Multiple comparison for binomial
proportions using bootstrap

Nádia Giaretta BIASE[1]

Daniel Furtado FERREIRA1

§     ABSTRACT: The multiple comparisons methods and the analysis of variance are not reliable alternatives for comparing two or more binomial proportions when the experiments have only Bernoulli trials. However, this comparison can be made using the intensive computational techniques named infinite bootstrap. This work aimed to evaluate the performance of two binomial proportions bootstrap tests, computing the experimentwise type-I error rates and power. These two infinite bootstrap tests are distinguished by the estimators of the parameter pi.One of these tests considered the maximum likelihood estimator (ML) and the other took into account the Pan's estimator. Both tests were evaluated in different configurations considering the number of populations and the parameter values resulting from 2,000 Monte Carlo simulations. Pan´s and ML bootstrap tests had excellent performances, controlling the experimentwise type-I error rates at the same levels or at  lower levels than  those of significance nominal values in addition to elevated powers. Pan's bootstrap tests is preferable due to the better performance in situations where the binomial proportions are distant from 1/2 and sample sizes are small ( n £ 10).

§     PALAVRAS-CHAVE: Bernoulli trials; Monte Carlo method; Maximum likelihood and Pan's estimators.



[1]Departamento de Ciências Exatas, Universidade Federal de Lavras - UFLA, Caixa Postal 37, CEP: 37200‑000, Lavras, MG, Brasil. E-mail: nadiabiase@yahoo.com.br / danielff@ufla.br