Standard Error Plot Query—Followup to the DOE FAQ Alert, Expert FAQ #2, March 2007

-----Original Question-----

From: India
"I have tried a central composite design with two factors at three levels.  Why am I not getting a circular contour plot as shown in the February 2004 FAQ 1 on 'Interpreting the standard error plot'*?  Instead I see four dimples at the corners."
* http://www.statease.com/news/faqalert4-2.html

Answer (from Stat-Ease Consultant Pat Whitcomb):
"The standard error (SE) plot is a function of the number of runs and where they are positioned.  The defaults Design-Expert® uses for a two-factor CCD are:
—1 each of the four factorial runs (2^2) at ±1 coded levels
—1 each of the four axial (star) runs at ±1.41
—5 replicates of the center point (0 in coded space)

This design is rotatable and thus it produces the circular SE plot noted in the FAQ you refer to. Your design, however, is different: It has the axial points pulled in to ±1 — thus making it a face-centered design (FCD) with three levels for each of your factors (as noted in our original question.) The reduced range in axial points increases the SE on the perimeter of the design space, particularly on the centers of the edges.**

To make matters even worse, your design has only one center point rather than the five that our software recommends.  Decreasing the number of center points naturally increases the SE in the center of the design space.  This generates a mound in the center that combined with the high SE on the perimeter creates 'dimples' on the contour plot." See the dimply contour plot and 3D view from this altered FCD below.