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…