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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

slide2

Designing experiments - keeping it simple

Three principles of experimental design

  • Replication
  • Randomisation
  • Blocking
slide3

Designing experiments - keeping it simple

Three principles of experimental design

slide4

Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication
  • Degrees of freedom
slide5

Designing experiments - keeping it simple

Three principles of experimental design

  • Replication
  • Randomisation
  • Blocking
slide6

Designing experiments - keeping it simple

Three principles of experimental design

slide7

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

slide8

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

slide9

Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication
  • Randomisation
  • Degrees of freedom
  • Valid estimate of EMS
slide10

Designing experiments - keeping it simple

Three principles of experimental design

slide11

Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication
  • Randomisation
  • Degrees of freedom
  • Valid estimate of EMS
slide12

Designing experiments - keeping it simple

Three principles of experimental design

  • Replication
  • Randomisation
  • Blocking
slide13

Designing experiments - keeping it simple

Three principles of experimental design

slide14

Designing experiments - keeping it simple

Three principles of experimental design

slide15

Designing experiments - keeping it simple

Three principles of experimental design

slide16

Designing experiments - keeping it simple

Three principles of experimental design

Design and analysis

  • Replication
  • Randomisation
  • Blocking
  • Degrees of freedom
  • Valid estimate of EMS
  • Elimination
slide19

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

slide20

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 +

slide21

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

slide22

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

slide23

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

slide24

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+

slide25

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+

slide26

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)

slide27

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

slide34

Designing experiments - keeping it simple

Orthogonality

Design and analysis

  • Replication
  • Randomisation
  • Blocking
  • Orthogonality
  • Degrees of freedom
  • Valid estimate of EMS
  • Elimination
  • Seq=Adj SS
slide35

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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