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Experimental Design

Experimental Design. Last Class. Need for appropriate experimental design. Single replicate designs. Completely randomized block designs. Randomized block designs. Block arrangement. Non-randomized. Fertility Gradient. Randomized. Completely Randomized Block. Randomized Complete Block.

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Experimental Design

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  1. Experimental Design

  2. Last Class • Need for appropriate experimental design. • Single replicate designs. • Completely randomized block designs. • Randomized block designs. • Block arrangement.

  3. Non-randomized Fertility Gradient Randomized

  4. Completely Randomized Block

  5. Randomized Complete Block

  6. Models Yij =  + gi + eij Yijk =  + ri +gj + eijk

  7. a. I II III IV I II b. III IV I III c. II IV

  8. Latin Square Lattice Square Rectangular Lattices

  9. 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).

  10. Latin Square I II III Rows IV V I II III IV V Columns

  11. Latin Square I II III Rows IV V I II III IV V Columns

  12. Latin Square I II III Rows IV V I II III IV V Columns

  13. Latin Square I II III Rows IV V I II III IV V Columns

  14. Latin Square I II III Rows IV V I II III IV V Columns

  15. Latin Square I II III Rows IV V I II III IV V Columns

  16. Latin Square I II III Rows IV V I II III IV V Columns

  17. Latin Square I II III Rows IV V I II III IV V Columns

  18. Latin Square I II III Rows IV V I II III IV V Columns

  19. Latin Square I II III Rows IV V I II III IV V Columns

  20. Latin Square I II III Rows IV V I II III IV V Columns

  21. Latin Square I II III Rows IV V I II III IV V Columns

  22. Latin Square I II III Rows IV V I II III IV V Columns

  23. Latin Square I II III Rows IV V I II III IV V Columns

  24. Latin Square I II III Rows IV V I II III IV V Columns

  25. Latin Square I II III Rows IV V I II III IV V Columns

  26. Latin Square I II III Rows IV V I II III IV V Columns

  27. Latin Square I II III Rows IV V I II III IV V Columns

  28. Latin Square I II III Rows IV V I II III IV V Columns

  29. Latin Square I II III Rows IV V I II III IV V Columns

  30. 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.

  31. 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.

  32. 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.

  33. Lattice Square I II III IV

  34. Lattice Square I II III IV

  35. Lattice Square I II III IV

  36. Lattice Square I II III IV

  37. Lattice Square I II III IV

  38. Lattice Square I II III IV

  39. Lattice Square I II III IV

  40. Lattice Square I II III IV

  41. Lattice Square I II III IV

  42. Lattice Square I II III IV

  43. Lattice Square I II III IV

  44. Lattice Square I II III IV

  45. 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.

  46. Lattice Square • Lattice squares are usually more effective than RCB’s. • Have restraints on the number of entries and replicates.

  47. Lattice Square • Lattice squares are resolvable. • However, they are not trulyrandomized. • Errors in plot arrangement (i.e. planting) renders them useless.

  48. 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].

  49. Rectangular Lattice I II

  50. Rectangular Lattice I II

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