Quantitative methods
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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

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Quantitative methods

Quantitative Methods

Designing experiments - keeping it simple


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design

  • Replication

  • Randomisation

  • Blocking


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication

  • Degrees of freedom


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design

  • Replication

  • Randomisation

  • Blocking


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design


Quantitative methods

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


Quantitative methods

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


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication

  • Randomisation

  • Degrees of freedom

  • Valid estimate of EMS


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication

  • Randomisation

  • Degrees of freedom

  • Valid estimate of EMS


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design

  • Replication

  • Randomisation

  • Blocking


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design


Quantitative methods

Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication

  • Randomisation

  • Blocking

  • Degrees of freedom

  • Valid estimate of EMS

  • Elimination


Quantitative methods

Designing experiments - keeping it simple

Fitted values and models


Quantitative methods

Designing experiments - keeping it simple

Fitted values and models


Quantitative methods

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


Quantitative methods

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 +


Quantitative methods

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


Quantitative methods

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


Quantitative methods

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


Quantitative methods

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+


Quantitative methods

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+


Quantitative methods

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)


Quantitative methods

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


Quantitative methods

Designing experiments - keeping it simple

Orthogonality


Quantitative methods

Designing experiments - keeping it simple

Orthogonality


Quantitative methods

Designing experiments - keeping it simple

Orthogonality


Quantitative methods

Designing experiments - keeping it simple

Orthogonality


Quantitative methods

Designing experiments - keeping it simple

Orthogonality


Quantitative methods

Designing experiments - keeping it simple

Orthogonality


Quantitative methods

Designing experiments - keeping it simple

Orthogonality

Design and analysis

  • Replication

  • Randomisation

  • Blocking

  • Orthogonality

  • Degrees of freedom

  • Valid estimate of EMS

  • Elimination

  • Seq=Adj SS


Quantitative methods

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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