Topics in the body text of this DOE FAQ Alert are headlined below (the "Expert" ones, if any, delve into statistical details):

P.S. Quote for the month: The joy of discovery when plotting your data produces an insight buried in the numbers.

(Page down to the end of this e-zine to enjoy the actual quote.)

1: FAQ: Why does Stat-Ease recommend maintaining model hierarchy?

Original question (1 of 2) from a Quality Consultant and Trainer:

“When demonstrating in a DOE class that a two-factor interaction may be significant when the main effect of one of the factors is not, I advocated that, nevertheless, both parents should be included, in other words, model hierarchy maintained. As I explained, not doing so is tantamount to saying a factor which does not create a significant main effect, plays no part in the results, when, of course, it does, since it is part of the significant interaction effect. However, one of my students remains unconvinced. Can you help me provide a clear answer on the question?”

Answer:

You are right to say that it makes no sense to exclude parent(s) of an active interaction—they must not be overlooked for them having a significant impact when their co-parent gets set at specific level(s).

For the mathematical reasons as to why non-hierarchical models are not well-formulated, see “A Property of Well-Formulated Polynomial Regression Models, by Julio L. Peixoto, The American Statistician, February 1990, Vol 44, No. 1. This article illustrates via a case study on winter temperatures in the United States as a function of latitude and longitude,* how measures of fit, e.g. R², degrade when models exclude hierarchical terms. Based on this demonstration, Professor Peixoto recommended that “as a general rule polynomial regression models should be hierarchically well formulated, especially in applications where the origin of the predictor variables is arbitrary.” He allows for deviation from this principle of modeling only when using a polynomial to describe exact laws of physics, chemistry or the like.

For these reasons, our Design-Expert® software warns users who create non-hierarchical models and, if they agree that this should be maintained, it fills in the missing parent terms.

*Being headquartered in Minneapolis, I took notice of it making the list of 56 locations, but, surprisingly, only being ranked second (2 degrees F) as the coldest location on average for January over the mid-part of the 1900s—us being eclipsed by Bismarck, North Dakota (0 degrees F) for frigidity. Another thing I noticed is that your home city of Portland matches Minneapolis for northerliness, but, yet, it averaged over 30 degrees warmer. Not fair! From all this I learned not only to maintain hierarchical models, but to factor longitude (not to mention being near an ocean) into my expectations for winter weather.
—Mark

(Learn more about modeling by attending the three-day computer-intensive workshop on Modern DOE for Process Optimization. Click on the title for a description of this class and link from this page to the course outline and schedule. Then, if you like, enroll online.)

2: FAQ: For estimation of pure error in a characterization design, why replicate center points as opposed to one or more of the factorial points?

Original question (2 of 2) from a Quality Consultant and Trainer:“What should I tell someone when they ask why it is better to replicate the center points to estimate noise instead the factorial points?”

Answer: Replication of center points not only estimates pure error, but also provides a measure of curvature. However, I am always suspicious that highly-trained and incredibly meticulous experimenters will ‘game’ center point (CP) replicates, that is, re-do them when the results do not come out to what they expect from these standard operating conditions. Another pitfall for CPs is them being done consecutively without a re-set, that is, simply resampled and retested.* This bypasses all the variability of bringing the process to the specified conditions, thus underestimating error, which causes false-positive effects.

*Many years ago, I taught a class on site for a chemical manufacturer. An extremely concerned student brought me a regression analysis showing an infinite lack of fit for his model. Having worked in this industry as a process-development engineer, I knew immediately that the technician running the experiment—seeing the same conditions coming up at random intervals—simply copied down the previous results to the nth decimal. We called that “dry labbing” and always remained vigilant for such shortcuts on the part of non-diligent operators.
—Mark

3: Info alert: New edition of Multivariate Data Analysis book

The 6th Edition of Multivariate Data Analysis: An introduction to Multivariate Analysis, Process Analytical Technology and Quality by Design is newly released! Pat Whitcomb and I contributed to the DOE section of this up-to-date resource on chemometrics and multivariate data analysis (MVA). Check it out here at Amazon!

4: Events alert: Come to ENBIS conference in September for tips on “Using Split-Plot Diagnostics to Reveal Hidden Information”

Consultant Pat Whitcomb will come to Nancy, France, for the 18th annual conference of ENBIS (European Network for Business and Industrial Statistics) on September 2-6. If you can make it there, please visit the Stat-Ease booth. Also, do not miss Pat’s talk on “Using Split-Plot Diagnostics to Reveal Hidden Information”, which you will be sure to find very enlightening.

Click here for these and other upcoming appearances by Stat-Ease professionals.

5: Workshop alert: DOE classes coming to Cleveland—rock on by enrolling in this Hall of Fame city (apologies for pun intended)

You can do no better for quickly advancing your DOE skills than attending a Stat-Ease workshop. In these computer-intensive classes, our expert instructors provide you with a lively and extremely informative series of lectures interspersed by valuable hands-on exercises with one-on-one coaching. Enroll at least 6 weeks prior to the date so your place can be assured—plus get a 10% “early-bird” discount.

• Experiment Design Made Easy (EDME)
• Sep 26-27, Cleveland, OH
• Modern DOE for Process Optimization (MDOE)
• Sep 26-28, Cleveland, OH
• Mixture and Combined Designs for Optimal Formulations (MIXC)
  • Oct 22-24, Boston, MA

See this web page for complete schedule and site information on all Stat-Ease workshops open to the public. To enroll, scroll down to the workshop of your choice and click on it, or email our Client Specialist Rachel Pollack at workshops@statease.com. If spots remain available, bring along several colleagues and take advantage of quantity discounts in tuition. Or, consider bringing in an expert from Stat-Ease to teach a private, on-site class at your site.*

I hope you learned something from this issue. Address your general questions and comments to me at mark@statease.com.

Please do not send me requests to subscribe or unsubscribe—follow the instructions at the end of this message.

Sincerely,

Mark

Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc.
2021 East Hennepin Avenue, Suite 480
Minneapolis, Minnesota 55413 USA

P.S. Quote for the month: The joy of discovery when plotting your data produces an insight buried in the numbers.

"The greatest moments are those when you see the result pop up in a graph .”

—Emily Oster, American economist

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Acknowledgments to contributors:
—Students of Stat-Ease training and users of Stat-Ease software
—Stat-Ease consultants Pat Whitcomb, Martin Bezener, and Shari Kraber
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