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Simplifying Experimental Design: Key Principles and Methods

This guide emphasizes the fundamental principles of experimental design: Replication, Randomization, and Blocking. It explains how these concepts enhance the design and analysis of experiments to obtain valid results. The text further covers methods for fitting values and the importance of degrees of freedom in analysis. With practical examples and straightforward explanations, this resource serves as an essential tool for researchers aiming to design effective experiments while maintaining simplicity. Understand how to implement these principles in your experimental work.

sarah-cooper
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Simplifying Experimental Design: Key Principles and 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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