IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v40y2025i3d10.1007_s00180-024-01537-7.html
   My bibliography  Save this article

A theory of contrasts for modified Freeman–Tukey statistics and its applications to Tukey’s post-hoc tests for contingency tables

Author

Listed:
  • Yoshio Takane

    (University of Victoria)

  • Eric J. Beh

    (University of Wollongong
    Stellenbosch University)

  • Rosaria Lombardo

    (University of Campania “Luigi Vanvitelli”)

Abstract

This paper presents a theory of contrasts designed for modified Freeman–Tukey (FT) statistics which are derived through square-root transformations of observed frequencies (proportions) in contingency tables. Some modifications of the original FT statistic are necessary to allow for ANOVA-like exact decompositions of the global goodness of fit (GOF) measures. The square-root transformations have an important effect of stabilizing (equalizing) variances. The theory is then used to derive Tukey’s post-hoc pairwise comparison tests for contingency tables. Tukey’s tests are more restrictive, but are more powerful, than Scheffè’s post-hoc tests developed earlier for the analysis of contingency tables. Throughout this paper, numerical examples are given to illustrate the theory. Modified FT statistics, like other similar statistics for contingency tables, are based on a large-sample rationale. Small Monte-Carlo studies are conducted to investigate asymptotic (and non-asymptotic) behaviors of the proposed statistics.

Suggested Citation

  • Yoshio Takane & Eric J. Beh & Rosaria Lombardo, 2025. "A theory of contrasts for modified Freeman–Tukey statistics and its applications to Tukey’s post-hoc tests for contingency tables," Computational Statistics, Springer, vol. 40(3), pages 1423-1446, March.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:3:d:10.1007_s00180-024-01537-7
    DOI: 10.1007/s00180-024-01537-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-024-01537-7
    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/s00180-024-01537-7?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. Beh, Eric J. & Lombardo, Rosaria & Alberti, Gianmarco, 2018. "Correspondence analysis and the Freeman–Tukey statistic: A study of archaeological data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 73-86.
    Full references (including those not matched with items on IDEAS)

    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. Eric J. Beh & Rosaria Lombardo, 2024. "Correspondence Analysis Using the Cressie–Read Family of Divergence Statistics," International Statistical Review, International Statistical Institute, vol. 92(1), pages 17-42, April.
    2. Ting-Wu Wang & Eric J. Beh & Rosaria Lombardo & Ian W. Renner, 2025. "Profile transformations for reciprocal averaging and singular value decomposition," Computational Statistics, Springer, vol. 40(3), pages 1217-1251, March.
    3. Rodrigues Teixeira, Ana Carolina & Machado, Pedro Gerber & Borges, Raquel Rocha & Felipe Brito, Thiago Luis & Moutinho dos Santos, Edmilson & Mouette, Dominique, 2021. "The use of liquefied natural gas as an alternative fuel in freight transport – Evidence from a driver's point of view," Energy Policy, Elsevier, vol. 149(C).

    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:compst:v:40:y:2025:i:3:d:10.1007_s00180-024-01537-7. 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.