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 GenotypeNitrogen 1Nitrogen 2 A3,4684,088 B2,5044,791 A B

7. Interactions Low NHigh N A B Yield

8. Interactions Low NHigh N A B Yield

9. Interactions Low NHigh N A B Yield

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

13. Factorial Experimental Design Irrigation Days between defoliation 04812 1 dayI1.D0I1.D4I1.D8I1.D12 2 dayI2.D0I2 D4I2D8I2D12 3 dayI3.D0I3.D4I3D8I3D12

14. 3 t21 t13 t32 t41 t33 t4 3 t12 t21 t42 t11 t22 t3 3 t31 t22 t21 t33 t43 t1 2 t33 t21 t12 t44 t11 t4 1 t23 t12 t11 t12 t43 t2 1 t33 t32 t23 t41 t42 t3 I II III Factorial Experimental Design

15. Two-Factor Factorial Model Y ijk =  + r i + d j + w k + dw jk + e ijk Where Y ijk is the performance of the the j th replicate, and the j th d factor and k th w factor;  in the overall mean; r j is the effect of the j th replicate; d i is the effect of the i th d-factor; w k is the effect of the k th w-factor; dw jk is the interaction effect between d j and w k ; and e ijk is the error term.

16. Three-Factor Factorial Model Y ijk =  +r i +d j +w k +g l +dw jk +dg jl +wg kl +dwg jki +e ijk Where Y ijk is the performance of the the j th replicate, and the j th d factor and k th w factor and l th g-factor;  in the overall mean; r j is the effect of the j th replicate; d i is the effect of the i th d-factor; w k is the effect of the k th w-factor; gl is the effect of the l th g-factor ; dw jk is the interaction effect between d j and w k ; dg jl is the interaction effect between d j and w l ; wg jl is the interaction effect between w k and g l ; dwg jkl is the interaction effect between d j, w k and g l ; and e ijk 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 III

20. III

21. aCdB AcDb III

22. aCdBDCbA AcDbdcba CbaDDcBA cBAddCba dabCbcDA DABcBCda III

23.  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. Main Plots...... Split-Plot Design

25. 1 423 Main Plots...... Split-Plot Design

26. 1111 444422223333 Main Plots Split-Plot Design

27. 1B1B 1A1A 1C1C 1D1D 4B4B 4C4C 4A4A 4D4D 2D2D 2C2C 2A2A 2B2B 3D3D 3B3B 3C3C 3A3A Main Plots Sub-Plots................ Split-Plot Design

28. AABA BBAB ABBA BAAB BBAA AABB BABB ABAA 3 2 1 4 3 1 4 2 3 1 2 4 2 4 1 3 I II III IV Split-Plot Design 3 2 1 4 3 1 4 2 3 1 2 4 2 4 1 3

29. 241343 134221 I B A C 434231 123142 II C A B 242431 131324 III B A C Split-Plot Design

30. Split-Split-Plot Design

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

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

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

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

35. Split-Plot Design Model Y ijk =  + r i + g j + e(1) ij + t k + gt jk + e(2) ijk

36. Split-Plot Design Model Y ijk =  + r i + g j + e(1) ij + t k + gt jk + e(2) ijk

37. Split-Plot Design Model Y ijk =  + r i + g j + e(1) ij + t k + gt jk + e(2) ijk Where Y ijk is the performance of the the j th replicate, and the j th main-plot and k th sub-plot;  in the overall mean; r j is the effect of the j th replicate; g i is the effect of the i th main-plot; e(1) ij is the main-plot error; t k is the effect of the k th sub-plot; gt jk is the interaction effect between g j and t k ; and e(2) ijk is the sub-plot error term.

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

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

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

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

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

43. Strip-Plot Design Model Y ijk =  +r i +g j +e(g) ij +t k +e(t) ij +gt jk +e(gt) ijk Where Y ijk is the performance of the the j th replicate, and the j th strip and k th strip;  in the overall mean; r j is the effect of the j th replicate; g i is the effect of the i th strip-plot; e(g) ij is the g- factor error; t k is the effect of the k th strip-plot; e(t) ij is the t-factor error; dw jk is the interaction effect between g j and t k ; and e(gt) ijk is the sub- plot error term.

44. Restraints