Homogeneity Tests for 2 x 2 Contingency Tables

Natalia Oliveira; Marcio Diniz; Adriano Polpo

doi:10.1007/978-3-319-12454-4_13

Homogeneity Tests for 2 x 2 Contingency Tables

Natalia Oliveira, Marcio Diniz, Adriano Polpo

Research output: Chapter in Book/Conference paper › Conference paper › peer-review

2 Citations (Scopus)

Abstract

Using the likelihood ratio statistic, we develop a significance index, called P-value, to test the hypothesis of homogeneity in 2 x 2 contingency tables. The P-value does not depend on asymptotic distributions, and is based on the elimination of the nuisance parameter. Therefore, we obtain the exact distribution of the likelihood ratio statistic in a way that is, moreover, compatible with the likelihood principle. For a better understanding of significance indices to test homogeneity, we perform a study comparing the P-value with some indices (likelihood ratio test (LRT), chi-square test) and with the full Bayesian significance test (FBST). This comparative study shows an interesting relation between all the analyzed indices, Bayesian and frequentist.

Original language	English
Title of host publication	INTERDISCIPLINARY BAYESIAN STATISTICS, EBEB 2014
Editors	A Polpo, F Louzada, LLR Rifo, JM Stern, M Lauretto
Publisher	Springer
Pages	163-171
Number of pages	9
ISBN (Print)	978-3-319-12453-7
DOIs	https://doi.org/10.1007/978-3-319-12454-4_13
Publication status	Published - 2015
Externally published	Yes
Event	12th Brazilian Meeting on Bayesian Statistics (EBEB) - Hotel Fazenda Hípica Atibaia, Atibaia, Brazil Duration: 10 Mar 2014 → 14 Mar 2014 https://www.ime.usp.br/~isbra/ebeb/ebeb2014/

Publication series

Name	Springer Proceedings in Mathematics & Statistics
Publisher	SPRINGER
Volume	118
ISSN (Print)	2194-1009

Conference

Conference	12th Brazilian Meeting on Bayesian Statistics (EBEB)
Country/Territory	Brazil
City	Atibaia
Period	10/03/14 → 14/03/14
Other	he Brazilian Meeting on Bayesian Statistics (EBEB) is in its twelfth edition. This series of meetings aims at strengthening the research on Bayesian methods and widening their application. It also provides an environment where Brazilian and international researchers collaborate, present their most recent developments and discuss on open problems. EBEB also allows graduate students to make contacts with experienced researchers. This year's meeting has a particular focus on discussing recent developments in the many viewpoints of Bayesian statistics, such as computational, theoretical, methodological and applied views.
Internet address	https://www.ime.usp.br/~isbra/ebeb/ebeb2014/

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10.1007/978-3-319-12454-4_13

Cite this

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title = "Homogeneity Tests for 2 x 2 Contingency Tables",

abstract = "Using the likelihood ratio statistic, we develop a significance index, called P-value, to test the hypothesis of homogeneity in 2 x 2 contingency tables. The P-value does not depend on asymptotic distributions, and is based on the elimination of the nuisance parameter. Therefore, we obtain the exact distribution of the likelihood ratio statistic in a way that is, moreover, compatible with the likelihood principle. For a better understanding of significance indices to test homogeneity, we perform a study comparing the P-value with some indices (likelihood ratio test (LRT), chi-square test) and with the full Bayesian significance test (FBST). This comparative study shows an interesting relation between all the analyzed indices, Bayesian and frequentist.",

author = "Natalia Oliveira and Marcio Diniz and Adriano Polpo",

year = "2015",

doi = "10.1007/978-3-319-12454-4\_13",

language = "English",

isbn = "978-3-319-12453-7",

series = "Springer Proceedings in Mathematics \& Statistics",

publisher = "Springer",

pages = "163--171",

editor = "A Polpo and F Louzada and LLR Rifo and JM Stern and M Lauretto",

booktitle = "INTERDISCIPLINARY BAYESIAN STATISTICS, EBEB 2014",

address = "Netherlands",

note = "12th Brazilian Meeting on Bayesian Statistics (EBEB) ; Conference date: 10-03-2014 Through 14-03-2014",

url = "https://www.ime.usp.br/\textasciitilde{}isbra/ebeb/ebeb2014/",

}

Oliveira, N, Diniz, M & Polpo, A 2015, Homogeneity Tests for 2 x 2 Contingency Tables. in A Polpo, F Louzada, LLR Rifo, JM Stern & M Lauretto (eds), INTERDISCIPLINARY BAYESIAN STATISTICS, EBEB 2014. Springer Proceedings in Mathematics & Statistics, vol. 118, Springer, pp. 163-171, 12th Brazilian Meeting on Bayesian Statistics (EBEB), Atibaia, Brazil, 10/03/14. https://doi.org/10.1007/978-3-319-12454-4_13

Homogeneity Tests for 2 x 2 Contingency Tables. / Oliveira, Natalia; Diniz, Marcio; Polpo, Adriano.
INTERDISCIPLINARY BAYESIAN STATISTICS, EBEB 2014. ed. / A Polpo; F Louzada; LLR Rifo; JM Stern; M Lauretto. Springer, 2015. p. 163-171 (Springer Proceedings in Mathematics & Statistics; Vol. 118).

Research output: Chapter in Book/Conference paper › Conference paper › peer-review

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T1 - Homogeneity Tests for 2 x 2 Contingency Tables

AU - Oliveira, Natalia

AU - Diniz, Marcio

AU - Polpo, Adriano

PY - 2015

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N2 - Using the likelihood ratio statistic, we develop a significance index, called P-value, to test the hypothesis of homogeneity in 2 x 2 contingency tables. The P-value does not depend on asymptotic distributions, and is based on the elimination of the nuisance parameter. Therefore, we obtain the exact distribution of the likelihood ratio statistic in a way that is, moreover, compatible with the likelihood principle. For a better understanding of significance indices to test homogeneity, we perform a study comparing the P-value with some indices (likelihood ratio test (LRT), chi-square test) and with the full Bayesian significance test (FBST). This comparative study shows an interesting relation between all the analyzed indices, Bayesian and frequentist.

AB - Using the likelihood ratio statistic, we develop a significance index, called P-value, to test the hypothesis of homogeneity in 2 x 2 contingency tables. The P-value does not depend on asymptotic distributions, and is based on the elimination of the nuisance parameter. Therefore, we obtain the exact distribution of the likelihood ratio statistic in a way that is, moreover, compatible with the likelihood principle. For a better understanding of significance indices to test homogeneity, we perform a study comparing the P-value with some indices (likelihood ratio test (LRT), chi-square test) and with the full Bayesian significance test (FBST). This comparative study shows an interesting relation between all the analyzed indices, Bayesian and frequentist.

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SN - 978-3-319-12453-7

T3 - Springer Proceedings in Mathematics & Statistics

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BT - INTERDISCIPLINARY BAYESIAN STATISTICS, EBEB 2014

A2 - Polpo, A

A2 - Louzada, F

A2 - Rifo, LLR

A2 - Stern, JM

A2 - Lauretto, M

PB - Springer

T2 - 12th Brazilian Meeting on Bayesian Statistics (EBEB)

Y2 - 10 March 2014 through 14 March 2014

ER -

Homogeneity Tests for 2 x 2 Contingency Tables

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