MANE 6313
Week 6, 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
Analyze factorial design using R
Two Factor Factorial Designs
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Will assume all factors are fixed and \(n\geq 2\)
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A completely randomized design was used to collect the data.
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Assume linear statistical model
\[
\begin{aligned}
y_{ijk}&=&\mu+\tau_i+\beta_j+(\tau\beta)_{ij}+\varepsilon_{ijk}
\left\{\begin{array}{l}i=1,2,\ldots,a\\
j=1,2,\ldots,b\\
k=1,2,\ldots,n\\ \end{array}\right.
\end{aligned}
\]
- Sum of squares formulas are given on pages 158-160
R and Design of Experiments
Model Formula in R
- An interaction in R is written A:B
- The model y~A*B indicates a crossed design and is equivalent to y~A+B+A:B
Problem 5-9 (9th Edition)
Preparation of Design of Experiments
- Non-randomized for homework problem
Response Variable
Model Analysis
- Notice the formula and the terms in the analysis of variance
Guidelines for Developing Models
- It is very common to build multiple models
- The general rule is that only terms that are statistically significant should be included in the model
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If an interaction is statistically significant, then all main effects and lower interactions must be included in the model whether they are statistically significant or not (term is hierarchy)
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For example if the A:B:C interaction is statistically significant, then the following terms must be in the model to preserve hierarchy (regardless if they are statististically significant or not statistically significant): A, B, C, A:B, A:C, B:C