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 StatEase web site. 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/gbraindrain/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 MITLemelson 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 halfnormal 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 StatEase
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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. FAQ: The statistical benefits of transforming responses Original Question Answer (from StatEase 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. The NIST/SEMATECH eHandbook 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 NonNormality via Response Transformations") in the book "DOE Simplified" (see http://www.statease.com/doe_simp.html). (Learn more about transformations by attending the threeday computerintensive 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.)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 2. FAQ: How to interpret a halfnormal plot of effects "Dear Mark, I have a doubt regarding the halfnormal 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."
3. Info alert: Links are provided to a bonanza of case studies published recently that detail the application of DOE to:
Answer: Since you already have Montgomery's book, it will be hard to come up with any better explanation of the halfnormal plot. You will find one at the NIST/SEMATECH eHandbook of Statistical Methods  http://www.itl.nist.gov/div898/handbook/pri/section5/pri598.htm. It is surprising that even though twolevel 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 twofactor 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 (nearzero). Since effects are based on averages of highs versus lows (the two levels tested), by central limit theorem the nearzero effects will likely be normally distributed with mean zero and variance sigma square (as noted in Montgomery's book). Thus, on halfnormal 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 twolevel factorial design.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  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 DoMarketers 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. :)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 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/040223/0402235.html." Eric refers to experiments I did with my son Hank for his 5thgrade science project over a decade ago, which culminated in a published article with him listed as coauthor (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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 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/faqalert43.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 fullfactorial 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 StatEase Click on http://www.statease.com/events.html for a list of appearances by StatEase professionals. We hope to see you sometime in the near future! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 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 threeday Robust Design: DOE Tools for Reducing Variability (RDRV) workshop at the StatEase training site in Minneapolis on April 1315. 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 oneday 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 StatEase workshops open to the public. To enroll, click the "register online" link on our web site or call StatEase 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 StatEase 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@statease.com Sincerely, Mark Mark J. Anderson, PE, CQE PS. Quote for the month  how a master inventor looks at the world: Trademarks: DesignEase, DesignExpert and StatEase are registered trademarks of StatEase, Inc. Acknowledgements to contributors: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Interested
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