Quantitative Methods Designing experiments - keeping it simple.
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Quantitative Methods Designing experiments - keeping it simple
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Transcript of Quantitative Methods Designing experiments - keeping it simple.
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 RandTr1 A2 A3 A4 A5 B6 B7 B8 B9 C10 C11 C12 C13 D14 D15 D16 D
sample 16 Tr RandTr
Designing experiments - keeping it simple
Three principles of experimental design
Unit Tr RandTr1 A C2 A B3 A D4 A B5 B B6 B A7 B D8 B A9 C D10 C B11 C A12 C C13 D C14 D D15 D C16 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
Designing experiments - keeping it simple
Fitted values and models
Term CoefConstant 16.6750BLOCK 1 0.0417 2 2.3917 3 -1.4750BEAN 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 CoefConstant 16.6750BLOCK 1 0.0417 2 2.3917 3 -1.4750BEAN 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 CoefConstant 16.6750BLOCK 1 0.0417 2 2.3917 3 -1.4750BEAN 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 CoefConstant 16.6750BLOCK 1 0.0417 2 2.3917 3 -1.4750BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.700016.6750 + 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 CoefConstant 16.6750BLOCK 1 0.0417 2 2.3917 3 -1.4750BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.700016.6750 + 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
So the fitted value for a plot in Block 2 planted with bean variety 6 is
Fitted values and models
Term CoefConstant 16.6750BLOCK 1 0.0417 2 2.3917 3 -1.4750BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.700016.6750 + 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
So the fitted value for a plot in Block 2 planted with bean variety 6 is
16.6750+
Fitted values and models
Term CoefConstant 16.6750BLOCK 1 0.0417 2 2.3917 3 -1.4750BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.700016.6750 + 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
So the fitted value for a plot in Block 2 planted with bean variety 6 is
16.6750+2.3917+
Fitted values and models
Term CoefConstant 16.6750BLOCK 1 0.0417 2 2.3917 3 -1.4750BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.700016.6750 + 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
So the fitted value for a plot in Block 2 planted with bean variety 6 is
16.6750+2.3917+(-6.2250)
Fitted values and models
Term CoefConstant 16.6750BLOCK 1 0.0417 2 2.3917 3 -1.4750BEAN 1 5.0750 2 5.7000 3 -0.6000 4 -0.2500 5 -3.7000 BEAN 1 5.0750 BLOCK 2 5.700016.6750 + 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
So the fitted value for a plot in Block 2 planted with bean variety 6 is
16.6750+2.3917+(-6.2250)
= 12.7817
Fitted values and models
Designing experiments - keeping it simple
Orthogonality
Designing experiments - keeping it simple
Orthogonality
Designing experiments - keeping it simple
Orthogonality
Designing experiments - keeping it simple
Orthogonality
Designing experiments - keeping it simple
Orthogonality
Designing experiments - keeping it simple
Orthogonality
Designing experiments - keeping it simple
Design and analysis
• Replication• Randomisation• Blocking• Orthogonality
• Degrees of freedom• Valid estimate of EMS• Elimination• Seq=Adj SS
Orthogonality
Designing experiments - keeping it simple
Next week: Combining continuous and categorical variables
Read Chapter 6
• 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
Last words…
