Monte Carlo evaluation of the ANOVA's F and Kruskal-Wallis tests under binomial distribution

Eric Batista Ferreira, Marcela C Rocha, Diego B Mequelino

Resumo


To verify the equality of more than two levels of a factor under interest in experiments conducted under a completely randomized design (CRD) it is common to use the F ANOVA test, which is considered the most powerful test for this purpose. However, the reliability of such results depends on the following assumptions: additivity of effects, independence, homoscedasticity and normality of the errors. The nonparametric Kruskal-Wallis test requires more moderate assumptions and therefore it is an alternative when the assumptions required by the F test are not met. However, the stronger the assumptions of a test, the better its performance. When the fundamental assumptions are met the F test is the best option. In this work, the normality of the errors is violated. Binomial response variables are simulated in order to compare the performances of the F and Kruskal-Wallis tests when one of the analysis of variance assumptions is not satisfied. Through Monte Carlo simulation, were simulated $3,150,000$ experiments to evaluate the type I error rate and power rate of the tests. In most situations, the power of the F test was superior to the Kruskal-Wallis and yet, the F test controlled the Type I error rates.

Palavras-chave


Poder; taxa de erro tipo I; simulação Monte Carlo; DIC

Referências


CAMPOS, H. de. Estatística experimental não-paramétrica. 4a ed. Piracicaba: FEALQ, 1983.349p.

FEIR, B.; TOOTHAKER, L. The ANOVA F-test versus the Kruskal-Wallis test: a robustness study. In: Annual Meeting of the American Educational Research Association, Chicago, 1974. URL http://eric.ed.gov/ERICWebPortal/search/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=ED091423&ERICExtSearch_Search$ Chicago, 1974.

KRUSKAL, W. H; WALLIS, W. A. Use of ranks in one-criterion variance analysis, Journal of the American Statistical Association, Washington, v. 47, p. 583-621, 1952.

LIMA, P. C.; ABREU, A. R. de. Estatística experimental: ensaios balanceados. Lavras:

UFLA, 2000. 99 p.

R CORE TEAM. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2011. ISBN 3-900051-07-0, URL http://www.R-project.org/.

REIS, G. M.; RIBEIRO, J. I. Jr. Comparação de testes paramétricos e não paramétricos aplicados em delineamentos experimentais. In: III Simpósio Acadêmico de Engenharia de Produção, Vicosa, 2007.Anais do III Simpósio Acadêmico de Engenharia de Produção, URL http:www.http://www.saepro.ufv.br/Image/artigos/SA03.pdf, Vicosa, 2007.

SIEGEL, S.; CASTELLAN, N. J. Jr. Estatística não-paramétrica para ciências do comportamento. 2 ed. Trad. S. I. C. Carmona. Porto Alegre: Artmed, 2006. 448p.

VIEIRA, S. Analise de variância (ANOVA). São Paulo: Atlas, 2006. 204p.

Sigmae, Alfenas,


Texto completo: PDF

Licença Creative Commons
Este trabalho está licenciado sob uma Licença Creative Commons Attribution 3.0 .