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

Yoshio Takane (), Eric J. Beh () and Rosaria Lombardo ()
Additional contact information
Yoshio Takane: University of Victoria
Eric J. Beh: University of Wollongong
Rosaria Lombardo: University of Campania “Luigi Vanvitelli”

Computational Statistics, 2025, vol. 40, issue 3, No 11, 1423-1446

Abstract: 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.

Keywords: Freeman–Tukey (FT) statistics; Modified FT statistics; One-way tables; Two-way tables; Variance stabilizing transformations; Multiple comparisons via the modified FT statistics; Tukey’s post-hoc tests; Scheffè’s post-hoc tests (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00180-024-01537-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:40:y:2025:i:3:d:10.1007_s00180-024-01537-7

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-024-01537-7

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().