Replicated Two-Level Full Factorial Experiment
Pilot Plant Example

Data Entry
:
  1. Do  Stat-->DOE-->Factorial-->Create Factorial Design  (we are not actually create experimentation schedule but to take advantage of this program to create layout and useful for analysis later)(images/pilot1.gif here)
  2. Create column of yield (C8) containing two replicates (one complete set followed by the other)
  3. Our data has the run order, so need to change RunOrder (C2) accordingly(images/pilot2.gif here)
Analysis: Do  Stat-->DOE-->Factorial-->Analyze Factorial Design(images/pilot3.gif here)


Session Output

Factorial Fit: yield versus temperature, concentration, catalyst 


Estimated Effects and Coefficients for yield (coded units)

Term                                Effect    Coef  SE Coef      T      P
Constant                                    64.250   0.7071  90.86  0.000
temperature                         23.000  11.500   0.7071  16.26  0.000 **
concentration                       -5.000  -2.500   0.7071  -3.54  0.008 **
catalyst                             1.500   0.750   0.7071   1.06  0.320
temperature*concentration            1.500   0.750   0.7071   1.06  0.320
temperature*catalyst                10.000   5.000   0.7071   7.07  0.000 **
concentration*catalyst               0.000   0.000   0.7071   0.00  1.000
temperature*concentration*catalyst   0.500   0.250   0.7071   0.35  0.733

Only temperature, concentration, and temperature*catalyst are significant.

S = 2.82843   R-Sq = 97.63%   R-Sq(adj) = 95.55%

Analysis of Variance for yield (coded units)

Source              DF   Seq SS   Adj SS   Adj MS      F      P
Main Effects         3  2225.00  2225.00  741.667  92.71  0.000
2-Way Interactions   3   409.00   409.00  136.333  17.04  0.001
3-Way Interactions   1     1.00     1.00    1.000   0.13  0.733
Residual Error       8    64.00    64.00    8.000
  Pure Error         8    64.00    64.00    8.000
Total               15  2699.00

Unusual Observations for yield

Obs  StdOrder    yield      Fit  SE Fit  Residual  St Resid
  3         3  50.0000  54.0000  2.0000   -4.0000     -2.00R
 11        11  58.0000  54.0000  2.0000    4.0000      2.00R

R denotes an observation with a large standardized residual.

Estimated Coefficients for yield using data in uncoded units

Term                                      Coef
Constant                              -85.5000
temperature                           0.925000
concentration                         -1.52500
catalyst                              -71.5000
temperature*concentration           0.00750000
temperature*catalyst                  0.425000
concentration*catalyst                -0.42500
temperature*concentration*catalyst  0.00250000


 
Effects Plot for yield
 
(images/pilot4.png here)


Alias Structure
I
temperature
concentration
catalyst
temperature*concentration
temperature*catalyst
concentration*catalyst
temperature*concentration*catalyst


 
Residual Plots for yield
 
(images/pilot5.png here)
The plot of the residuals plotted in the order of data collection does appear to be suspicious.
 

Factorial Plots:
Do  Stat-->DOE-->Factorial-->Factorial Plots(images/pilot6.gif here)


Graphical Output From Factorial Plots

Main Effect Plot: Pilot Plant Example
 
(images/pilot7.png here)
Factor catalyst does appear to be insignificant.
 

Interaction Plot: Pilot Plant Example
 
(images/pilot8.png here)
The interaction temperature*catalyst does appear to be significant.
 

Cube Plot (data means) for yield
(images/pilot9.png here)

 
Since the interaction  temperature*catalyst  is significant, it makes sense to produce a cube plot in these two factors:
  1. Do  Stat-->DOE-->Factorial-->Factorial Plots
  2. Select only Cube Plot and only the factors involoved
(images/pilot10.gif here)

Cube Plot (data means) for yield
(images/pilot11.png here)
The changes of mean yields from 160°C  to  180°C at the two levels of catalyst A and B are 13 and 33 units respectively.  The changes are judged to be different (Why? hint: s.e.(diff in change)=?? )