## 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 |
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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 | |

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 |
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Publisher | SPRINGER |

Volume | 118 |

ISSN (Print) | 2194-1009 |

### Conference

Conference | 12th Brazilian Meeting on Bayesian Statistics (EBEB) |
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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 |