Issue: Volume 8, Number 8
Date: August 2008
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:StatHelp@StatEase.com.

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):

—A nod for elemental videos from U Nottingham
—The bear necessity for experimenting
—Heads up: A great web site for keeping tabs on workday baseball.

Topics in the body text of this DOE FAQ Alert are headlined below. Given a plenitude of things worth alerting you too, I slacked off on FAQs and their answers. My excuse is taking some summer vacation that coincides with celebrating Independence. (Do you suppose I am referring to the separation of the United States from England; or could it be that I am celebrating the statistical assumption that one observation be independent of every other? Flip a coin!)

1. FAQ: How to interpret response plots after applying a transformation
2. FAQ: Is it good to delete an insignificant factor?
3. Expert-FAQ: Can Design-Expert® handle a response surface method (RSM) design on a simulation with over two dozen factors?
4. Book Giveaway: One copy of first edition of "Empirical Model-Building and Response Surfaces" by Box & Draper
5. Info Alert: Many more successful applications of DOE — check them out to see if any relate to your area of interest
6. Feature Alert: Published case study on mixture design illustrates ability of Design-Expert to handle inverted simplex
7. Review Alert: Design-Expert the software of choice for DOE
8. Webinar Alert: "Best ‘Pat-Tricks’ on Model Diagnostics"
9. Reader Response: Corrected total sums of squares in ANOVA
10. Events Alert: Need a speaker on DOE
11. Workshop Alert: See when and where to learn about DOE

P.S. Quote for the month: Message on statistician's voicemail.

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1. FAQ: How to interpret response plots after applying a transformation

-----Original Question-----
From: A senior systems engineer at a major aerospace company
"I have a question about data transformation. I know that you transform a response to achieve the statistical assumptions underlying the analysis of variance (ANOVA); for examples to achieve residuals being normally distributed. My question is about viewing the model graphs after a transformation: Do you have to go back and un-transform your response data? For example, what if you applied the inverse function — would your conclusions all be opposite if you used the transformed data when you looked at the model graphs?"

Answer (from Stat-Ease Consultant Wayne Adams):
"Everything you said about transforms is true. It is generally easier to interpret the graphs in the original scale (un-transformed). However, Stat-Ease software will un-transform things for you. When you are looking at the model graph, (or optimization, or point prediction) go to Display Options on the main menu and choose the "Responses in Original Scale" option to un-transform the graph and put things back into the units used to measure the response."

P.S. From Stat-Ease Consultant Shari Kraber:
"Be advised that Display Options only converts the final results — the analysis is still in the transformed units. The software provides a 'heads-up' on graphs by the legend "Original Scale." Savvy Stat-Ease software users who see this will then know that the predictions come from a model based on transformed response units."

(Learn more about transformations 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 then link from this page to the course outline and schedule. Then, if you like, enroll online.)

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2. FAQ: Is it good to delete an insignificant factor?

-----Original Question-----
From: Applied statistician at a specialty chemical manufacturer
"Mark, Let's say you've done a 2^3 factorial with some center points. Suppose then that one of the factors is not significant. Would you ever delete that factor altogether giving you more degrees of freedom for "pure" error? Thanks!"

Answer:
My philosophy is not to ever delete factors and presenting the freed up df's of residual as "pure" error. I worry that in a weak design important main effects may go unrecognized due to their lack of statistical significance. What sealed this concern for me was that I once ran a 7 factor in 8-run Res III ruggedness test that failed — it produced significant results with important effects. I then deleted insignificant factors and folded it over. Evidently some of the factors really were important but they were buried by the aliasing of two-factor interactions. It's safer not to do this!

"It is my own practice to recommend great caution in dropping factors. The simplification so produced is illusory."
—Cuthbert Daniel

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3. Expert-FAQ: Can Design-Expert handle a response surface method (RSM) design on a simulation with over two dozen factors?

-----Original Question-----
From: A DOE practitioner from France
"I am setting up a design for a simulation that depends on 27 factors. I would like to design a central composite design (CCD), that is to say a fractional factorial 2^(27-18) + 2*27 star points + 1 center point in order to get a clean quadratic model with interactions. Unfortunately, my old version of Design-Expert refuses to build such a DOE. It’s limited to only 21 factors! So this is a suggestion to improve Design Expert: Allow at least 31 factors in fractional factorial design. This will obtain a resolution V fractional factorial design with only 512 points. In order to do such a 2^(27-18) design by hand, do you know where I can find good factor generators for more than 21 factors?"

Answer:
I have good news: Our current version (V7.1) of Design-Expert ("DX") offers CCDs up to 50 factors by making use of new minimum-run resolution V (MR5) fractional factorial cores. For example, for 27 factors DX presents a design with 440 runs at a default of 'practical' alpha level going out 2.28 units (vs rotatable of over 4.4). For the free trial download of DX7.1, go to http://www.statease.com/soft_ftp.html. I think that after seeing all the great features of V7.1, especially its ability to handle dozens of factors, you will want to upgrade your obsolete version of DX.

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4. Book Giveaway: One copy of first edition of "Empirical Model-Building and Response Surfaces" by Box & Draper

(Sorry, due to the high cost of shipping, this offer applies only to residents of the United States and Canada.) Simply reply to this e-mail by August 15 if you'd like a free first-edition of "Empirical Model-Building and Response Surfaces" George E. P. Box, Norman R. Draper. Originally published in 1987 (John Wiley and Sons, New York), this book is a classic in the field of response surface methods (RSM) for process optimization.*

I will forward your e-mail entries to my assistant Karen. Do not expect to hear from either of us unless your name is drawn as a winner. However, we do appreciate your participation in these giveaways. Watch for more of these in future DOE FAQ Alerts. Your odds of winning a free book increase by entering each time around!

Reminder: If you reside outside the US or Canada, you are NOT eligible for the drawing because it costs too much to ship the books.

P.S. See my brief review of the second edition by George E. P. Box, Norman R. Draper — re-titled "Response Surfaces, Mixtures and Ridge Analysis" — in Book Alert item #4 of the April 2007 DOE FAQ Alert at http://www.statease.com/news/faqalert7-4.html.

*(Learn more about RSM by attending the three-day computer-intensive workshop "Response Surface Methods for Process Optimization." See http://www.statease.com/clas_rsm.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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5. Info Alert: Many more successful applications of DOE — check them out to see if any relate to your area of interest

Here are quite a number of outstanding case studies on DOE applied over a broad range of applications. I hope you see something relevant to your area of interest. If not, take a look at many others posted by us at http://www.statease.com/articles.html.

—"Benet Uses DOE to Reduce Time Required to Optimize Complex Design": Via a series of carefully selected computer simulations Dan Cler and his team at U.S. Army Benét Laboratories developed a new generation of muzzle brakes (this device redirects part of the gun’s propellant flow backwards to reduce recoil). See http://www.mil-embedded.com/articles/id/?3369 for published details, or view the original manuscript at http://www.statease.com/pubs/benetlabs.pdf.

—"Using Response Surface Methods (RSM)": Using RSM, Senior Research Scientist Robert identified a combination of factor values that increased a Wyeth biopharmaceutical yield by 11.6% and made the process much more robust. See the original manuscript at http://www.statease.com/pubs/wyeth_eutomer_yield.pdf.

—"Designed Experiment Optimizes Method for Removing Endocrine Disrupters," published by Environmental Science & Engineering Magazine in their March issue ,details a full-factorial design done by J. Peter Jones — a Canadian professor of chemical engineering, see http://preview.tinyurl.com/6rdj7c. Another version of this story is told by Laboratory Equipment — view this via http://preview.tinyurl.com/65yup9.*

* Note that I use TinyUrl to shorten links. This handy utility was developed by a fellow engineer from the University of Minnesota — see the 'heads-up' in this blog by technology columnist Julio Ojeda-Zapata for the St. Paul Pioneer Press: http://yourtech.typepad.com/main/2008/07/didja-know-tiny.html.
Also see http://www.startribune.com/lifestyle/style/24040159.html. Both of these links fit on one line so there is no need to shorten them!

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6. Feature Alert: Published case study on mixture design illustrates ability of Design-Expert to handle inverted simplex

In an article titled "Design of Experiments Helps Reduce Time to Remove Aerospace Coatings" Chris Hensley of Aerochem Inc. illustrates his use of mixture DOE to develop a chemical paint remover - see page 21 of the publication posted at http://www.sae.org/aeromag/techupdate/06-2008/2-28-5-7.pdf or view the manuscript at http://www.statease.com/pubs/aerochem.pdf. What I find remarkable (aside from Chris accomplishing a breakthrough improvement in performance of Aerochem's formulation!) is that our Design-Expert software recognizes an inverted simplex, which then can be automatically recoded from
lower to upper pseudocomponents — a much better geometry for modeling the response.*

If you have access to the latest version of DX, choose the simplex lattice design of the mixture tab, select 3 components and enter the total of 12 % with A: 0-5, B: 0-5 and C: 2-7. Click Yes when DX suggests U_Pseudo coding. Finish building the design and Evaluate it by going to Graphs and View Contour. Go back to Results and look over the VIFs (variance inflation factors). With View chosen for Annotated Evaluation you will be provided with explanation on this and other design statistics offered by Design-Expert.

Now rebuild the design, but this time click No to leave it in L_Pseudo. You then must switch to a D-optimal design. Evaluate this design and see that it is an inverted triangle.

*(To learn about coding of mixture components, attend the three-day computer-intensive workshop "Mixture Design for Optimal Formulations." For a complete description of this class, see http://www.statease.com/clas_mix.html. Link from this page to the course outline and schedule. Then, if you like, enroll online.)

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7. Review Alert: Design-Expert the software of choice for DOE

"Dissecting DoE Software" in May's Six Sigma Forum Magazine (Volume 7,Number 3) provides a review of alternative statistical programs from design and analysis of industrial experiments. It's posted at http://www.asq.org/pub/sixsigma/ (available only to ASQ members with appropriate membership type and/or Six Sigma Forum Magazine subscription).

"Design-Expert offers the most enjoyable interface, leading users through every step of the way." — Reviewers Tanco, Viles, Ilzarbe and Álvarez

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8. Webinar Alert: "Best ‘Pat-Tricks’ on Model Diagnostics"

You are invited to attend a free web conference by Stat-Ease Consultant Pat Whitcomb, who will offer up his "Best ‘Pat-Tricks’ on Model Diagnostics (What are they? Why use them? What good do they do?)." This free conference, which Pat will keep at an intermediate level statistically, will be broadcast on Tuesday, August 12 at 8 AM, USA Central Daylight Time (CDT), which is 13:00 in Coordinated Universal Time (UTC). (We are at UTC -5 under CDT.) It will be offered again at 8 PM that evening (01:00 UTC August 13 — Wednesday) and one more time the following day at 12 PM noon (17:00 UTC August 13).

For a copy of Pat's Powerpoint slides and a download of his data sets, go to http://www.statease.com/webinar.html. When developing these one-hour educational sessions, our
presenters often draw valuable material from Stat-Ease DOE workshops. Attendance may be limited, so sign up as soon as you see your way clear by contacting our Communications Specialist, Karen, via karen@statease.com . If you can be accommodated, she will send you the link for the WebConnect and dial-in for ConferenceNow voice via telephone (toll-free access extends worldwide, but not to all countries).

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9. Reader Response: Corrected total sums of squares in ANOVA

-----Original Response-----
From: Dr. Nico Laubscher, South Africa (formerly a Professor in the Department of Statistics at University of Stellenbosch)
Re: June's DOE FAQ Alert #2 FAQ. What is the applied use of "Corrected Total" in the analysis of variance (ANOVA) table? (See http://www.statease.com/news/faqalert8-06.html)

"Dear Mark,
I think you are pretty close in your assessment. In the pre- computer age it was relatively easy to compute (even by an electrical calculator such as the Marchant or Friden) the total sum of squares as well as the correction factor N(Y-bar)^2. All you then have to do is to subtract the "correction factor" and get the SSQ of deviations from the overall mean. The latter was then known as the corrected SSQ. See Box Hunter & Hunter, "Statistics for Experimenters" (1978), page 172.* It was called the corrected total SSQ in contrast to the raw SSQ. Frank Yates told me a long time ago, at Rothamsted in 1967, that many years before that time it took them 3 months on one occasion to compute the inverse of a 30 x 30 matrix! Today's statisticians have no idea how tough it was in those years. Thanks for an always interesting e-newsletter.
*PS. I could not find reference to Corrected SSQ in BHH2."

(Nico was featured in the last page of our May 2004 Stat-Teaser newsletter in a "Spotlight on South Africa." It pictures him and a majestic lion he shot (with a camera!) at Kruger National Park. See this posted at http://www.statease.com/news/news0405.pdf.)

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10. Events Alert: Need a speaker on DOE?

Click http://www.statease.com/events.html for a list of upcoming appearances by Stat-Ease professionals. We hope to see you sometime in the near future!

P.S. Do you need a speaker on DOE for a learning session within your company or technical society at regional, national, or even international levels? If so, contact me. It may not cost you anything if Stat-Ease has a consultant close by, or if a web conference will be suitable. However, for presentations involving travel, we appreciate reimbursements for airfare, hotel and meals — expenses only. In any case, it never hurts to ask Stat-Ease for a speaker on this topic. Contact Mark@StatEase.com if you have an event coming up with an open slot for a presentation.

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11. Workshop Alert: See when and where to learn about DOE

Seats are filling fast for the following DOE classes. If possible, enroll at least 4 weeks prior to the date so your place can be assured. However, do not hesitate to ask whether seats remain on classes that are fast approaching!

—> Experiment Design Made Easy (EDME)
(Detailed at http://www.statease.com/clas_edme.html)
> August 19-21 (Minneapolis, MN)
> September 30 through October 2 (Philadelphia, PA)

—> Response Surface Methods for Process Optimization (RSM)
(http://www.statease.com/clas_rsm.html)
> September 23-25 (Minneapolis)

—> Mixture Design for Optimal Formulations (MIX)
(http://www.statease.com/clas_mix.html)
> October 21-23 (Minneapolis)

—> DOE for DFSS: Variation by Design (DDFSS)
(http://www.statease.com/clas_ddfss.html)
> November 11-12 (Minneapolis)

—> Designed Experiments for Life Sciences (DELS)
> November 18-20 (Minneapolis)

See http://www.statease.com/clas_pub.html for complete 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 Elicia at 612.746.2038. 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.*

*Once you achieve a critical mass of about 6 students, it becomes very economical to sponsor a private workshop, which is most convenient and effective for your staff. For a quote, e-mail workshops@statease.com.

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

PS. Quote for the month — message on statistician's voicemail:

"Hello, this is probably 314-1592, yes, the house of the famous statistician. I'm probably not at home, or not wanting to answer the phone, most probably the latter, according to my latest calculations. Supposing that the universe doesn't end in the next 30 seconds, the odds of which I'm still trying to calculate, you can leave your name, phone number, and message, and I'll probably phone you back. So far the probability of that is about 0.645. Have a nice day."
—Alan Silverstein

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, especially Tryg Helseth and Neal Vaughn (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, #3-7 Jul 03, #3-8 Aug 03, #3-9 Sep 03 #3-10 Oct 03, #3-11 Nov 03, #3-12 Dec 03, #4-1 Jan 04, #4-2 Feb 04, #4-3 Mar 04, #4-4 Apr 04, #4-5 May 04, #4-6 Jun 04, #4-7 Jul 04, #4-8 Aug 04, #4-9 Sep 04, #4-10 Oct 04, #4-11 Nov 04, #4-12 Dec 04, #5-1 Jan 05, #5-2 Feb 05, #5-3 Mar 05, #5-4 Apr 05, #5-5 May 05, #5-6 Jun 05, #5-7 Jul 05, #5-8 Aug 05, #5-9 Sep 05, #5-10 Oct 05, #5-11 Nov 05, #5-12 Dec 05, #6-01 Jan 06, #6-02 Feb 06, #6-03 Mar 06, #6-4 Apr 06, #6-5 May 06, #6-6 Jun 06, #6-7 Jul 06, #6-8 Aug 06, #6-9 Sep 06, #6-10 Oct 06, #6-11 Nov 06, #6-12 Dec 06, #7-1 Jan 07, #7-2 Feb 07, #7-3 Mar 07, #7-4 Apr 07, #7-5 May 07, #7-6 Jun 07, #7-7 Jul 07, #7-8 Aug 07, #7-9 Sep 07, #7-10 Oct 07, #7-11 Nov 07, #7-12 Dec 07, #8-1 Jan 08, #8-2 Feb 08, #8-3 Mar 08, #8-4 Apr 08, #8-5 May 08, #8-6 June 08, #8-7 July 08, #8-8 August 08 (see above)

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