IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v58y2017i1d10.1007_s00362-015-0690-2.html
   My bibliography  Save this article

A comparison of different synchronized permutation approaches to testing effects in two-level two-factor unbalanced ANOVA designs

Author

Listed:
  • Sonja Hahn

    (Friedrich-Schiller-University Jena)

  • Luigi Salmaso

    (University of Padova)

Abstract

Analysis of variance (ANOVA) is used to compare the means of various samples. Parametric ANOVA approaches assume normally distributed error terms within subsamples. Permutation tests like synchronized permutation tests are computationally intensive and distribution free procedures. Hence they overcome the limitations of parametric methods. Unbalanced designs with differing subsample sizes are quite frequent in various disciplines. There is a broad literature about unbalanced designs and parametric testing. For permutation tests this topic received some attention recently. This paper extends the synchronized permutation method to unbalanced two-level ANOVA designs. A simulation study investigates the behavior of different procedures for various types of unbalanced designs. It compares the results to other permutation approaches. The synchronized permutation method yields comparable results to the best performing competing permutation approaches. However the approach is limited to certain kinds of unbalanced designs.

Suggested Citation

  • Sonja Hahn & Luigi Salmaso, 2017. "A comparison of different synchronized permutation approaches to testing effects in two-level two-factor unbalanced ANOVA designs," Statistical Papers, Springer, vol. 58(1), pages 123-146, March.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0690-2
    DOI: 10.1007/s00362-015-0690-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-015-0690-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-015-0690-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Edgar Brunner & Madan Puri, 2001. "Nonparametric methods in factorial designs," Statistical Papers, Springer, vol. 42(1), pages 1-52, January.
    2. Kherad-Pajouh, Sara & Renaud, Olivier, 2010. "An exact permutation method for testing any effect in balanced and unbalanced fixed effect ANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1881-1893, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ditzhaus, Marc & Smaga, Łukasz, 2022. "Permutation test for the multivariate coefficient of variation in factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Friedrich, Sarah & Pauly, Markus, 2018. "MATS: Inference for potentially singular and heteroscedastic MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 166-179.
    2. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Finos, Livio, 2011. "A note on Left-Spherically Distributed test with covariates," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 639-641, June.
    4. Gunawardana, Asanka & Konietschke, Frank, 2019. "Nonparametric multiple contrast tests for general multivariate factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 165-180.
    5. Fan, Chunpeng & Zhang, Donghui, 2014. "Wald-type rank tests: A GEE approach," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 1-16.
    6. Denis A. Shah & Laurence V. Madden, 2013. "A comment on Mendeş and Yiğit (2013), ‘Type I error and test power of different tests for testing interaction effects in factorial experiments’, Statistica Neerlandica, 67:1–26," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 397-399, November.
    7. Sara Kherad-Pajouh & Olivier Renaud, 2015. "A general permutation approach for analyzing repeated measures ANOVA and mixed-model designs," Statistical Papers, Springer, vol. 56(4), pages 947-967, November.
    8. Konietschke, F. & Bathke, A.C. & Hothorn, L.A. & Brunner, E., 2010. "Testing and estimation of purely nonparametric effects in repeated measures designs," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1895-1905, August.
    9. Debajit Chatterjee & Uttam Bandyopadhyay, 2019. "Testing in nonparametric ANCOVA model based on ridit reliability functional," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 327-364, April.
    10. Edgar Brunner & Frank Konietschke & Arne C. Bathke & Markus Pauly, 2021. "Ranks and Pseudo‐ranks—Surprising Results of Certain Rank Tests in Unbalanced Designs," International Statistical Review, International Statistical Institute, vol. 89(2), pages 349-366, August.
    11. Edgar Brunner & Frank Konietschke & Markus Pauly & Madan L. Puri, 2017. "Rank-based procedures in factorial designs: hypotheses about non-parametric treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1463-1485, November.
    12. Arne Bathke, 2009. "A unified approach to nonparametric trend tests for dependent and independent samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 69(1), pages 17-29, January.
    13. Edgar Brunner & Madan L. Puri, 2013. "Comments on the paper ‘Type I error and test power of different tests for testing interaction effects in factorial experiments’ by M. Mendes and S. Yigit (Statistica Neerlandica, 2013, pp. 1–26)," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 390-396, November.
    14. Dennis Dobler & Sarah Friedrich & Markus Pauly, 2020. "Nonparametric MANOVA in meaningful effects," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 997-1022, August.
    15. Bathke, Arne C. & Harrar, Solomon W. & Madden, Laurence V., 2008. "How to compare small multivariate samples using nonparametric tests," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4951-4965, July.
    16. M. Akritas & A. Stavropoulos & C. Caroni, 2009. "Asymptotic theory of weighted -statistics based on ranks," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 177-191.
    17. Jan De Neve & Olivier Thas, 2015. "A Regression Framework for Rank Tests Based on the Probabilistic Index Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1276-1283, September.
    18. Oleg Museyko & Robert Percy Marshall & Jing Lu & Andreas Hess & Georg Schett & Michael Amling & Willi A. Kalender & Klaus Engelke, 2015. "Registration of 2D histological sections with 3D micro-CT datasets from small animal vertebrae and tibiae," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 18(15), pages 1658-1673, November.
    19. Kandianos Emmanouil Sakalidis & Stein Gerrit Paul Menting & Florentina Johanna Hettinga, 2023. "The Role of Cognition and Social Factors in Competition: How Do People with Intellectual Disabilities Respond to Opponents?," IJERPH, MDPI, vol. 20(3), pages 1-14, February.
    20. Friedrich, Sarah & Konietschke, Frank & Pauly, Markus, 2017. "A wild bootstrap approach for nonparametric repeated measurements," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 38-52.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0690-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.