MANE 6313
Week 6, 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
Interpreting interactions in factorial designs.
Resources for the Week 6, Module C micro-lecture are:
SS Calculation for Interaction
Consider two factors \(A\) and \(B\)
- Step 1. Calculate sum of squares between the \(ab\) cell totals (subtotals)
\[
SS_{\mbox{Subtotals}}=\frac{1}{n}\sum_{i=1}^{a}\sum_{j=1}^by^2_{ij\cdot}-\frac{y^2_{\cdot\cdot\cdot}}{abn}
\]
-
Step 2. Calculate \(SS_A\) and \(SS_B\)
-
Step 3. \(SS_{AB}=SS_{\mbox{Subtotals}}-SS_{A}-SS_{B}\)
Rules for Interpreting Interactions
Limited to models with two-factor interactions and main effects
- If an interaction is statistically significant for a two-factor interaction, use the interaction plot to select the optimal setting
- If the interaction is not statistically significant for a two-factor interaction, use the main effect plot to select the optimal setting
- For more sophisticated designs, use the Response Optimizer