Dimensionamento amostral para análise de trilha em caracteres de milho

Abstract

The objective of this study was to determine the sample size necessary to estimate the average, the coefficient of variation, the Pearson linear correlation coefficient and the direct effects of explanatory variables on grain yield in maize. In 361, 373 and 416 plants, respectively, of the simple, triple and double hybrids of the 2008/09 crop and, in 1,777, 1,693 and 1,720 plants, respectively, of the simple, triple and double hybrids of the 2009/10 crop, were measured eleven explanatory variables: plant height at harvest (AP), ear height (AIE), ear weight (PE), number of grain rows per ear (NF), ear length (CE), ear diameter (DE), cob weight (PS), cob diameter (DS), weight of hundred grains (MCG), number of grains per ear (NGR), grain length (CGR) and the main variable, grain yield (PROD). For each hybrid and crop, descriptives statistics for each variable were calculated and the correlation coefficients and direct effects of explanatory variables on PROD were estimated, in nine scenarios of traditional and ridge path analysis. Then, the sample size necessary to estimate the average, the coefficients of variation and of correlation and the direct effects of each explanatory variable on PROD were determined, for each type of hybrid, crop, scenario and type of path analysis, by resampling with replacement. The sample size necessary to estimate the mean and the coefficients of variation and of correlation ranges among hybrids, crops and variables or pairs of variables. The sample size necessary to estimate the direct effects ranges among hybrids, crops, scenarios, types of path analysis and explanatory variables. Independently of hybrid, crop and variable, 375 plants are enough to estimate the mean and the coefficient of variation with amplitude of the confidence interval of 95% (AIC95%) maximum of 10% and for the estimation of the correlation coefficients with a AIC95% maximum of 0.25. For the estimation of direct effects, with AIC95% maximum of 0.25, are required from 10 to 530 plants, depending of the type of hybrid, crop, scenario, type of path analysis and explanatory variable. The measurement of 120 plants is sufficient to estimate the average with AIC95% maximum of 20%, for the estimation of the coefficient of variation with AIC95% maximum of 15% and for the estimation of correlation coefficients with AIC95% maximum of 0.45, independently of the hybrid, crop and variable. The measurement of 120 plants is also sufficient for the estimation of the direct effects of AIE, CE and DE on PROD in the ninth scenario, with AIC95% maximum of 0.25, and in the ninth scenario, CE and DE have greater direct effects on PROD, independent of the type of hybrid, the crop and the type of path analysis.