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Determination of Minimum and Maximum Experimental Size in One-, Two- and Three-way ANOVA with Fixed and Mixed Models by R

Abstract

In the paper for all classifications, the models of analysis of variance (ANOVA) have up to three factors and all have the fixed factor A which has to be tested. R-programs of the package OPDOE for the determination of the experimental size are given.

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References

  1. Lindman HR (1992) Analysis of variance in experimental design. Springer, New York. https://doi.org/10.1007/978-1-4613-9722-9

    Book  MATH  Google Scholar 

  2. Rasch D, Schott D (2018) Mathematical statistics. Wiley, Chichester

    Book  Google Scholar 

  3. Rasch D, Pilz J, Gebhardt A, Verdooren R (2011) Optimal experimental design with R. Chapman and Hall, Boca Raton

    Book  Google Scholar 

  4. Rasch D, Spangl B, Wang M (2012) Minimal experimental size in the three way ANOVA cross classification model with approximate F-tests. Commun. Stat. Simul. Comput. 41:1120–1130

    Article  MathSciNet  Google Scholar 

  5. Rasch D, Verdooren R, Pilz J (2020) Applied statistics, theory and problems solutions with R. Wiley, Oxford

    MATH  Google Scholar 

  6. Spangl B, Kaiblinger N, Ruckdeschel P, Rasch D (2021) Minimum experimental size in balanced ANOVA models of crossed, nested and mixed classifications. J. Stat. Theory. Pract. (under review)

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Correspondence to Dieter Rasch.

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Part of special issue guest edited by Dieter Rasch, Jürgen Pilz, and Subir Ghosh—Advances in Statistical and Simulation Methods.

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Rasch, D., Verdooren, R. Determination of Minimum and Maximum Experimental Size in One-, Two- and Three-way ANOVA with Fixed and Mixed Models by R. J Stat Theory Pract 14, 57 (2020). https://doi.org/10.1007/s42519-020-00088-6

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  • DOI: https://doi.org/10.1007/s42519-020-00088-6

Keywords

  • One-way ANOVA
  • Two-way ANOVA
  • Three-way ANOVA
  • Non-centrality parameter λ of F(df1, df2, λ)
  • Minimal experimental size