G., andP.K. Sen: Some Aspects of the Statistical Analysis of the Mixed Model. Biometrics24, 1968, 27–48.

    Article  MathSciNet  Google Scholar 

  • Lemmer, H.H.: Some Empirical Results on the Two-Way Analysis of Variance by Ranks. Commun. Statist.A9 (14), 1980, 1427–1438.

    Article  MATH  Google Scholar 

  • Lemmer, H.H., andD.J. Stoker: A Distribution-Free Analysis of Variance for the Two-Way Classification. South Afr Statist. J.1, 1967, 67–74.

    Google Scholar 

  • Patel, K.M., andD.G. Hoel: A Nonparametric Test for Interaction in Factorial Experiments. JASA68, 1973, 615–620.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abtellung Medizinische Statistik, Universität Göttingen, Windausweg 2, D-3400, Göttingen

    E. Brunner &  N. Neumann

Authors
  1. E. Brunner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Neumann
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brunner, E., Neumann, N. Rank tests for the 2×2 split plot design. Metrika 31, 233–243 (1984). https://doi.org/10.1007/BF01915206

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01915206

Keywords

Search

Navigation