Modifications for the tukey test procedure and evaluation of the power and efficiency of multiple comparison procedures

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Conagin et al.

MODIFICATIONS FOR THE TUKEY TEST PROCEDURE AND EVALUATION OF THE POWER AND EFFICIENCY OF MULTIPLE COMPARISON PROCEDURES
Armando Conagin 1 ; Décio Barbin 2 *; Clarice Garcia Borges Demétrio 2
1 2

IAC - C.P. 28 - 13001-970 - Campinas, SP - Brasil. USP/ESALQ, Depto. de Ciências Exatas, C.P. 09 - 13418-900 - Piracicaba, SP - Brasil. *Corresponding author

ABSTRACT: Multiple pairwise comparison tests of treatment means are of great interest in applied research. Two modifications for the Tukey test were proposed. The power of unilateral and bilateral Student, Waller-Duncan, Duncan, SNK, REGWF, REGWQ, Tukey, Bonferroni, Sidak, unilateral Dunnet statistical tests and the modified tests, Sidak, Bonferroni 1 and 2, Tukey 1 and 2, has been compared using the Monte Carlo method. Data were generated for 600 experiments with eight treatments in a randomized block design, of which 400 had four and 200 eight blocks. The differences between the treatment means in relation to the control were 30%, 20%, 15%, 10%, 5%. Two extra treatments did not differ from the control. A coefficient of variation of 10% and a probability Type I error of a = 0.05 were adopted. The power of all the tests decreased when the differences to the control, decreased. The unilateral and bilateral Student t, Waller-Duncan and Duncan tests showed greater number of significative differences, followed by unilateral Dunnett, modified Sidak, modified Bonferroni 1 and 2, modified Tukey 1, SNK, REGWF, REGWQ, modified Tukey 2, Tukey, Sidak and Bonferroni. There is great loss of efficiency for all tests in relation to the unilateral Student t test for each difference of the treatment to the control, when the differences between means decrease. The modified tests were always more efficient than their original ones. Key words: multiple comparison statistical tests, type I errors, Monte Carlo method, power of tests

MODIFICAÇÕES NO PROCEDIMENTO PARA O TESTE DE TUKEY E PODER E EFICIÊNCIA