The DOE FAQ Alert Vol. 4 No. 4

Issue: Volume 4, Number 4
Date: April 2004
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. 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 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, but be forewarned it might drain your brain of its intelligence quotient (IQ): http://web.mit.edu/invent/g-braindrain/game.html. When you get tired of playing games, explore the wealth of inventor resources offered throughout this site sponsored by Massachusetts Institute of Technology (MIT). Via the MIT-Lemelson Program they offer the world’s largest single cash prize for invention: 500,000 US dollars. The award, dubbed the "Oscar for Inventors," is named for Jerome Lemelson, a prolific inventor who amassed over 500 patents. Many of his endless ideas came while sleeping, proving that it pays to keep that scientific notebook handy at all times!

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: The statistical benefits of transforming responses

2. FAQ: How to interpret a half-normal plot of effects

3. Info alert: Links are provided to a bonanza of case studies published recently that detail the application of DOE to:

- Testing of automotive coatings

- Adhesives formulation

- Postcard advertising

- Cosmetic chemistry

4. Reader contribution: Experimenting on popcorn

5. Reader comments: Numerical optimization -- can it be done on factorial designs? (A topic discussed last month)

6. Events alert: Link to a schedule of appearances by Stat-Ease

7. Workshop alert: Robust Design: DOE Tools for Reducing Variability -- a must for Six Sigma Black Belts

PS. Quote for the month -- how a master inventor looks at the world.

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1. FAQ: The statistical benefits of transforming responses

-----Original Question-----
From: San Francisco Bay Area

"We designed a full-factorial, two-level design of experiments with five factors using Design-Expert® software. When the experiments were completed, we discovered that for two responses, we had to apply transformations -- in one case a square root transformation and for the other response a log transformation. This was our first experience with the need to apply transformations in order to get good model fits. After applying these transformations, we obtained R-squared, Pred R-squared and adjusted R-squared all greater than 0.98, which indicates a good model. I am wondering if I can get your help in interpreting the need for a transformation regarding the design space."

Answer (from Stat-Ease Consultant Shari Kraber):

"Transformations are needed when the model residuals do not satisfy the basic assumptions underlying the analysis of variance (ANOVA):

- normal distribution,

- constant variance, and

- independence (one response does not influence the next).

In many cases, the residuals are a function of the percentage of response, rather than a set constant, thus violating the second assumption noted above. For example, when you weigh something on a mechanical scale, the error will likely be a constant fraction of the measured weight. Thus, the absolute deviations will be smaller for a light item than for one that is very heavy.

Transformations are a way of accounting for some curvature in the design space. It may be that with a large design space a transformation is needed, but when the design space is restricted, a transformation is no longer necessary because the behavior is linear within that restricted range.

Obviously you are on the right track when, after applying the transformation, the R-squared values go as high as they did."

The NIST/SEMATECH e-Handbook of Statistical Methods offers a good discussion on this topic at http://www.itl.nist.gov/div898/handbook/pmd/section4/pmd452.htm. Also, refer to Chapter 4 ("Dealing with Non-Normality via Response Transformations") in the book "DOE Simplified" (see http://www.statease.com/doe_simp.html).

(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 course description. Link from this page to the course outline and schedule. Then, if you like, enroll online.)

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2. FAQ: How to interpret a half-normal plot of effects

-----Original Question-----
From: India

"Dear Mark, I have a doubt regarding the half-normal plot of effects. On page 318 of the book by D.C. Montgomery's "Design and Analysis of Experiments" [available for purchase at http://www.statease.com/prodbook.html] it is mentioned that the negligible effects are normally distributed, with mean zero and variance sigma square, and that they tend to fall along a straight line. I am not clear which mean and variance it is referring to since we have only a single replicate."

Answer:

Since you already have Montgomery's book, it will be hard to come up with any better explanation of the half-normal plot. You will find one at the NIST/SEMATECH e-Handbook of Statistical Methods -- http://www.itl.nist.gov/div898/handbook/pri/section5/pri598.htm. It is surprising that even though two-level factorial designs (2^k, k being the number of factors) generally are done unreplicated, one can derive an estimate of error for generating statistical tests of significance. However, as a general rule (called "Sparsity of Effects"), only about 20 percent of main effects and two-factor interactions may be 'active,' that is -- create a significant effect on the response. Therefore, the majority of effects that can be estimated from a 2^k will be negligible (near-zero). Since effects are based on averages of highs versus lows (the two levels tested), by central limit theorem the near-zero effects will likely be normally distributed with mean zero and variance sigma square (as noted in Montgomery's book). Thus, on half-normal probability paper, these 'trivial many' originate from the plot's zero point (lower left) in a line with a slope that relates to the variation in your process/sample/test (but reduced due to the power of averaging). That's how experimental error can be estimated from only a single replicate of a two-level factorial design.

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3. Info alert: Links are provided to a bonanza of case studies published recently that detail the application of DOE to:

- Testing of automotive coatings

- Adhesives formulation

- Postcard advertising

- Cosmetic chemistry

An unusually large number of links are offered this month for the following publications:

- "Taber Test or Oscillating Sand? DOE Improves Polycarbonate Plasma Coating Process" from the March issue of Paint and Coatings Industry at http://makeashorterlink.com/?F60623CD7.

- "Formulating by Design" by Kip Hillshafer, published in the March issue of Adhesives and Sealants Industry (ASI), see http://makeashorterlink.com/?S28641CD7

- "That Voodoo We Do--Marketers Are Embracing Statistical Design of Experiments" by Richard Burnham, published in The Direct Marketing Association (DMA) March 3rd page at
http://www.statease.com/pubs/marketingvoodoo.pdf

- "Optimizing Formulas By Experimental Design" by Joseph Albanese, published in the March issue of the NY Chapter Society of Cosmetic Chemists' newsletter "Cosmetiscope" and posted at http://www.nyscc.org/news/archive/tech0304.htm

I was happy to see in this last article that the author recommends that readers subscribe to the DOE FAQ Alert. :)

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4. Reader contribution: Experimenting on popcorn

From: Eric Adamec, Assistant Sr. Statistician, Eli Lilly and Co Tippecanoe Laboratories, Indiana

"Just in case you want to do another DOE demonstration using popcorn, here is an article from Nature, 2/25/04: http://www.nature.com/nsu/040223/040223-5.html."

Eric refers to experiments I did with my son Hank for his 5th-grade science project over a decade ago, which culminated in a published article with him listed as co-author (see http://www.statease.com/pubs/popcorn.pdf). If your child considers experimenting on popcorn, check out this site posted by Pop Weaver: http://www.popweaver.com/scifair.htm (Update 3/07: Link changed to http://www.popweaver.com/popcorn101/science/science_list.html.

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5. Reader comments: Numerical optimization -- can it be done on factorial designs? (A topic discussed last month)

Re: Last month's issue of the DOE FAQ Alert (Volume 4, Number 3, March 2004, http://www.statease.com/news/faqalert4-3.html), item 2 - "FAQ: Numerical optimization -- can it be done on factorial designs?"

From: Peter Ceuppens, Discovery Statistician, Astrazeneca International

"In my view this is really just a question of semantics. Even in a factorial design it may be required to find a set of conditions that is likely to yield the best results. This sounds simple (for example in a full-factorial just look down the list of numbers) but there are some complicating factors. If the design is fractional, it could be that the set of conditions that yields the 'best' results was not included in the experiment and hopefully an optimization procedure would still pull this out. Also if the response involves several variables, it may not be easy to pick the best set of conditions by eye. So in conclusion it could still be beneficial to optimize."

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6. Events alert: Link to a schedule of appearances by Stat-Ease

Click on 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!

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7. Workshop alert: Robust Design: DOE Tools for Reducing Variability -- a must for Six Sigma Black Belts

Time is short, but it's not too late to enroll in the three-day Robust Design: DOE Tools for Reducing Variability (RDRV) workshop at the Stat-Ease training site in Minneapolis on April 13-15. This is a must for anyone at the Black Belt level of expertise on Six Sigma quality improvement tools. For a course description on RDRV, see http://www.statease.com/clasrdrv.html. Link from this page to the course outline and schedule. Then, if you like, enroll online.

At the other end of the scale, for those who may be just beginning their education on design of experiments, we offer a one-day overview called DOE Simplified on April 29, also in Minneapolis. Click http://www.statease.com/does.html for details on this presentation.

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

Sincerely,

Mark

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

PS. Quote for the month -- how a master inventor looks at the world:

"I am always looking for problems to solve. I cannot look at a new technology without asking: How it can it be improved?"

- Jerome Lemelson (see this inventor's biography at http://web.mit.edu/invent/w-lemelsonbio.html)

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, #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 (see above)

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