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Learn about the importance of appropriate experimental design, including Latin squares, lattice squares, and rectangular lattices in research. Discover advantages, disadvantages, and key features of each design for accurate and reliable results.
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Last Class • Need for appropriate experimental design. • Single replicate designs. • Completely randomized block designs. • Randomized block designs. • Block arrangement.
Non-randomized Fertility Gradient Randomized
Models Yij = + gi + eij Yijk = + ri +gj + eijk
a. I II III IV I II b. III IV I III c. II IV
Latin Square Lattice Square Rectangular Lattices
Latin Square • Latin square designs have blocking in two directions at right angles to each other. • The blocks are referred to as rows and columns. • If there are n treatments to be tested there will be n x n experimental units (i.e. plots).
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square I II III Rows IV V I II III IV V Columns
Latin Square Yijk = +gi + rj + ck + eijk Where Yijk is the performance of the ith genotype in the jth row and kth column; in the overall mean; gi is the effect of the ith genotype; rj is the effect of the jth row; ck is the effect of the kth column; and eijk is the error term.
Latin Square • Advantage of latin square designs is their accuracy and ability to remove gradients in two directions. • Disadvantage is that they require large levels of replication. A 10 entry experiment would require 100 experimental units. • Latin square analyses are intolerant to missing values.
Lattice Square • Lattice squares look a little like Latin squares. • Lattice squares must consist of test entries that are the square of a whole number (4, 9, 16, 25, …), termed n x n lattices. • The number of replicates is determined by the number of entries; where the number of replicates is n +1.
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square I II III IV
Lattice Square Yijk = +gai + bak + rj + eijk Where Yijk is the performance of the ith genotype in the jth replicate and kth sub-block; in the overall mean; gai is the effect of the ith genotype adjusted according to sub-blocks; bak is the effect of the kth sub-block adjusted according to the entries in that block; rj is the effect of the jth replicate; and eijk is the error term.
Lattice Square • Lattice squares are usually more effective than RCB’s. • Have restraints on the number of entries and replicates.
Lattice Square • Lattice squares are resolvable. • However, they are not trulyrandomized. • Errors in plot arrangement (i.e. planting) renders them useless.
Rectangular Lattice • Lattice squares must have n x n, rectangular lattices have m x n entries. • Every entry in the rectangular lattice can appear in the same sub-block with any other entry in the test only once [(0,1) designs].
Rectangular Lattice I II
Rectangular Lattice I II