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MANE 6313

Week 16, Module B

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

Select split-plot designs

Introduction to Split Plot Designs

  • When a design cannot be completely randomized, a split plot deisgn may occur
  • "All industrial experiments are split-plot experiments" - attributed to industrial statistician Daniel
  • Split plot designs have random effects
  • An example is provided at http://qualityengineering.utrgv.edu/RailwayGreaseOIT-Predictor/
  • Terminology uses agricultural terms

Split-plot Design

  • Textbook provides an excellent example

Split-plot Example, Description

A batch of pulp is produced by one of the three methods under study. Then this batch is divided into four samples, and each sampleis cooked at one of the four temperatures. Then a second batch of pulp is made up using another of the three methods. This second batch is also divided into four samples that are tested at the four temperature. The process is then repeated, until all three replicates (36 runs) of the experiment are obtained.

  • This is not a completely randomized design
  • The whole plot variable is the pulp preparation method
  • The sub plot (or split-plot) variable is the temperature
  • Design contains elements of nested designs (not covered)
  • This design incorporates random effect terms

Split-plot Example, Linear Model (Textbook 10th edition)

Split-plot Example, Expected Mean Squares

Split-plot Example, ANOVA

R Support

  • Two packages support split-plot designs:
  • agricolae
  • FrF2

Split-plot Summary

  • Are fairly common design occuring in the lab and industry
  • Variable are typically classified as hard or easy to change
  • It is important to identify that a split-plot has been conducted so correct analysis can be applied
  • If you have doubts, find someone with more statistical knowledge to consult with