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MANE 6313

Week 8, 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

Explain blocking on replicates in two-level factorial designs.

Blocking a Replicated \(2^k\) Factorial Design

  • A \(2^k\) factorial design with \(n\) replicates is identical to a blocked design where the block size is greater than \(2^k\)

  • See Example 7.1 on page 256

  • Make sure to randomly assign treatments within a block (or replicate)

  • Each block contains all \(2^k\) treatment combinations

  • Simplest experiments to design and analyze

A Simple Example of Confounding

  • Consider a \(2^2\) experiment with factors A and B

  • The experiment is run in two blocks. Block 1 contains the treatments \(a\) and \(ab\); block 2 contains the treatments \((1)\) and \(b\)

  • Write an estimator (contrast) for the block effects

  • Construct the contrasts for the effects \(A\), \(B\) and \(AB\)

A Simple Example of Confounding, continued

Block Size \(< 2^k\)

  • Often the block size is \(2^p\) for \(k\) factors where \(k>p\). This design is called incomplete because all the treatment combinations can not be performed in each block

  • Requires an intelligent method to assign treatments to blocks

  • These designs are run in two blocks, four blocks, eight blocks, etc.

  • Confounding usually occurs in these designs. Confounding occurs when information about certain treatment effects can not be distinguished from the block effect.