Issue: Volume 9, Number 5
Date: May 2009
From: Mark J. Anderson, Stat-Ease, Inc., Statistics Made Easy® Blog

Dear Experimenter,

Here's another set of frequently asked questions (FAQs) about doing design of experiments (DOE), plus alerts to timely information and free software updates. If you missed the previous DOE FAQ Alert, see below.

==> Tip: Get immediate answers to questions about DOE via the Search feature on the main menu of the Stat-Ease® web site. This not only pores over previous alerts, but also the wealth of technical publications posted throughout the site.

Feel free to forward this newsletter to your colleagues. They can subscribe by going to http://www.statease.com/doealertreg.html. If this newsletter prompts you to ask your own questions about DOE, please address them via mail to:[email protected].

For an assortment of appetizers to get this Alert off to a good start, see these new blogs at http://statsmadeeasy.net* (beginning with the most recent one):

—Awesome demonstration of design of experiments
—Technology facilitates building a stronger database on blood pressure and other medical measurements
—TV detectives stumble over odds of matching birthdays
—The science of "guesstimation"

* Need a feed from StatsMadeEasy to Microsoft's Outlook? See http://office.microsoft.com/en-us/outlook/HA101595391033.aspx.
** (See the comment to this blog and follow its link to an amazing collection of stats and graphs on record temps across the USA)

Also, Stat-Ease offers an interactive web site — its Support Forum for Experiment Design at http://forum.statease.com. Whereas this monthly ezine — the DOE FAQ Alert — shares one-on-one communications with Stat-Ease StatHelp, anyone (after gaining approval for registration) can post questions and answers to the Forum, which is open for all to see (with moderation). Check it
out and weigh in!

Here's a synopsis the most recent question posted (found in the DOE "Analysis" section):
>From: A Registered Member
"I'm analyzing a 2^3 full-factorial design with 2 blocks... What are the practical consequences of accepting the non-hierarchical model?"

See the answer (from Stat-Ease consultant Wayne Adams) and feel free to contribute to this discussion thread by getting registered as a user of the Support Forum for Experiment Design (if you're not already).

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

1. FAQ: How do predictive equations differ in terms of coded versus actual factors?
2. Expert FAQ: Why do some minimum-run resolution V (MR5) designs include one additional run beyond that needed to fit the two-factor interaction model?
3. Info Alert: Tablet formulators succeed via mixture design
4. Reader Response: Modeling mixture behavior as polynomials
5. Reader Contribution: Frustration with scientist objecting to the use of statistically designed experiments
6. Webinar alert (3rd): "DOE — What's In It for Me" — an executive summary on the power of matrix-based multifactor testing
7. Events Alert: Several quality talks on tap
8. Workshop Alert: Designed Experiments for Life Sciences (DELS) coming to Cambridge, Mass.

P.S. Quote for the month: What Gerry Hahn sees as major challenges to statisticians working in industry today.

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1. FAQ: How do predictive equations differ in terms of coded versus actual factors?

-----Original Question-----
From: Senior Research Associate and Applications Engineer
"We are working on DOE, and want to use the equation in the ANOVA in a spreadsheet. Two appear at the bottom of the sheet, 'Final equation in terms of coded factors,' and, 'Final equation in terms of actual factors.' There was no transform used, but the coefficients are different between the two equations (attached). Why is this, and which should we use for our spreadsheet exercise? The goal is to run confirmation tests, and the chemist would like to incorporate the solution equation into the spreadsheet and his notes."

Answer (from Stat-Ease Consultant Shari Kraber):
"Thank you for your question. Both the coded and the actual equations make the same predictions. To use the coded equation, you enter factor values such as -1 and +1 to represent the low and high levels of your design. To use the actual equation, you can enter factor levels in the original units of measure. The chemist would likely prefer to use the actual equation because it is in the natural units.

The coefficients in the coded equation for the main effects tell you how much the response is changing (and which direction) as you move one coded unit (-1 to 0, or 0 to +1) of the factor level. Because all factors are coded to the same range (-1 to +1) the regression is not overly weighted by a factor that might have a large range versus one that has a small range. You can look at the coded coefficients and see which factor has a larger effect.

However, the presence of interactions does start confusing any simple interpretations. The coefficients in the actual equation have to do double duty. They not only represent how much the response is changing, but also have to account for varying factor ranges. Typically, a factor that has a large range will end up with a small coefficient, while a factor with a small range will have a large coefficient.

So, to summarize: both equations will make the same predictions, but as an engineer or chemist, I prefer to use the Actual equation in practice. However, if someone plans to interpret the coefficients to understand which factor has a greater or lesser effect on the response, only the coded equation will provide the correct answer."

(Learn more about factorial models by attending the three-day computer-intensive workshop "Experiment Design Made Easy." See http://www.statease.com/clas_edme.html for a description of this class and link from this page to the course outline and schedule. Then, if you like, enroll online.)

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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. (http://www.statease.com)
2021 East Hennepin Avenue, Suite 480
Minneapolis, Minnesota 55413 USA

PS. Quote for the month —What Gerry Hahn sees as major challenges to statisticians working in industry today:

"The use of statistics...especially design of experiments...and the so-called democratization of statistics — providing increased accessibility to statistical software and on-line advice on how to use it... Today, indeed is a golden age for statistics in business and industry! But it is not a golden age for statisticians... This should be of concern, not only to the profession but also to management, because it can result in ineffective use of statistics and, more importantly, incorrect conclusions."

—Gerry Hahn, excerpted from p140 of "A Conversation with Gerry Hahn," Quality Engineering, V21, #2, 2009, April-June.

Trademarks: Stat-Ease, Design-Ease, Design-Expert and Statistics Made Easy are registered trademarks of Stat-Ease, Inc.

Acknowledgements to contributors:
—Students of Stat-Ease training and users of Stat-Ease software
—Stat-Ease consultants Pat Whitcomb, Shari Kraber and Wayne Adams (see http://www.statease.com/consult.html for resumes)
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert (http://www.statease.com/garyoehl.html)
—Stat-Ease programmers, led by Neal Vaughn and Tryg Helseth (http://www.statease.com/pgmstaff.html)
—Heidi Hansel Wolfe, Stat-Ease sales and marketing director, and all the remaining staff that provide such supreme support!

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