MANE 6313
Week 7, Module F
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 a Single Replicate of a 2k with Center Points using Minitab
Resources for the Week 7, Module F micro-lecture are:
Adding Center Points
-
Good idea if possible. Allows test for non-linearity.
-
Notation
\[
\begin{aligned}
n_c&-&\mbox{number of center points}\\
n_f&-&\mbox{number of observations at factorial points}\\
\bar{y}_f&-&\mbox{the average value at the factorial points}\\
\bar{y}_c&-&\mbox{the average value at the center point}
\end{aligned}
\]
Test for Pure Quadratic Curvature
- A second-order response model is defined to be
\[
y=\beta_0+\sum_{j=1}^k\beta_jx_j+\sum_{i<j}\sum\beta_{ij}x_ix_j+\sum_{j=1}^k\beta_{jj}x_j^2+\varepsilon
\]
-
Notice the model contains interaction terms and pure quadratic terms
-
Tests the hypothesis that \(H_0:\sum_{j=1}^k\beta_{jj}=0\) vs. \(H_1:\sum_{j=1}^k\beta_{jj}\neq 0\)
-
Calculate one degree of freedom sum of squares for pure quadratic curvature
\[
SS_{\mbox{pure quadratic}}=\frac{n_cn_f(\bar{y}_f-\bar{y}_c)^2}{n_f+n_c}
\]
- Perform \(F\) test
Problem 6.35
