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MANE 6313

Week 8, Module C

Student Learning Outcome

  • Select an appropriate experimental design with one or more factors,
  • Select an appropriate model with one or more factors,
  • Evaluate statistical analyses of experimental designs,
  • Assess the model adequacy of any experimental design, and
  • Interpret model results.

Module Learning Outcome

Describe block generation techniques.

Techniques to Design Blocked 2-level Factorial Experiments

  • Technique to create two-level factorial designs in two blocks

  • Use highest possible interaction to generate blocks

  • Use linear combination

Interaction Technique

Use the ABC interaction to create two blocks for a \(2^3\) factorial experiment

Effect Generator

Designing a Blocked Experiment

  • Define a linear combination
\[ L=\alpha_1x_1+\alpha_2x_2+\cdots+\alpha_kx_k \]

  • We say that \(L\) is the defining contrast

  • Represent the treatment levels (\(x_i\)) as 0 (low level) and 1 (high level) and \(\alpha_i\) = 0 or 1

  • Choose an effect to confound with blocks

  • Calculate the quantity \(L\mbox{ mod } 2\) for the chosen effect

  • This approach is implemented in the R package DoE.base

  • Examine a \(2^3\) example in two blocks

Linear Combination Approach

Linear Combination Generator

Summary

  • Two techniques have been presented to design experiments in two blocks

  • The block that contains \((1)\) is the principal block

  • If you can replicate the experiment, use partial confounding to improve your design. For each replicate, select a different effect to generate the blocks. Thus, some information is available for each variable (more difficult to correctly design and analyze; not covered in this course).