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Experimental Design

Experimental Design. So Far In Experimental Design. Single replicate Designs. Completely Randomized Blocks. Randomized Complete Blocks . Latin Square Designs. Lattice Square Designs. Rectangular Lattice Designs. Two, or more, factor designs. Multiple Factor Designs.

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Experimental Design

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  1. Experimental Design

  2. So Far In Experimental Design • Single replicate Designs. • Completely Randomized Blocks. • Randomized Complete Blocks. • Latin Square Designs. • Lattice Square Designs. • Rectangular Lattice Designs.

  3. Two, or more, factor designs

  4. Multiple Factor Designs • An organism may vary in one factor according to conditions set by another factor. • Single factor experiments have limitations as they only relate to the conditions under which the factor is examined.

  5. Multiple Factor Designs • Examine the effect of differences between factor 1 levels. • Examine the effect of differences between factor 2 levels. • Examine the interaction between factor 1 levels and factor 2 levels.

  6. Interactions A B

  7. Interactions Yield A B Low N High N

  8. Interactions Yield A B Low N High N

  9. Interactions Yield A B Low N High N

  10. Split-Plot Designs Factorial Designs Strip-plot Designs

  11. Factorial Experimental Designs • Experimental design where all possible combinations of levels from two (or more) factors is called a factorial design. • Factorial designs are usually balanced, but unbalanced designs are possible (but not advised).

  12. Species Genotype Nutrient Water Soil type Seeding time Seeding rate Intercepted radiation Day length Location Temperature Feed stock Tillage Machinary Factors

  13. Factorial Experimental Design

  14. Factorial Experimental Design I II III

  15. Two-Factor Factorial Model Yijk =  + ri + dj + wk + dwjk + eijk Where Yijk is the performance of the the jth replicate, and the jth d factor and kth w factor;  in the overall mean; rj is the effect of the jth replicate; di is the effect of the ith d-factor; wk is the effect of the kth w-factor; dwjk is the interaction effect between dj and wk; and eijk is the error term.

  16. Three-Factor Factorial Model Yijk = +ri+dj+wk+gl+dwjk+dgjl+wgkl+dwgjki+eijk Where Yijk is the performance of the the jth replicate, and the jth d factor and kth w factor and lth g-factor;  in the overall mean; rj is the effect of the jth replicate; di is the effect of the ith d-factor; wk is the effect of the kth w-factor; gl is the effect of the lth g-factor; dwjk is the interaction effect between dj and wk; dgjl is the interaction effect between dj and wl; wgjl is the interaction effect between wk and gl; dwgjkl is the interaction effect between dj, wk and gl; and eijk is the error term.

  17. Factorial Experimental Designs • Can be used with any number of factors and factor levels. • Gives equal precision to estimating all factors and levels. • Greatest mistake by researchers is to include too many factors where interpretation of three-way interactions can be difficult.

  18. Split-Plot Designs • Three irrigation treatments • Four cultivars. • Two seeding rates (HIGH and low)

  19. Split-Plot Designs I II

  20. Split-Plot Designs I II

  21. Split-Plot Designs I II

  22. Split-Plot Designs I II

  23. Split-Plot Designs • Greater precision of measurement is required on one of the factors (assigned to sub-plots). • Less precision required on the other factor (assigned to main-plots). • The relative size of the main effect of two factors is different. • Management practices do not allow factorial designs.

  24. Split-Plot Design Main Plots . . . . . .

  25. Split-Plot Design Main Plots . . . . . .

  26. Split-Plot Design Main Plots

  27. Split-Plot Design Main Plots . . . . . . . . . . . . . . . . Sub-Plots

  28. Split-Plot Design I II III IV 3 2 1 4 3 1 4 2 3 1 2 4 2 4 1 3 3 2 1 4 3 1 4 2 3 1 2 4 2 4 1 3

  29. Split-Plot Design B A C I C A B II B A C III

  30. Split-Split-Plot Design

  31. Split-Split-Plot Design MP.3 MP.4 MP.1 MP.2

  32. Split-Split-Plot Design SP.1 MP.3 SP.2 SP.2 MP.4 SP.1 SP.1 MP.1 SP.2 SP.1 MP.2 SP.2

  33. Split-Split-Plot Design SP.1 MP.3 SP.2 SP.2 MP.4 SP.1 SP.1 MP.1 SP.2 SP.1 MP.2 SP.2

  34. Split-Split-Plot Design SP.1 MP.3 SP.2 SP.2 MP.4 SP.1 SP.1 MP.1 SP.2 SP.1 MP.2 SP.2

  35. Split-Plot Design Model Yijk =  + ri + gj + e(1)ij + tk + gtjk + e(2)ijk

  36. Split-Plot Design Model Yijk =  + ri + gj + e(1)ij + tk + gtjk + e(2)ijk

  37. Split-Plot Design Model Yijk =  + ri + gj + e(1)ij + tk + gtjk + e(2)ijk Where Yijk is the performance of the the jth replicate, and the jth main-plot and kth sub-plot;  in the overall mean; rj is the effect of the jth replicate; gi is the effect of the ith main-plot; e(1)ij is the main-plot error; tk is the effect of the kth sub-plot; gtjk is the interaction effect between gj and tk; and e(2)ijk is the sub-plot error term.

  38. Strip-Plot Design I IV B A C A C B III II

  39. Strip-Plot Design B A C A C B I II IV B A C A C B III IV II

  40. Strip-Plot Design B A C A C B I IV B A C A C B III II

  41. Strip-Plot Design B A C A C B 1 1 2 2 I IV 4 4 3 3 B A C A C B 3 3 1 1 III II 2 2 4 4

  42. Strip-Plot Design B A C A C B 1 1 2 2 I IV 4 4 3 3 B A C A C B 3 3 1 1 III II 2 2 4 4

  43. Strip-Plot Design Model Yijk = +ri+gj+e(g)ij+tk+e(t)ij+gtjk+e(gt)ijk Where Yijk is the performance of the the jth replicate, and the jth strip and kth strip;  in the overall mean; rj is the effect of the jth replicate; gi is the effect of the ith strip-plot; e(g)ij is the g-factor error; tk is the effect of the kth strip-plot; e(t)ij is the t-factor error; dwjk is the interaction effect between gj and tk; and e(gt)ijk is the sub-plot error term.

  44. Restraints

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