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Quantitative Methods

Quantitative Methods. Designing experiments - keeping it simple. Designing experiments - keeping it simple. Three principles of experimental design. Replication Randomisation Blocking. Designing experiments - keeping it simple. Three principles of experimental design.

elvis-kirby
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Quantitative Methods

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  1. Quantitative Methods Designing experiments - keeping it simple

  2. Designing experiments - keeping it simple Three principles of experimental design • Replication • Randomisation • Blocking

  3. Designing experiments - keeping it simple Three principles of experimental design

  4. Designing experiments - keeping it simple Three principles of experimental design Design and analysis • Replication • Degrees of freedom

  5. Designing experiments - keeping it simple Three principles of experimental design • Replication • Randomisation • Blocking

  6. Designing experiments - keeping it simple Three principles of experimental design

  7. Designing experiments - keeping it simple Three principles of experimental design Unit Tr RandTr 1 A 2 A 3 A 4 A 5 B 6 B 7 B 8 B 9 C 10 C 11 C 12 C 13 D 14 D 15 D 16 D sample 16 Tr RandTr

  8. Designing experiments - keeping it simple Three principles of experimental design Unit Tr RandTr 1 A C 2 A B 3 A D 4 A B 5 B B 6 B A 7 B D 8 B A 9 C D 10 C B 11 C A 12 C C 13 D C 14 D D 15 D C 16 D A sample 16 Tr RandTr

  9. Designing experiments - keeping it simple Three principles of experimental design Design and analysis • Replication • Randomisation • Degrees of freedom • Valid estimate of EMS

  10. Designing experiments - keeping it simple Three principles of experimental design

  11. Designing experiments - keeping it simple Three principles of experimental design Design and analysis • Replication • Randomisation • Degrees of freedom • Valid estimate of EMS

  12. Designing experiments - keeping it simple Three principles of experimental design • Replication • Randomisation • Blocking

  13. Designing experiments - keeping it simple Three principles of experimental design

  14. Designing experiments - keeping it simple Three principles of experimental design

  15. Designing experiments - keeping it simple Three principles of experimental design

  16. Designing experiments - keeping it simple Three principles of experimental design Design and analysis • Replication • Randomisation • Blocking • Degrees of freedom • Valid estimate of EMS • Elimination

  17. Designing experiments - keeping it simple Fitted values and models

  18. Designing experiments - keeping it simple Fitted values and models

  19. Designing experiments - keeping it simple Fitted values and models Term Coef Constant 16.6750 BLOCK 1 0.0417 2 2.3917 3 -1.4750 BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000

  20. Designing experiments - keeping it simple Fitted values and models Term Coef Constant 16.6750 BLOCK 1 0.0417 2 2.3917 3 -1.4750 BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 16.6750 +

  21. Designing experiments - keeping it simple Fitted values and models Term Coef Constant 16.6750 BLOCK 1 0.0417 2 2.3917 3 -1.4750 BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BLOCK 16.6750 + 1 0.0417 + 2 2.3917 3 -1.4750 4 -0.9584

  22. Designing experiments - keeping it simple Fitted values and models Term Coef Constant 16.6750 BLOCK 1 0.0417 2 2.3917 3 -1.4750 BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.7000 16.6750 + 1 0.0417 + 3 -0.6000 2 2.3917 4 -0.2500 3 -1.4750 5 -3.7000 4 -0.9584 6 -6.2250

  23. Designing experiments - keeping it simple Fitted values and models Term Coef Constant 16.6750 BLOCK 1 0.0417 2 2.3917 3 -1.4750 BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.7000 16.6750 + 1 0.0417 + 3 -0.6000 2 2.3917 4 -0.2500 3 -1.4750 5 -3.7000 4 -0.9584 6 -6.2250 So the fitted value for a plot in Block 2 planted with bean variety 6 is

  24. Designing experiments - keeping it simple Fitted values and models Term Coef Constant 16.6750 BLOCK 1 0.0417 2 2.3917 3 -1.4750 BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.7000 16.6750 + 1 0.0417 + 3 -0.6000 2 2.3917 4 -0.2500 3 -1.4750 5 -3.7000 4 -0.9584 6 -6.2250 So the fitted value for a plot in Block 2 planted with bean variety 6 is 16.6750+

  25. Designing experiments - keeping it simple Fitted values and models Term Coef Constant 16.6750 BLOCK 1 0.0417 2 2.3917 3 -1.4750 BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.7000 16.6750 + 1 0.0417 + 3 -0.6000 2 2.3917 4 -0.2500 3 -1.4750 5 -3.7000 4 -0.9584 6 -6.2250 So the fitted value for a plot in Block 2 planted with bean variety 6 is 16.6750+2.3917+

  26. Designing experiments - keeping it simple Fitted values and models Term Coef Constant 16.6750 BLOCK 1 0.0417 2 2.3917 3 -1.4750 BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.7000 16.6750 + 1 0.0417 + 3 -0.6000 2 2.3917 4 -0.2500 3 -1.4750 5 -3.7000 4 -0.9584 6 -6.2250 So the fitted value for a plot in Block 2 planted with bean variety 6 is 16.6750+2.3917+(-6.2250)

  27. Designing experiments - keeping it simple Fitted values and models Term Coef Constant 16.6750 BLOCK 1 0.0417 2 2.3917 3 -1.4750 BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.7000 16.6750 + 1 0.0417 + 3 -0.6000 2 2.3917 4 -0.2500 3 -1.4750 5 -3.7000 4 -0.9584 6 -6.2250 So the fitted value for a plot in Block 2 planted with bean variety 6 is 16.6750+2.3917+(-6.2250) = 12.7817 Advantages of mean and differences

  28. Designing experiments - keeping it simple Orthogonality

  29. Designing experiments - keeping it simple Orthogonality

  30. Designing experiments - keeping it simple Orthogonality

  31. Designing experiments - keeping it simple Orthogonality

  32. Designing experiments - keeping it simple Orthogonality

  33. Designing experiments - keeping it simple Orthogonality

  34. Designing experiments - keeping it simple Orthogonality Design and analysis • Replication • Randomisation • Blocking • Orthogonality • Degrees of freedom • Valid estimate of EMS • Elimination • Seq=Adj SS

  35. Designing experiments - keeping it simple Last words… • Experiments should be designed and not just happen • Think about reducing error variation and • replication: enough separate datapoints • randomisation: avoid bias and give separateness • blocking: managing the unavoidable error variation • The statistical ideas we’ve been learning so far in the course help us to understand experimental design and analysis Next week: Combining continuous and categorical variables Read Chapter 6

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