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Testing Effects in ANOVA Experiments: Direct Combination of All Pair-Wise Comparisons Using Constrained Synchronized Permutations

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COMPSTAT 2008

Abstract

Synchronized permutation tests have been introduced to test for main effects and interaction in two-way ANOVA problems (Pesarin, 2001, Salmaso, 2003, Basso et al., 2007). The permutation space is restricted in order the test statistic for each factor or interaction to depend only on the true effects (if any) under testing and on exchangeable errors. The proposed test statistics can be viewed as a direct combination (i.e. the sum) of partial statistics to perform all pair-wise comparisons between the effects of a main factor. Note that the tests for each comparison are dependent. Constrained synchronized permutations allow to test all pair-wise comparisons between pairs of effects of a main factor. Simultaneous and individual confidence intervals for each comparison can be provided through CSP tests.

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References

  • BASSO, D., CHIARANDINI, M., SALMASO, L. (2007): Synchronized permutation tests in I × J designs. Journal of Statistical Planning and Inference 137(8), 2564-2578.

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Author information

Authors and Affiliations

  1. Department of Management and Engineering, University of Padova, Str.lla S. Nicola 14, 36100, Vicenza, Italy

    Dario Basso & Luigi Salmaso

  2. Department of Statistics, University of Padova, Via Cesare Barttisti 241-243, 35100, Padova, Italy

    Fortunato Pesarin

Authors
  1. Dario Basso
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  2. Fortunato Pesarin
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  3. Luigi Salmaso
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Corresponding author

Correspondence to Dario Basso .

Editor information

Editors and Affiliations

  1. Faculdade de Economia, Rua Dr. Roberto Frias, 4200-464, Porto, Portugal

    Paula Brito

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© 2008 Physica-Verlag Heidelberg

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Basso, D., Pesarin, F., Salmaso, L. (2008). Testing Effects in ANOVA Experiments: Direct Combination of All Pair-Wise Comparisons Using Constrained Synchronized Permutations. In: Brito, P. (eds) COMPSTAT 2008. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2084-3_34

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