Designing experiments - keeping it simple Quantitative Methods Designing experiments - keeping it simple

Three principles of experimental design Designing experiments - keeping it simple Three principles of experimental design Replication Randomisation Blocking

Three principles of experimental design Designing experiments - keeping it simple Three principles of experimental design

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

Three principles of experimental design Designing experiments - keeping it simple Three principles of experimental design Replication Randomisation Blocking

Three principles of experimental design Designing experiments - keeping it simple Three principles of experimental design

Three principles of experimental design 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

Three principles of experimental design 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

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

Three principles of experimental design Designing experiments - keeping it simple Three principles of experimental design

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

Three principles of experimental design Designing experiments - keeping it simple Three principles of experimental design Replication Randomisation Blocking

Three principles of experimental design Designing experiments - keeping it simple Three principles of experimental design

Three principles of experimental design Designing experiments - keeping it simple Three principles of experimental design

Three principles of experimental design Designing experiments - keeping it simple Three principles of experimental design

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

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

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

Fitted values and models 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

Fitted values and models 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 +

Fitted values and models 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 + 1 0.0417 + 4 -0.9584

Fitted values and models 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 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

Fitted values and models 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 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

Fitted values and models 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 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+

Fitted values and models 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 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+

Fitted values and models 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 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)

Fitted values and models 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 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

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

Design and analysis Orthogonality Replication Randomisation Blocking Designing experiments - keeping it simple Orthogonality Design and analysis Replication Randomisation Blocking Orthogonality Degrees of freedom Valid estimate of EMS Elimination Seq=Adj SS

Next week: Combining continuous and categorical variables 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