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MANE 6313

Week 7, 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 \(2^k\) factorial designs

\(2^3\) Design

  • Very similar to the \(2^2\)

  • Geometric interpretation is a cube

  • You should be able to construct table 6.3 on page 203

  • Interesting properties of table 6.3

    • The AB interaction contrast can be found by multiplying the column for A times the column for B

  • Except for \(I\), every column sums to zero

  • The sum of the procedure of the signs in any two columns is zero (orthogonal)

    • Column \(I\) multiplied by any column leaves that column unchanged

    • The exponents in the product of any two columns are formed by using modulus arithmetic.

Design Matrix for \(2^3\) Design

Generalizing to \(2^k\) Designs

  • Very simple and straightforward

  • Calculate effect estimate (contrast)

  • Find sum of squares using contrast

  • Note: number of interactions grows rapidly. See Table 6.9 on page 216.

  • Recommended analysis given in table 6.8 on page 215 is very good.

Table 6.8