A Nonparametric Test for Symmetry Based on Freeman and Halton's Ideas on Contingency Tables

Autor:	José M. González-Barrios, Alberto Contreras-Cristán
Rok vydání:	2009
Předmět:	Statistics and Probability Contingency table Bivariate data Distribution (number theory) Integer Modeling and Simulation Statistics Nonparametric statistics Symmetry (geometry) Statistical hypothesis testing Mathematics Test (assessment)
Zdroj:	Communications in Statistics - Simulation and Computation. 38:1856-1869
ISSN:	1532-4141 0361-0918
DOI:	10.1080/03610910903151443
Popis:	In this article, we propose a nonparametric method to test for symmetry in bivariate data. By using the extension of Fisher's exact treatment for 2 × 2 contingency tables proposed by Freeman and Halton (1951), we can test the hypothesis of equal distribution for two samples of integer valued variables. Then, by counting the number of observations belonging to each cell of a symmetric, appropriately built grid, we can produce the two samples of integers required to use this test for equal distribution. The resulting test for symmetry is potentially extendible to higher dimensions. A simulation study is performed to compare with some known tests (Bowker, 1948; Hollander, 1971; and its improvement given in Krampe and Kuhnt, 2007). Our proposal represents a competitive option as a test for symmetry.
Databáze:	OpenAIRE
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