Issue: Volume 6, Number 2
Date: February 2006
From: Mark J. Anderson, Stat-Ease, Inc. (http://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 the previous DOE FAQ Alert, please click on the links at the bottom of this page. If you have a question that needs answering, click the Search tab and enter the key words. This finds not only answers from previous Alerts, but also other documents posted to the Stat-Ease web 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.

This plain text message may be easier to read if you do not remove the line breaks. If you use Microsoft Outlook, press the bar labeled "Extra line breaks in this message were removed." In newer versions select "Restore line breaks."

Here's an appetizer to get this Alert off to a good start: A photo of the wondrous Ferris Wheel at the 1893 Chicago World’s Fair http://www.randomhouse.com/crown/devilinthewhitecity/ferris.html which I came across while reading a great book—"The Devil in the White City" by Erik Larson. According to the web site posted by the publisher (Random House), this 250-foot diameter wheel carried 36 cars holding 60 riders each (2160 people total!). It was supported by two 140-foot steel towers connected by a 45-foot axle—the largest single piece of forged steel ever made at the time. This original Ferris wheel moved on to another location before being scrapped after the turn of the century. A hundred years later the London Eye became the sensation for this millennium. The operators distinguish their wheel from Ferris's because its capsules are enclosed, positioned on the outside and supported by an A-Frame. On a beautiful cloudless day without a breath of wind, I waited in line to get on the Eye when I was last in London, but it then closed down due to high temperatures (80 degrees F) and the greenhouse warming within its 32 glassy capsules. John H. Lienhard, Professor Emeritus of Mechanical Engineering and History at the University of Houston, reports that the Eye carries up to 800 people (25 per capsule) through one 30 minute rotation—far less than that of Ferris's Wheel over a century before. For Professor Lienhard's report on the London Eye, including photos, see http://www.uh.edu/engines/epi1923.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. FAQ: Variations in how r-squared is calculated
2. Response to Stat-Teaser quote: Not so simple
3. Tutorial alert: Five new guided tours of features offered in version 7 (new!) of Design-Expert® software
4. Winners of free books (US/Canada only): Drawing for two copies of Montgomery's "Design and Analysis of Experiments" (5th Edition) plus "DOE Simplified" and "RSM Simplified" (both books autographed by authors Anderson and Whitcomb)
5. Events alert: First European DOE User Meeting for Design-Expert and Design-Ease Users, Belgium, April 24-25
6. Workshop alert: See when and where to learn about DOE

PS. Quote for the month: Wise words on experimental design by Box, Hunter and Hunter from their new edition of "Statistics for Experimenters."

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1. FAQ: Variations in how r-squared is calculated

-----Original Question-----
From: Indiana
"I recently came across a simple randomized complete block design (RCBD) in one of Montgomery's DOE books where the output is from Design-Expert (DX) software. When I reproduced this case with my general statistical software, it reported a higher r-squared—0.938 versus 0.828 from DX. Here are the sum squares (SS) reported by Design-Expert:

Block 0.825
Model 0.385
Residual 0.080
Total 1.29

Can you explain the difference in r-squared?"

Answer (from Stat-Ease Consultant Wayne Adams):
"When computing the analysis of variance (ANOVA), Stat-Ease software removes the sum of squares (SS) due to the blocks from the sum of squares for the model (SSModel) and total (SSTotal—corrected for the mean). In this case the r-squared is computed by this simple formula*:
R-squared = SSModel/(SSTotal-SSBlock) = 0.385/(1.29-0.825) = 0.385/0.465 = 0.828

On the other hand, your statistical software computed it this way:
R-squared = (SSModel+SSblock)/SSTotal = (0.385+0.825)/1.29 = 1.21/1.29 = 0.938

We assume blocking is introduced to deal with unavoidable changes—for example, day-by-day differences. By including the block sum of squares ("SSBlock") in the SSModel, your general statistics program assumes that differences such as days can be controlled. This obviously cannot be expected in real life."

*(Users of Design-Expert version 7 software will find more detailed formulas in program Help under the topic of "ANOVA Output.")

PS. Looking through my copy of the 6th Edition of Montgomery's "Design and Analysis of Experiments" (available for purchase at http://www.statease.com/prodbook.html), I see that this question stems from a study on hardness testing equipment provided at the outset of Chapter 4 on randomized blocks, latin squares and related designs. Instructors using this textbook for class gain access to a great deal of supplementary material on the internet. For example to see a brief presentation on the case discussed above, including Design-Expert outputs, click the "pt_03.ppt" link at http://www.math.aau.dk/~slb/kurser/design-04/slides/.

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2. Response to Stat-Teaser quote: Not so simple

From: Stat-Ease Consultant Wayne Adams*

"A little something about the Albert Einstein quote in your December Stat-Teaser cover-page article "Struggle for Power vs. Resolution vs. Simplicity in an ASTM Standard" (see http://www.statease.com/news/news0512.pdf): "Everything should be made as simple as possible, but not one bit simpler." Occam's Razor is not equivalent to the idea that 'perfection is simplicity'. Albert Einstein probably had this in mind when he wrote in 1933 that "The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience" often paraphrased as "Theories should be as simple as possible, but no simpler." It often happens that the best explanation is much more complicated than the simplest possible explanation because it requires fewer assumptions. Some people have oversimplified Occam's Razor as 'The simplest explanation is the best (or true) one'."

For more on Occam's Razor from the Department of Mathematics of the University of California Riverside, see this Physics and Relativity FAQ by Scott Chase, Michael Weiss, Philip Gibbs, Chris Hillman, and Nathan Urban (copyright 1992—2002): http://math.ucr.edu/home/baez/physics/General/occam.html.

*(Wayne just joined Stat-Ease last Fall. See his picture and credentials at http://www.statease.com/wayneadams.html.)

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3. Tutorial alert: Five new guided tours of features offered in version 7 (new!) of Design-Expert software

A few weeks ago I posted a number of new Design-Expert version 7 (DX7) tutorials at http://www.statease.com/dx70_man.html:
—"DX7-02E-SplitPlotGen" on split plot general factorials
—"DX7-02F-NestedGen" for general factorials with nested factors
—"DX7-03D-TwoLevelSplitPlot" on a two-level factorial split plot
—"DX7-03C-Foldover" the whimsical story of Lance Legstrong and friend/trainer Sheryl Songbird, and how they win a bicycle race using a low-resolution two-level factorial, and then figure out what really happened via full and semi foldovers.

If you download any of these portable document formats (pdf), click the link titled "dx7tutor.exe" to a self-extracting Zip file with new and revised DX7 tutorial data files.

For a free, fully-functional 45-day trial of Design-Expert V7 , click this link: http://www.statease.com/dx7trial.html. Pricing for new licenses and upgrades can be seen at the Stat-Ease e-commerce site: http://www.statease.com/prodsoft.html.

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4. Winners of free books (US/Canada only): Drawing for two copies of Montgomery's "Design and Analysis of Experiments" (5th Edition) plus "DOE Simplified" and "RSM Simplified" (both books autographed by authors Anderson and Whitcomb)

Sorry, due to the high cost of shipping, this offer applied only to residents of the United States and Canada, scores of whom sent me an e-mail that they'd appreciate a free book on design of experiments.

The winners of Montgomery's "Design and Analysis of Experiments" (5th Edition), chosen at random (via a tool in Design-Expert software) from 49 requests, are:
—Jim Barren, Kalsec, Inc., Michigan
—Mary Krenceski, New York.

The copy of "DOE Simplified" by the authors (myself and Stat-Ease consultant Patrick Whitcomb) goes to:
—Jack Pipkin, Avail Medical Products, Inc., Texas Jack was picked from 44 entrants.

Our autographed "RSM Simplified" goes to:
—Eric Kvaalen, Paris (care of his family in the USA). I received 49 requests for this book.

Thank you to all who participated in this drawing. If it's any consolation for those who did not win, Stat-Ease will likely free up more of these textbooks, or others of like quality, in future as they are replaced with newer editions.

For a complete list of books offered for sale by Stat-Ease, go to it's e-commerce site at http://www.statease.com/prodbook.html.

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5. Events alert: First European DOE User Meeting for Design-Expert and Design-Ease Users, Belgium, April 24-25

The First European Design of Experiments (DOE) User Meeting, co-organized by Stat-Ease Inc. and its European partners, will be held in Leuven, Belgium, on April 24 and 25. This 2-day meeting offers a unique opportunity to learn about the latest developments in DOE. For more details on this conference, which is hosted by CQ Consultancy, see http://www.cq.be/DOEconference/. Link from this web site to an online registration form.

Stat-Ease contract consultant John Guerin http://www.statease.com/johnguer.html will present a talk titled "Statistical Experimental Design to Optimize Products and Processes" for the Philadelphia Society for Coating Technology Inc. (PSCT) at their meeting on March 9th.

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

PS. Do you need a speaker on DOE for a learning session within your company or technical society at regional or national levels? If so, contact me. It may not cost you anything if Stat-Ease has a consultant close by. For example, last month I gave a talk on DOE at no expense for the Twin Cities Rubber Group.* However, for presentations involving travel, we appreciate reimbursements for airfare, hotel and meals—expenses only.

*(One attendee provided this gratifying feedback: "Your talk was lively and quite informative. I have heard many talks, in several disciplines, and the fundamental message of all of them is, '..this is interesting and complicated and useful stuff, but it is too complicated for me to actually teach you in one hour. My major aim is to show you why you should refer these matters to me...' So you can see that I am a cynic. But despite my cynical prejudice, I thought your talk was very good. I actually did learn, or rather re-learn, some very useful concepts.")

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6. Workshop alert: See when and where to learn about DOE

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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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—Wise words on experimental design by Box, Hunter and Hunter from their new edition of "Statistics for Experimenters":

"When your television set misbehaves, you may discover that a kick in the right place often fixes the problem, at least temporarily. However, for a long-term solution the reason for the fault must be discovered. In general, problems can be fixed or they may be solved. Experimental design catalyzes both fixing and solving."

—"Statistics for Experimenters: Design, Innovation, and Discovery, 2nd Edition" by George E. P. Box, J. Stuart Hunter, William G. Hunter, June 2005, John Wiley & Sons, New York.

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, 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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