Type I error and power of five multiple comparison procedures for means

Luís Henrique GIRARDI[1]


Lindolfo STORCK 2

§    ABSTRACT: The objective of this work was to evaluate the t, Tukey’s, Bonferroni’s, Duncan’s and Student-Newman-Keuls (SNK) tests for type I error and power, in scenarios formed by combinations of number of treatments, number of repetitions and coefficients of variation on condition of residuals normality. Were simulated, by Monte Carlo, eighty and twenty-five scenarios, respectively, for the type I error and to the power. The t-test controls the type I comparisonwise error rate (TPC) and tests Tukey, Bonferroni and SNK control the type I experimentwise error rate (TPE). The Duncan’s tests does not control neither the TPC or TPE. There are decreasing TPC of Tukey’s, Bonferroni’s, Duncan’s and SNK tests and the increase in TPE t and Duncan’s tests with the increasing number of treatments. There is increased power of the five tests with the increase in the size of the difference between means adjacent to the increase in the number of treatment. The t and Duncan’s tests have more power in relation to Tukey’s and Bonferroni’s, in that order, and SNK showed intermediate situation.

§    KEYWORDS: Simulation, Monte Carlo, comparisonwise error rate, experimentwise error rate.


[1] Departamento de Estatística, Instituto de Matemática, Universidade Federal do Rio Grande do Sul - UFRGS, CEP 91509-900, Porto Alegre, RS, Brasil. E-mail: henrique.girardi@gmail.com

[2] Departamento de Fitotecnia, Centro de Ciências Rurais - CCR, Universidade Federal de Santa Maria - UFSM, CEP 97105-900, Santa Maria, RS, Brasil. E-mail: cargnelutti@pq.cnpq.br / ,lindolfo@pq.cnpq.br