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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.

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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


Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication

  • Degrees of freedom


Designing experiments - keeping it simple

Three principles of experimental design

  • Replication

  • Randomisation

  • Blocking


Designing experiments - keeping it simple

Three principles of experimental design


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


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


Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication

  • Randomisation

  • Degrees of freedom

  • Valid estimate of EMS


Designing experiments - keeping it simple

Three principles of experimental design


Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication

  • Randomisation

  • Degrees of freedom

  • Valid estimate of EMS


Designing experiments - keeping it simple

Three principles of experimental design

  • Replication

  • Randomisation

  • Blocking


Designing experiments - keeping it simple

Three principles of experimental design


Designing experiments - keeping it simple

Three principles of experimental design


Designing experiments - keeping it simple

Three principles of experimental design


Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication

  • Randomisation

  • Blocking

  • Degrees of freedom

  • Valid estimate of EMS

  • Elimination




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


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 +


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


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


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


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+


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+


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)


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








Designing experiments - keeping it simple

Orthogonality

Design and analysis

  • Replication

  • Randomisation

  • Blocking

  • Orthogonality

  • Degrees of freedom

  • Valid estimate of EMS

  • Elimination

  • Seq=Adj SS


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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