The regression coefficient proposed by Smith was estimated in accordance with Hatheway & Williams' method for linear plots to determine the optimal size of experimental plots for Eucalyptus grandis Hill, in a six-year-old uniformity trial located in Paraibuna, São Paulo. To estimate the soil heterogeneity coefficient, the method takes into account the correlation among the variance estimates, weighing the logarithms of the variance estimates by the information matrix elements. The basic estimates of reduced variance were obtained through the analysis of variance of a hierarchical classification using a random model. Optimal plot size was determined considering the number of replications required by the t test to detect a true mean difference at 80% level and 5% of probability for 10 and 20 treatments in a randomized block design. The soil heterogeneity coefficient estimated was 0.9049, indicating absence of correlation between contiguous plots. For fixed d and r values, results show that the plot size increases with the coefficient of variation. For fixed CV and d, the plot size decreases as r increases and for fixed CV and r, the plot size reduces with the increases of the true differences between the treatment means.
Soil heterogeneity coefficient; optimal size of linear plots; number of replications; difference between means
