Optimum size of plots in cocoa (Theobroma cacoa L.) a multivariate case
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Date
1987
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Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy
Abstract
A procedure to determine optimum size of experimental units in the multivariate case was proposed. For the purpose, the matrix of relative dispersion was defined and its determinant was used as the measure of variation for comparison of plots of different sizes. This procedure was illustrated with the help of observations on three characters of 738 trees of 'Forastero1 variety of cocoa raised in the' KADP farm of the Kerala Agricultural University, Vellanikkara. Optimum plot size also was obtained in the univariate case.
The following three different methods of plot formation were used in this investigation. Method I
The whole set of trees were divided into compact blocks of different sizes and plots of one to fifteen trees were formed by combining adjacent trees in the field.
Method II
All trees were arranged in descending order of magnitude of trunk girth and of the canopy spread separately and were divided into blocks of required size. Plots of one to fifteen trees were formed by combining adjacent trees in the list in each block for each arrangement.
Method III
The trees were first arranged in descending order of magnitude of each character and they were divided into blocks of required size. Plots of different sizes were formed within each block by the following procedure, let there be 'nk* trees in a block. The nk trees were divided into 1 n 1 groups of 'It* trees each bearing continuous serial numbers * When 'n' is even, the 1st plot was formed by combining 1th tree from each of the first 'n/2* groups and (k-i+j)st tree from each of the remaining 'n/2' groups, where i=1,2,....n. When 'n1 is odd, ith plot was formed by combining the i^h tree from each of the first (J[n+iy2) groups and (k-i+fy9^ tree from each of the remaining [(n-lj/2) groups, whore 1=1,2, n.
Of the three methods of plot formation Method III, which was proposed in this study was found to be superior to Methods I and II for experiments in established gardens and Method I for experiments for which fresh planting is required
Optimum size of plots were al so determined by three different methods viz.,
(a) that which requires minimum experimental material for a specified precision
(b) that which has maximum efficiency and
(c) that for which the best fitting model has maximum curvature.
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