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Relative Efficiency of Two Randomized Block Designs Having Different Plot Sizes and Numbers of Replications and of Plots per Block 1
Author(s) -
Lin C. S.,
Binns M. R.
Publication year - 1986
Publication title -
agronomy journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.752
H-Index - 131
eISSN - 1435-0645
pISSN - 0002-1962
DOI - 10.2134/agronj1986.00021962007800030029x
Subject(s) - mathematics , randomized block design , statistics , plot (graphics) , split plot , efficiency , restricted randomization , block (permutation group theory) , block size , variance (accounting) , replicate , main effect , combinatorics , ecology , biology , accounting , randomization , estimator , key (lock) , business , bioinformatics , clinical trial
Equations for estimating relative efficiency of two randomized block designs having different numbers of replications, plot sizes, and numbers of plots per block are presented. The purpose is to use information of past experiments to improve the proposed design either through increasing the number of replications, or plot size, or both. A decision rule is presented, based on the soil heterogeneity index, b when b < 0.2, increase the number of replications; when b > 0.7, increase the plot size; when b is between 0.2 and 0.7, changes in both numbers of replications and plot size will be effective. To simpliy the case, 0.2 < b < 0.7, two tables are presented: one shows the relative variance for various plot sizes, and the other shows the ratio of required number of replications and experimental area to obtain a desired relative efficiency. By judicious use of these two tables, the optimum combination of replicate number and plot size can be obtained. Examples are given to demonstrate how the basic equations can be used to answer specific design questions such as: can the efficiency be improved while using the same experimental area, and how can a design be obtained with the same relative efficiency and with no restriction on area.