Sample size involving multiple traits: An application to digestibility in cattle

The objective of this work was to estimate minimum sample size (n) for comp arison of treatments in experiments of consumption and digestibility of cat tle in a multitrait analysis. Data from digestibility of 72 heifers aging a pproximately 18 months and with 250 kg off live weight were used. A complet ely randomized experiment was conducted at Embrapa-Centro de Pesquisa de Pe cuaria do Sudeste, Sao Carlos, SP, Brazil, from 1988 to 1989, considering t he combination of nine treatments organized in a factorial 3 x 3 (three gen etic groups: Canchim, Nellore and 1/2 Canchim + 1/2 Nellore, and three diet ary levels of crude protein: 6, 10 and 13%, and eight heifers each). The en d points analyzed were feed consumption (g/kg(0.75)), digestible energy, re tained nitrogen (RN), RN (mg/kg(0.75)), and digestibilities of dry matter, crude protein, neutral detergent fiber and acid detergent fiber. The minimu m sample size required to detect significant differences (Delta) between me an vectors was calculated by a SAS program considering a t-variate normal d istribution with mean vector 0 and covariance matrix Sigma, Hotelling's T-2 test, F-distribution with noncentrality parameter (delta(Delta)(2)) and co mbinations of type I error (alpha) and power of the test (1-beta) and Delta . The calculated n ranged from 6 to 47, and was affected more by variation in Delta than variation in alpha or power of the test.