Issue: Volume 3, Number 6
Date: June 2003
From: Mark J. Anderson, Stat-Ease, Inc. (www.statease.com)

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 previous DOE FAQ Alerts, please click on the links at the bottom of this page. 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 ask to your own questions about DOE, please address them to stathelp@statease.com.

Here's an appetizer to get this Alert off to a good start:

Click http://www.kettering.edu/~drussell/bats.html to see what one of Canada's leading producers of composite hockey sticks is doing to the good old American game of baseball. They've underwritten research by Kettering University applied physics professor Dr. Dan Russell to use a variety of high-tech tools, including math modeling software, to research the physics of composite baseball bats. Russell hopes to "tune" them for greater effect via the "trampoline effect." This increases the amount of energy transferred to the baseball. Pity the poor pitchers targeted by steroid-enhanced major league sluggers with bats optimized by Russell. Since this is a carry-over from hockey, maybe the baseball Commissioner will allow pads such as those that protect goalies from slap-shot pucks.

P.S. In the past few days, slugger Sammy Sosa of the Chicago Cubs created a scandal by drilling a hole in his wooden baseball bat and filling it with cork, thus making it lighter and possibly giving it the trampoline effect. However, Robert Adair in his book "The Physics of Baseball" said a ball hit off a corked bat loses about 1 per cent in distance. Sosa obviously needs some physics schooling! For more about Adair's experiments on baseball, see http://www.decatursports.com/articles/base/physics.htm.

Here's what I cover in the body text of this DOE FAQ Alert (topics that delve into statistical detail are designated "Expert"):

1. Info alert: The June issue of the Stat-Teaser (link provided) features a DOE semifolded to minimize misses from medieval missile machines
2. FAQ: A half-fraction on 3 factors at two-levels does not produce much information
3. FAQ: Treating multilevel factors as categorical versus numerical
4. Info alert: The May issue of Quality Progress features a DOE that uncovered the cause for bread not rising in a kitchen machine
5. Events alert: Stat-Ease is exhibiting and hosting a roundtable discussion at the Joint Statistical Meetings in San Francisco
6. Workshop alert: Stat-Ease is coming to San Jose later this Summer
7. Letter from reader: Inspiring comments about success with DOE

PS. Quote for the month: Wise words on screening for the unknown from a US government official (I challenge you to make sense of this press statement).

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1—Info alert: The June issue of the Stat-Teaser (link provided) features a DOE semifolded to minimize misses from medieval missile machines

Many of you by now have received a printed copy of the latest Stat-Teaser, but others, by choice or because you reside outside of North America, will get your first look at the June issue at http://www.statease.com/news/news0306.pdf. (Adobe recently upgraded their Reader software to version 6. For a free download, click http://www.adobe.com/products/acrobat/readstep2.html. You need Reader for viewing files in "pdf"—Portable Document Format.)

The feature article, "Messing with Medieval Missile Machines" describes how I uncovered the secrets to operating a simulated trebuchet operated by MoreSteam.com, a provider of web-based Six Sigma training. As a special favor to Stat-Ease, the developer of the trebuchet DOE-simulator, Bill Hathaway, offers temporary access at http://www.moresteam.com/trebuchet_se.cfm (simulator no longer available). For more details on the simulator, see item #3 in the January 2002 Alert posted at http://www.statease.com/news/faqalert2-1.html. At that time, the trebuchet was still at the beta-testing stage, so it was made available to readers of the DOE FAQ Alert.

The other story in the Stat-Teaser, authored by consultant Shari Kraber, provides details on the DOE that I used on the trebuchet. Her article is entitled "Semifolding—More Information, Fewer Runs."

Shari authored a new web-based course called "PreDOE" developed to give students a chance to review basic statistics prior to attending workshops offered by Stat-Ease. Details are provided in the current issue of the Stat-Teaser. Click on http://www.statease.net to take a look at the "PreDOE" site.

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2—FAQ: A half-fraction on 3 factors at two-levels does not produce much information

-----Original Question-----
From: Singapore
"I did a half fractional factorial of 3 factors (A,B,C) in 4 runs where the main effects are aliased with the 2-factor interactions. In the analysis, I picked factors B and C but the summary statistics indicated that factors B and C are not significant and accordingly the model is also not significant.

However, Log transformation was recommended. After applying a Log transformation, the model became significant and so did the factors B and C.

As I had picked factors B and C because they are significant, why was the Model Graph showing only the One Factor Plot and not the Interaction Graph? Is it because there is no real interaction between factors B and C? Even if it is so, I would still find it useful if the Interaction Graph can be made a default. Is there any way of making it so?"

Answer:
I'm sorry to say that you cannot do much with only 4 runs. The half-normal plot of the 3 effects cannot discriminate which, if any, might be significant. Nor can one properly assess transformations.

You went ahead and chose B(=AC) and C(=AB) for your model. ANOVA shows this to be significant relative to the remaining estimable effect of A(=BC). However, with such meager data, I would not put much faith in the statistics! The software then only shows one-factor plots of B and C, because that is what you put in the predictive model. To get the interaction of BC you must go back to Effects and click A into the model (you can also do this via View, Effects List). Then go to View, Alias List, right-click on A and change it to its alias BC. Then do ANOVA (no term now for residual, so ignore this) and press ahead to Model Graphs.

I advise that you not choose this design again. Instead perform the full 2^3 factorial. Furthermore, if you are studying numerical factors that may be near optimum levels, consider adding 4 center-points so you can test for curvature. These additional runs will also provide an estimate of pure error, thus strengthening your DOE considerably.

(Learn more about fractional two-level designs by attending the 3-day computer-intensive workshop "Experiment Design Made Easy." See http://www.statease.com/clasedme.html for a complete description. Link from this page to the course outline and schedule. Then, if you like, enroll online.)

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3—FAQ: Treating multilevel factors as categorical versus numerical

-----Original Question-----
From: Student in Missouri
"I am a graduate student using Design-Expert® software. I had some problems with my design. I am analyzing two factors over 3 and 4 levels; respectively, with 5 responses. I used the factorial design and used the factors categorically. Now if I change it to numerical what is the difference? With categorical factors it's not possible to get graphical optimization, am I right? What would be the best way to analyze this data and which design should be used that would give accurate and also help in the optimization?"

Answer (from Stat-Ease consultant Pat Whitcomb):
"In general it is best not to model numeric factors categorically. Categorical factors have discrete levels while numeric factors are continuous. Full second-order polynomials can be used with numeric factors, but NOT categorical factors. For example, squared terms, such as A^2 or B^2, cannot be modeled categorically. Furthermore, with categorical factors each optimum is a point as opposed to the continuum achieved with numeric factors."

I'd just like to add that users of Design-Ease® or Design-Expert software are allowed to change categorical factors by right-clicking over the header and choosing Make Numeric. (Mark)

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4—Info alert: The May issue of Quality Progress features a DOE that uncovered the cause for bread not rising in a kitchen machine

The May issue of Quality Progress features:

Augmented Ruggedness Testing To Prevent Failures
A breadmaking case study shows a medium resolution design is a good compromise between experimental runs and the information return in manufacturing settings.
MARK J. ANDERSON, principal, Stat-Ease Inc., Minneapolis

See this and other abstracts for articles that month at http://www.asq.org/pub/qualityprogress/past/0503/. However, to view the magazine online you must be a member of the American Society of Quality (ASQ). Otherwise see the original manuscript at http://www.statease.com/pubs/ruggednesstest.pdf.

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5—Events alert: Stat-Ease is exhibiting and hosting a roundtable discussion at the Joint Statistical Meetings in San Francisco

See http://www.amstat.org/meetings/jsm/2003/ for details on this year's Joint Statistical Meetings (JSM) on August 3 - 7, 2003 in San Francisco, California. JSM is the largest gathering of statisticians held in North America. It is sponsored by the American Statistical Association (ASA), the International Biometric Society (ENAR and WNAR), the Institute of Mathematical Statistics, and the Statistical Society of Canada. Activities include "oral presentations, panel sessions, poster presentations, continuing education courses and an exhibit hall with state-of-the-art statistical products" (such as Design-Expert software at booth 205!). A Stat-Ease consultant will lead roundtable Session 140 over lunch on Monday 12:30 PM, sponsored by the Section on Quality & Productivity. The topic is "Practical versus Statistical Aspects of Altering Central Composite Designs." See http://makeashorterlink.com/?Z336269C4 for more details. It will be interesting to share knowledge with expert practitioners of response surface methods (RSM).

Click http://www.statease.com/events.html for a list of where Stat-Ease consultants will be giving talks and doing DOE demos. We hope to see you sometime in the near future!

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6—Workshop alert: Coming to San Jose later this Summer

I am slated to teach the August 5-7 Experiment Design Made Easy (EDME) workshop in San Jose, California. I hope to see a good turn-out of students from the Far West and elsewhere. We've got lots of other classes coming up, mostly in Minneapolis, but in other cities too. See http://www.statease.com/clas_pub.html for schedule and site information on all Stat-Ease workshops open to the public. To enroll, click the "register online" link on our web site or call Stat-Ease at 1.612.378.9449. 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 class at your site. Call us to get a quote.

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7—Letter from reader: Inspiring comments about success with DOE

From: Philip Kneisl, Senior Chemical Engineer, Texas
"Dear Mark, I took one of your DOE workshops many years ago. I just thought I'd take some time and let you know that I still think you have a fantastic product in Design-Expert. I no longer get to do much DOE work myself (management gets us all someday) but I recently helped someone else design an experiment. Even though it has been 3 years since my last look at Design-Expert, it all came back in minutes. In less than 30 minutes my co-worker was sent off to start his experiments. Two weeks later he came back with his data sheets filled out. In another 30 minutes we had learned more about our process than in the previous 15 years!"

Response:
Philip, this is a great testimonial that supports my contention that learning DOE via hands-on workshops supported by easy-to-use software can be likened to learning how to ride a bicycle: In both cases, even if years intervene, it's still easy to do effectively, especially with the aid of easy-to-use software dedicated to DOE.

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I hope you learned something from this issue. Address your general questions and comments to me at:

mark@statease.com

Sincerely,

Mark

Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc. (http://www.statease.com)
Minneapolis, Minnesota USA

PS. Quote for the month—Wise words on screening for the unknown from a US government official (I challenge you to make sense of this press statement):

"There are known knowns. These are things we know that we know.
There are known unknowns. That is to say, there are things that we know we don't know.
But there are also unknown unknowns. These are things we do not know we don't know."

—Secretary of Defense Donald Rumsfeld on the war against terrorism

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

Acknowledgements to contributors:

—Students of Stat-Ease training and users of Stat-Ease software
—Fellow Stat-Ease consultants Pat Whitcomb and Shari Kraber (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, especially Tryg Helseth (http://www.statease.com/pgmstaff.html)
—Heidi Hansel, Stat-Ease marketing director, and all the remaining staff

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Interested in previous FAQ DOE Alert e-mail newsletters?
To view a past issue, choose it below.

#1 Mar 01, #2 Apr 01, #3 May 01, #4 Jun 01, #5 Jul 01 , #6 Aug 01, #7 Sep 01, #8 Oct 01, #9 Nov 01, #10 Dec 01, #2-1 Jan 02, #2-2 Feb 02, #2-3 Mar 02, #2-4 Apr 02, #2-5 May 02, #2-6 Jun 02, #2-7 Jul 02, #2-8 Aug 02, #2-9 Sep 02, #2-10 Oct 02, #2-11 Nov 02, #2-12 Dec 02, #3-1 Jan 03, #3-2 Feb 03, #3-3 Mar 03, #3-4 Apr 03, #3-5 May 03, #3-6 Jun 03 (see above)

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