Issue: Volume 6, Number 6
Date: June 2006
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, 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 If this newsletter prompts you to ask your own questions about DOE, please address them via mail

Here's an appetizer to get this Alert off to a good start: An experiment you can do at your home with a microwave oven and some chocolate chips that will verify the speed of light! It comes from Matthew who writes for Superpositioned — an internet site ( that provides "Electronics news and projects in the frequency domain." The details on this unbelievable experiment can be found at

Also, if you have a moment, check out the latest entries in, including a 'heads-up' about "dyscalculia."

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: How does DOE differ from linear regression?
2. Info Alert: "Trimming the FAT: Part II"
3. Reader Response: Many comments about DOE on dog food
4. Reader Input: A measure of blocking efficiency by Cornell
5. Events Alert: Talks on the application of DOE in plastics and food
6. Reader Input: Workshop alert: San Jose "Experiment Design Made Easy" and Chicago "Crash Course on DOE for Sales & Marketing"

PS. Quote for the month: A pessimistic view on planned experimentation by Box, Hunter and Hunter.


1. FAQ: How does DOE differ from linear regression?

-----Original Question-----
"I really enjoyed the class that Stat-Ease taught. You guys did a great job. You really answered a lot of the nagging questions in the back of my mind. I am now trying to defend the usage of DOE in my research and development (R&D). It seems like a lot of people have experience with related statistical methods, but conceptually don't understand how DOE is used in R&D. One question I get is 'How is DOE different than multiple linear regression and similar techniques?'"

Answer (from Stat-Ease Consultant Wayne Adams): "The old saying 'you can lead a horse to water, but you cannot make it drink' comes to mind, doesn't it? I didn't get it at first either why R&D people don't see how useful DOE can be for their work. People are always baffled that a well-planned experiment design requires fewer runs (less time) versus the one-factor-at-a-time (OFAT) scientific method and it provides more information about how a process/design really works. It sounds too much like getting something for nothing — too good to be true. Yet these same people are not fazed by application of multiple linear regression and similar techniques for mining happenstance data collected over some period of time. The big difference with DOE is that it controls the factors that generate changes in the responses rather than just relating (regressing) factors to responses. Ideally one tries to keep the changes in the factors independent of each other. The easiest way to accomplish this is to run all combinations in a full-factorial design. DOE and regression use the same math for the analysis, and use the same diagnostics, but regression methods without the benefit of design and forethought will have less power than a comparable controlled, designed experiment."

PS from Mark: Our Design-Expert® version 7 software (DX7)* offers a "Historical" option in its response surface method (RSM) design tab, which makes it easy to enter in happenstance results. Then use the program's unique design evaluation to assess statistical power term-by-term for linear and any higher order models that are estimable.

*Download DX7 freely from See what it can do as a regression tool by completing the two Historical Data RSM tutorials (parts 1 and 2) posted at and

(Learn more about modeling by attending the three-day computer-intensive workshop "Response Surface Methods for Process Optimization." See for a complete description. Link from this page to the course outline and schedule. Then, if you like, enroll online.)


2. Info alert: "Trimming the FAT: Part II"

This article in OE (Optical Engineering) magazine's September 2005 issue offers a case study that illustrates how a two-level factorial DOE can reveal a breakthrough interaction: It is a follow-up to an article in the June/July issue* that contrasted multifactor DOE with one factor at a time (OFAT) experimentation.



3. Reader response: Many comments about DOE on dog food

The most recent edition of the Stat-Teaser* featured an article titled "A Wonderful Day for a Boy and his Dog," by 6th grader Jon Kraber. With a bit of coaching from his mother, Stat-Ease Consultant Shari Kraber, he experimented on which treats enticed their family pet Jasper. It generated so many responses
that we decided to post them on our web site — see



4. Reader input: A measure of blocking efficiency by Cornell

-----Original Comments-----
From: John Cornell, author of "Experiments with Mixtures"
(available via Stat-Ease e-commerce site for DOE textbooks at

"I generally look forward to reading the monthly DOE FAQ Alert by Stat-Ease that you e-mail me because they are very informative. The most recent alert, March 2006, however, contained a response to the FAQ (#1) "Why a p-value is not provided for variance from blocks" where you say "Since blocking restricts randomization (by design), it violates the assumption of independence. Thus it wouldn't be proper statistically to perform the F-test." Then you proceed to give an engineering rule of thumb. (See

As one who spent 37 years as a statistical consultant in an agricultural experiment station, I helped literally hundreds of clients set up and analyze data collected from randomized complete block designs (RCBD’s). In a majority of the cases, the clients were the ones who suggested blocks be used to remove a source of variation that otherwise would be included in and perhaps inflate the magnitude of "error" in the analysis of variance table. I might also add that the more knowledgeable clients would generally ask if it was possible to determine whether or not anything was gained by blocking. That is when I used a formula that allowed me to estimate the relative efficiency of the RCBD compared with that to be expected from a completely random design (CRD). This formula for b blocks and t treatments is

(1) Eff(RCBD to CRD) = [(b-1)MSBlks + b(t-1)MSE]/(bt-1)MSE

where MSBlks and MSE are the block and error mean squares, respectively, in the analysis of variance table for the RCBD. If the degrees of freedom, (b-1)(t-1) for the RCBD error are less than 20, it is important to consider the loss in precision resulting from fewer degrees of freedom with which to estimate the error mean square of the RCBD experiment as compared to the CRD. This is accomplished by multiplying the quantity in (1) by the precision factor

(2) PrFac = {[(b-1)(t-1)+1][t(b-1)+3]}/{[t(b-1)+1][(b-1)(t-1)+3]}

so that the adjusted relative efficiency of the RCBD to the CRD is
(1) times PrFac (2).

It doesn't take a rocket scientist to see from (1) that the efficiency of the RCBD to the CRD increases the more significantly different blocks are (or MSBlks is) since MSBlks lies in the numerator of (1). Should you wish to see a proof of (1), the textbook by Cochran, W. G. and G.M. Cox (1957) "Experimental
Designs," 2nd. Ed., John Wiley & Sons, Inc., New York, Chapter 8, is a good source. I suspect it was just an oversight on Robert O. Kuehl’s part to suggest "There is little interest in formal inferences ... of a computer program," but then he probably never had to provide an answer to the question, "Was anything gained by blocking?" as I had to many times.

I hope this helps to clear up the question, "Mighten I learn something from an F-test of Blocks in the ANOVA of a RCBD?" My answer is "Yes, Indeed." So with this information in mind, why don't you provide a p-value for the client? For the more significantly different blocks are, the greater the gain in setting up the design as a RCBD rather than a CRD.

If you have any questions about the above, please let me know. Once again, keep the DOE FAQ alerts coming for I believe they serve the public nicely.

All the very best,"

John A. Cornell
Professor Emeritus of Statistics, University of Florida


5. Events alert: Talks on application of DOE in plastics and food

2ND NOTICE: Stat-Ease contract-trainer Carl McAfee will give an invited paper at the National Plastics Exhibition (NPE) on June 19-23 in Chicago. His talk on "Case Studies and Technical Perspectives on TPEs/TSRs: The Paradigm Shift" features Design-Expert and its capabilities as a tool for innovation and positive change. The NPE is one of the largest venues in the country — over 80,000 attendees last year. See for details.

2ND NOTICE: Stat-Ease Consultant Pat Whitcomb will be one of the featured speakers on "Approaching Product Design Systematically and Strategically" — offered June 23-24 in Orlando before the Annual Meeting and Food Expo of the Institute of Food Technologists (IFT). For information on the preconference class, in which Pat will detail application of screening, full factorial, response surface (RSM) and mixture designs, see

Click for a list of appearances by Stat-Ease professionals. We hope to see you sometime in the near future!


6. Workshop alert: San Jose "Experiment Design Made Easy" and Chicago "Crash Course on DOE for Sales & Marketing"

"Experiment Design Made Easy" will be presented on June 6-8 in San Jose, California. If you work in western USA and need to master the basics of DOE, do not miss this opportunity for a computer-intensive workshop by a Stat-Ease statistical consultant.

(If you are a corporate technical professional, please pass this news on to your business people!) Quickly identify those factors which affect your sales and marketing results. Learn how they interact and apply that knowledge to make breakthrough increases in sales and profits. Attend the one-day "Crash Course on DOE for Sales & Marketing" in Chicago on June 22. See the course description and links to the syllabus and online enrollment at

Stat-Ease also presents Mixture Design for Optimal Formulations this month — June 13-15 at its Minneapolis training facility. Don't miss this chance to enhance your chances of discovering the ideal recipe that puts your product ahead of the pack.

See 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.


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



Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc. (
2021 East Hennepin Avenue, Suite 480
Minneapolis, Minnesota 55413 USA

PS. Quote for the month — a pessimistic view on planned experimentation:

"When running an experiment the safest assumption is that unless extraordinary precautions are taken, it will be run incorrectly."

— Box, Hunter and Hunter from their textbook "Statistics for Experimenters" second edition.

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
—Stat-Ease consultants Pat Whitcomb, Shari Kraber and Wayne Adams (see for resumes)
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert (
—Stat-Ease programmers, especially Tryg Helseth and Neal Vaughn (
—Heidi Hansel, Stat-Ease marketing director, and all the remaining staff


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#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, #6-5 Jun 06 (see above)

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