Unreplicated Two-Level Factorial Experiment with Center Points
Chemical Yield Example

T
Set Up Design Matrix and Data Entry
DO Stat-->DOE-->Factorial-->Create Factorial Design
(images/chemical1.gif here)

Then enter data
(images/chemical2.gif here)

Full Factorial Design 


Factors:  2   Base Design:         2, 4
Runs:     9   Replicates:             1
Blocks:   1   Center pts (total):     5

All terms are free from aliasing.

Do  Stat--> DOE--> Factorial --> Factorial Plots
(images/chemical3.png here)


Do  Stat--> DOE --> Factorial --> Analyze Factorial Design

Factorial Fit: yield versus Time, Temperature 


Estimated Effects and Coefficients for yield (coded units)

Term               Effect     Coef  SE Coef       T      P
Constant                   40.4250   0.1037  389.89  0.000
Time               1.5500   0.7750   0.1037    7.47  0.002 **
Temperature        0.6500   0.3250   0.1037    3.13  0.035 *
Time*Temperature  -0.0500  -0.0250   0.1037   -0.24  0.821
Ct Pt                       0.0350   0.1391    0.25  0.814 <-- insignificant
                         Curvature  SE Curv

S = 0.207364   R-Sq = 94.27%   R-Sq(adj) = 88.54%
   est stdev


Analysis of Variance for yield (coded units)

Source              DF   Seq SS   Adj SS   Adj MS      F      P
Main Effects         2  2.82500  2.82500  1.41250  32.85  0.003
2-Way Interactions   1  0.00250  0.00250  0.00250   0.06  0.821
  Curvature          1  0.00272  0.00272  0.00272   0.06  0.814
Residual Error       4  0.17200  0.17200  0.04300 <-- est variance
  Pure Error         4  0.17200  0.17200  0.04300
Total                8  3.00222

Least Squares Means for yield
 
              Mean  SE Mean
Time
 30          39.65   0.1466
 40          41.20   0.1466
Temperature
 150         40.10   0.1466
 160         40.75   0.1466

Mean for Center Point = 40.46