Designing experiments keeping it simple

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• Designing experiments - keeping it simple

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Designing experiments - keeping it simple
Three principles of experimental design

• Replication
• Randomisation
• Blocking

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Designing experiments - keeping it simple
Three principles of experimental design
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Designing experiments - keeping it simple
Three principles of experimental design
Design and analysis

• Replication

• Degrees of freedom

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Designing experiments - keeping it simple
Three principles of experimental design

• Replication
• Randomisation
• Blocking

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Designing experiments - keeping it simple
Three principles of experimental design
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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
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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
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Designing experiments - keeping it simple
Three principles of experimental design
Design and analysis

• Replication
• Randomisation

• Degrees of freedom
• Valid estimate of EMS

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Designing experiments - keeping it simple
Three principles of experimental design
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Designing experiments - keeping it simple
Three principles of experimental design
Design and analysis

• Replication
• Randomisation

• Degrees of freedom
• Valid estimate of EMS

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Designing experiments - keeping it simple
Three principles of experimental design

• Replication
• Randomisation
• Blocking

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Designing experiments - keeping it simple
Three principles of experimental design
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Designing experiments - keeping it simple
Three principles of experimental design
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Designing experiments - keeping it simple
Three principles of experimental design
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Designing experiments - keeping it simple
Three principles of experimental design
Design and analysis

• Replication
• Randomisation
• Blocking

• Degrees of freedom
• Valid estimate of EMS
• Elimination

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


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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

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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
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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
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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 16.67502.3917(-6.2250)
12.7817
Advantages of mean and differences
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Designing experiments - keeping it simple
Orthogonality
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Designing experiments - keeping it simple
Orthogonality
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Designing experiments - keeping it simple
Orthogonality
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Designing experiments - keeping it simple
Orthogonality
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Designing experiments - keeping it simple
Orthogonality
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Designing experiments - keeping it simple
Orthogonality
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Designing experiments - keeping it simple
Orthogonality
Design and analysis

• Replication
• Randomisation
• Blocking
• Orthogonality

• Degrees of freedom
• Valid estimate of EMS
• Elimination
• SeqAdj SS

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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 weve 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