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MANE 6313

Week 16, Module A

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

Critique three-level factorial designs

Three -Level Factorial Designs

  • It is possible to build three-level factorial designs
  • Discussed in sections 9.1 - 9.3
  • Everything that can be done with 2-level factorial designs can be done with 3-level factorial designs:
  • Full factorial designs,
  • Designs with blocking
  • Fractional factorial designs

Three-Level Design

Three-Level Designs

  • Advantages:
  • Simple to design and understand
  • Allow for fitting of second-order models
  • Disadvantages:
  • Requires lots of runs (inefficient)
  • Confounding and block require modulus 3 math
  • Interactions are more difficult to interpret.

Example Problem

Example Problem, R

Degrees of Freedom

  • Notice that the main effects have two degrees of freedom: linear (L) and quadratic (Q)
  • The two-factor interaction contains four degrees of freedom: \(AB_{L\times L},\,AB_{L\times Q},\,AB_{Q\times L},\,AB_{Q\times Q}\)