Catanova for two-way contingency tables with ordinal variables using orthogonal polynomials

Luigi D'Ambra; Eric J. Beh; Pietro Amenta

Catanova for two-way contingency tables with ordinal variables using orthogonal polynomials

Luigi D'Ambra, Eric J. Beh, Pietro Amenta

Research output: Contribution to journal › Article

32 Citations (Scopus)

Abstract

The analysis of variance of cross-classified (categorical) data (CATANOVA) is a technique designed to identify the variation between treatments of interest to the researcher. There are well-established links between CATANOVA and the Goodman and Kruskal tau statistic as well as the Light and Margolin R2 for the purposes of the graphical identification of this variation. The aim of this article is to present a partition of the numerator of the tau statistic, or equivalently, the BSS measure in the CATANOVA framework, into location, dispersion, and higher order components. Even if a CATANOVA identifies an overall lack of variation, by considering this partition and calculations derived from them, it is possible to identify hidden, but statistically significant, sources of variation.

Original language	English
Number of pages	15
Journal	Communications in statistics : theory and methods
Publication status	Published - 2005

Keywords

Goodman and Kruskal tau statistic
location, dispersion, and higher-order components
orthogonal polynomials

Cite this

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title = "Catanova for two-way contingency tables with ordinal variables using orthogonal polynomials",

abstract = "The analysis of variance of cross-classified (categorical) data (CATANOVA) is a technique designed to identify the variation between treatments of interest to the researcher. There are well-established links between CATANOVA and the Goodman and Kruskal tau statistic as well as the Light and Margolin R2 for the purposes of the graphical identification of this variation. The aim of this article is to present a partition of the numerator of the tau statistic, or equivalently, the BSS measure in the CATANOVA framework, into location, dispersion, and higher order components. Even if a CATANOVA identifies an overall lack of variation, by considering this partition and calculations derived from them, it is possible to identify hidden, but statistically significant, sources of variation.",

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author = "Luigi D'Ambra and Beh, {Eric J.} and Pietro Amenta",

year = "2005",

language = "English",

journal = "Communications in statistics : theory and methods",

issn = "0361-0926",

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TY - JOUR

T1 - Catanova for two-way contingency tables with ordinal variables using orthogonal polynomials

AU - D'Ambra, Luigi

AU - Beh, Eric J.

AU - Amenta, Pietro

PY - 2005

Y1 - 2005

N2 - The analysis of variance of cross-classified (categorical) data (CATANOVA) is a technique designed to identify the variation between treatments of interest to the researcher. There are well-established links between CATANOVA and the Goodman and Kruskal tau statistic as well as the Light and Margolin R2 for the purposes of the graphical identification of this variation. The aim of this article is to present a partition of the numerator of the tau statistic, or equivalently, the BSS measure in the CATANOVA framework, into location, dispersion, and higher order components. Even if a CATANOVA identifies an overall lack of variation, by considering this partition and calculations derived from them, it is possible to identify hidden, but statistically significant, sources of variation.

AB - The analysis of variance of cross-classified (categorical) data (CATANOVA) is a technique designed to identify the variation between treatments of interest to the researcher. There are well-established links between CATANOVA and the Goodman and Kruskal tau statistic as well as the Light and Margolin R2 for the purposes of the graphical identification of this variation. The aim of this article is to present a partition of the numerator of the tau statistic, or equivalently, the BSS measure in the CATANOVA framework, into location, dispersion, and higher order components. Even if a CATANOVA identifies an overall lack of variation, by considering this partition and calculations derived from them, it is possible to identify hidden, but statistically significant, sources of variation.

KW - Goodman and Kruskal tau statistic

KW - location, dispersion, and higher-order components

KW - orthogonal polynomials

UR - http://handle.uws.edu.au:8081/1959.7/10673

M3 - Article

SN - 0361-0926

JO - Communications in statistics : theory and methods

JF - Communications in statistics : theory and methods

ER -

Catanova for two-way contingency tables with ordinal variables using orthogonal polynomials

Abstract

Keywords

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