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 R-2 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.

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

Amenta P.
Methodology
2005

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 R-2 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.
Goodman and Kruskal tau statistic; Location, dispersion, and higher-order components; Orthogonal polynomials
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12070/2612
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