1. Quantitative Methods Designing experiments - keeping it simple

2. 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 ReplicationDegrees 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 UnitTrRandTr 1A 2A 3A 4A 5B 6B 7B 8B 9C 10C 11C 12C 13D 14D 15D 16D sample 16 Tr RandTr

8. Designing experiments - keeping it simple Three principles of experimental design UnitTrRandTr 1AC 2AB 3AD 4AB 5BB 6BA 7BD 8BA 9CD 10CB 11CA 12CC 13DC 14DD 15DC 16DA 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. 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 Designing experiments - keeping it simple Fitted values and models

20. 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 + Designing experiments - keeping it simple Fitted values and models

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

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

23. 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 Designing experiments - keeping it simple So the fitted value for a plot in Block 2 planted with bean variety 6 is Fitted values and models

24. 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 Designing experiments - keeping it simple So the fitted value for a plot in Block 2 planted with bean variety 6 is 16.6750+ Fitted values and models

25. 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 Designing experiments - keeping it simple So the fitted value for a plot in Block 2 planted with bean variety 6 is 16.6750+2.3917+ Fitted values and models

26. 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 Designing experiments - keeping it simple So the fitted value for a plot in Block 2 planted with bean variety 6 is 16.6750+2.3917+(-6.2250) Fitted values and models

27. 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 Designing experiments - keeping it simple So the fitted value for a plot in Block 2 planted with bean variety 6 is 16.6750+2.3917+(-6.2250) = 12.7817 Fitted values and models

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 Design and analysis Replication Randomisation Blocking Orthogonality Degrees of freedom Valid estimate of EMS Elimination Seq=Adj SS Orthogonality

35. Designing experiments - keeping it simple Next week: Combining continuous and categorical variables Read Chapter 6 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 Last words…