A new contribution on the problem of plot size in experiments with trees

Abstract

In a previous paper, a new method was proposed for the estimation of the optimum plot size of experimental plots for trees. The method, which takes in consideration the guard rows and uses the intraclass coefficient of correlation (p) among test trees within plots, defines as optimum size the number k of test trees which minimizes the variance of the estimate of a treatment mean for a fixed total number (N) of trees per treatment. In that previous paper the optimurn size was determined, for plots with one half or complete guard rows, with one or two test rows. In the present paper, the problem is generalized, the optimum size being searched when both the number of test trees (k) and the number of test rows (n) are variable. For the case of one half guard row the optimum number of test rows in n = [(1 - p)/p]^0.333, and for the case of a complete guard row is n = [2(1 - p)/p]^0.333, always with k = n², p>0. On the other hand, it is shown that, with complete guard rows, when changing a trial with k test trees per plot in n rows, with total number of trees per treatment N and area A, into another one with these parameters indicated by k', n', N' and A', keeping constant the variance of the estimate of a treatment mean, we have: A'/A = N'/N = {(1 + 2/n') (1 + 2n'/k') [1 + (k' - 1)p]}/ {(1 + 2/n) (1 + 2n/k)[1 + (k - 1)p]}.