Issue: Volume 9, Number 3
Date: March 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):

— Statistics on education and education on statistics
— How to arrest what’s-his-name’s forgetting curve
— Feeling belittled? Cut off relations with short people!

* 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 e-zine shares one-on-one communications with Stat-Ease StatHelp, anyone can post questions and answers to the Forum, which is open for everyone to see (with moderation). Check it out and weigh in!

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

1. FAQ: Selecting effects graphically via the half-normal plot
2. Expert-FAQ: How can I improve the overall desirability from my multiple response numerical optimization?
3. Book Giveaway: Winners announced
4. Info Alert: No more "spray & pray" by cosmetic formulators — Alberto Culver leads the way with mixture design
5. Webinar Alert (1st): "DOE — What's In It for Me" — an executive summary on the power of matrix-based multifactor testing
6. Events Alert: Learn "Best Practices to Plan/Analyze a Verification DOE"
7. Workshop Alert: See when and where to learn about DOE
8. A heads-up on web-based statistics training: Statistics.com

P.S. Quote for the month: A different twist on why the world needs engineers — not just scientists.

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1. FAQ: Selecting effects graphically via the half-normal plot

-----Original Question-----
From: Graduate researcher at a University in Scotland
"After taking your free statistics self-assessment at http://www.statease.net I now realize that I've got a lot to learn on the underlying fundamentals for design of experiments!*

Nevertheless, with the aid of Design-Expert® ("DX") software, I pressed ahead with the design and analysis of an experiment done for my PhD. I am trying to write up this part of my thesis, and I realize there are holes in my knowledge (lots of them!), especially in terms of what DX is doing to the data to get the results. In my two-level five-factor experiment, I managed to do a number of center points. I understand how the estimate of pure error are calculated based on these replicated runs. However, when I select the significant effects from the half-normal plot and then perform the analysis of variance (ANOVA), does DX automatically 'discard' the factors which are not involved in the significant effects and then use the data as a way of gaining 'hidden replication' (as Douglas Montgomery describes in his textbook "Design and Analysis of Experiments")?

I am not sure how the data set changes after I decide which effects are significant; what is the difference between testing every effect/interaction for significance and only testing those that appear to be significant from the half normal plot?"

*(The assessment steers those who need it to the web-based PreDOE course, which teaches the fundamental statistics used in design of experiments. For more details on this interactive resource, see
http://www.statease.com/clas_pre.html.)

Answer (from Consultant Shari Kraber):
"When you choose effects on the half-normal, you are simply separating the effects into the "model" pool and the "error" pool. The error pool becomes the denominator for all the F tests done on the individual model terms. If you selected everything for the model, then nothing would be left in error and the F test would not be very valid. Using the half-normal plot for your initial selection really gives a quick way of getting your best estimate of the total error, and then testing the "most likely" terms against a good base.

The hidden replication in a two-level factorial design comes from the fact that every low and high level for a factor is done multiple times, even though there were no actual design point replicates. If you did 32 runs, then 16 of those had A set low and 16 runs had A set high. The calculation of the effect estimate for
A is then the difference between the average of the "high" A's and the average of the "low" A's. So there is a lot of inherent power in averages of 16, thus this idea of hidden replication. This is the magic of DOE! It provides more information with more accuracy than one factor at a time experimentation."

(Learn more about selecting effects 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 —A different twist on why the world needs engineers — not just scientists:

"Science seeks to understand the world as it is; only engineering can change it."

—Henry Petroski, a professor of civil engineering at Duke University, paraphrasing a quote by Von Karman presented in a prior DOE FAQ Alert: "The scientist seeks to understand what is; the engineer seeks to create what never was." This reinforcement by Petroski of the engineering role was written in response to President Obama's inaugural address call for restoring "science to its rightful place." Let's not forget engineers! See the editorial by Petroski at http://preview.tinyurl.com/cjhna7.

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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