A discussion on significance indices for contingency tables under small sample sizes

Autor(es)

Oliveira, Natalia L. ^[1] ; Pereira, Carlos A. de B. ^[2] ; Diniz, Marcio A. ^[3] ; Polpo, Adriano ^[3]

Afiliação do(s) autor(es)

^[1] Carnegie Mellon Univ, Dept Stat & Data Sci, Pittsburgh, PA 15213 - USA

^[2] Univ Sao Paulo, Dept Stat, Sao Paulo - Brazil

^[3] Univ Fed Sao Carlos, Dept Stat, Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: PLoS One; v. 13, n. 8 AUG 2 2018.
• Citações Web of Science: 3

Resumo

Hypothesis testing in contingency tables is usually based on asymptotic results, thereby restricting its proper use to large samples. To study these tests in small samples, we consider the likelihood ratio test (LRT) and define an accurate index for the celebrated hypotheses of homogeneity, independence, and Hardy-Weinberg equilibrium. The aim is to understand the use of the asymptotic results of the frequentist Likelihood Ratio Test and the Bayesian FBST (Full Bayesian Significance Test) under small-sample scenarios. The proposed exact LRT p-value is used as a benchmark to understand the other indices. We perform analysis in different scenarios, considering different sample sizes and different table dimensions. The conditional Fisher's exact test for 2 x 2 tables and the Barnard's exact test are also discussed. The main message of this paper is that all indices have very similar behavior, except for Fisher and Barnard tests that has a discrete behavior. The most powerful test was the asymptotic p-value from the likelihood ratio test, suggesting that is a good alternative for small sample sizes. (AU)

• Processo FAPESP: 12/16669-4 - Índices de significância para tabelas de contingência
• Beneficiário: Natália Lombardi de Oliveira
• Modalidade de apoio: Bolsas no Brasil - Iniciação Científica