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Issue:
Volume 9, Number 12
Date:
December 2009
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: [email protected].
Also, Stat-Ease offers an interactive web site—the Support Forum for Experiment Design at http://forum.statease.com. Anyone (after gaining approval for registration) can post questions and answers to the Forum, which is open for all to see (with moderation). Furthermore, the Forum provides program help for Design-Ease® and Design-Expert® software. Check it out and search for answers. If you come up empty, do not be shy: Ask your question! Also, this being a forum, we encourage you to weigh in!
For an assortment of appetizers to get this Alert off to a good start, follow this link, http://www.StatsMadeEasy.net* (-> new web site!), and see a number of new blogs (listed below, beginning with the most recent one):
—Running hot and cold in Apalachicola — steaming to cook clams and steaming to make ice
—New math sums digits from left to right: Does this add up as an improvement?
—Gambling with the devil
Also see the new comment on the post #390 (9/25/09) "Digging into numbers to the last vigintillionth of a yoctometer."
*Need a feed or e-mail updates from StatsMadeEasy? Go to http://feeds.feedburner.com/StatsMadeEasy. It's easy!
"Your StatsMadeEasy blogs brighten up a dreary workday!"
—Applied Statistician, Florida
Topics in the body text of this DOE FAQ Alert are headlined below (the "Expert" ones, if any, delve into statistical details).
1. FAQ: Coded versus actual equation: Still better even when factor ranges are all equal?
2. FAQ: Which trace plot should I use for assessing the impact of components from a mixture design of experiment?
3. Expert-FAQ: What level of adequate precision do you recommend for a model generated via response surface methods (RSM)?
4. Book Giveaway : Three classics seeking owners who appreciate statistical tools for process and quality improvement
5. Info Alert: A gold mine on mixture design for formulators
6. Events Alert: International Aerospace Sciences Meeting
7. Workshop Alert: Last chance to sharpen tools before 2010 via dynamic duo of DOE-RSM workshops — save $395 by attending both
P.S. Quote for the month: An apple fell on his head, causing Newton to realize that no great discovery was ever made without what? (Answer provided below.)
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1. FAQ: Coded versus actual equation: Still better even when factor ranges are all equal?
-----Original Question-----
From: Pharmaceutical Researcher
"I have a quick question, I hope. I've been researching whether I should use coded or actual factors in an equation if my goal is to measure the effect of each factor and interaction. I've found two great DOE Alert FAQs online regarding this.* Both agree that using the coded equation to measure the effect of each factor/interaction is best, however, they seem to indicate that it’s because the design may include factors with different ranges. In my case, however, I have ranges that are equal between all the factors. Which is the most appropriate equation for my uses?"
*Aug '09, #2 at http://www.statease.com/news/faqalert9-08.html by Stat-Ease Consultant Wayne Adams, which provides a link to Consultant Shari Kraber's take on this in the May '09 issue, #1 seen at http://www.statease.com/news/faqalert9-05.html.
Answer (from Stat-Ease Consultant Wayne Adams):
"Always use coded models for understanding the effects of the factors. Our default coding centers the factor ranges across the range tested to get the coefficient (effect) estimates. When the coding is -1 for low and +1 for high, 0 is in the center of the range tested. Actual equations have coefficients that are centered on where the factors are all set to 0. Same range or not, the coefficients in the actual model are corrections to get the predictions right over the range tested and may have very little to do with the relative size of the effects."
Further comments:
It's rare that process factors would have the same range, but in my work as a chemical engineer I worked on reactors with a number of zones that could be varied between set levels, in which case one could experiment on all the combinations of low versus high. Just for fun I set up a simulation using the design tool for this that we provide in Design-Expert (its also in Design-Ease). Then I ran a full two-level factorial experiment on three factors ranging from 100 to 200 each, ostensibly producing a yield measured in weight percent. Here are the model equations:
Coded simulation: Y = 70 - 10A + 20B + 15AB (s = 5)
Coded (experimental): Y = 70.64 - 9.77A + 21.79B + 12.80AB
Actual (exp.): Y = 149.76 - 0.9633A - 0.33215B + 0.00512AB
Notice that the intercept in actuals (149.76) is meaningless, whereas in coded form it provides a measure of the overall response average (70.64). For that reason alone I prefer the coded model. Then you get into the other issues that Wayne points out about the coefficients — they only provide comparative value in coded form as demonstrated above. For example, the coefficient on the B goes from being a relatively big positive main effect (21.79) in the coded model to a deceptively negative impact (-0.33215) in actuals. So there you go!
—Mark
(Learn more about coding factors by attending the computer-intensive workshop "Experiment Design Made Easy." See http://www.statease.com/clas_edme.html for a description of this class and link from this page to the course outline and schedule. Then, if you like, enroll online.)
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2. FAQ: Which trace plot should I use for assessing the impact of components from a mixture design of experiment?
-----Original Question-----
From: Food Technologist
"I am working with the mixture design. Which trace plots, Piepel or Cox, would be the best to use in drawing our conclusions?"
Answer (from Stat-Ease Consultant Wayne Adams):
"Use both Piepel and Cox directions AFTER finding optimal blends to understand how changes in the formulation effect the outcomes. Traces with steep effects near the optimal blend need to be tightly controlled, whereas, flat traces can vary a bit without effecting the outcome."
PS. More details on trace plots are given at FAQ 2 in the February 2007 Alert at http://www.statease.com/news/faqalert7-2.html.
(Learn more about trace plots by attending the computer-intensive workshop "Mixture Design for Optimal Formulations." See http://www.statease.com/clas_mix.html for a complete description of this class. Link from this page to the course outline and schedule. Then, if you like, enroll online.)
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3. Expert-FAQ: What level of adequate precision do you recommend for a model generated via response surface methods (RSM)?
-----Original Question-----
From: Senior Statistician
"Mark, Here is a question I probably should have asked a long time ago regarding adequate precision ("AP"). I know your software recommends that with an AP greater than 4 "the model can be used to navigate the design space." What does that phrase actually mean?"
Answer:
As defined in the glossary of RSM Simplified,* adequate precision is a "measure of the experimental signal to-noise ratio. It compares the range of the predicted values, y-hat, at the design points to the average variance, V-bar, of the prediction (a function of model parameters, p, the number of points, n, and the variance, sigma^2, estimated by the root mean square residual from ANOVA)." Our rule-of-thumb favors models with AP > 4 for predicting responses within the space that the experimenter explored, for example the factorial region of a central composite design (CCD).
The overall (model) F-value does not measure whether a model does a good job of predicting — only that it is better than chance. Interestingly enough, one rule of thumb** is that whatever F value you deem critical (at p of 0.05, or whatever) should be multiplied by 4 if you will be using the model for prediction. However, the AP evidently provides a better measure for this purpose (assessing a model’s adequacy for predictive purposes).
Assuming the model is significant and R^2-Predicted is positive, then if AP exceeds 4 I might include this response in my optimization. Obviously there’s a lot more to this decision, so maybe it would be more prudent to say that in these circumstances one needn't reject the model necessarily.
*"RSM Simplified: Optimizing Processes Using Response Surface Methods for Design of Experiments," co authored by Pat and me, is detailed at http://www.statease.com/rsm_simplified.html. From there you can link to order online.
**Raymond H. Myers, Douglas C. Montgomery and Christine M. Anderson-Cook in their textbook "Response Surface Methodology," 3rd edition (2009), attribute this to Box & Wetz ("Criteria for Judging Adequacy of Estimation for an Approximating Response Function," Report #9, University of Wisconsin, Statistics Department, 1973).
Statistician Pat Whitcomb adds these comments:
"If the model is significant, lack of fit insignificant, there is good agreement between adjusted and predicted R^2, adequate precision is over 4 and the residuals are well behaved; then the model predicts the mean well. The mean is what is usually of interest during optimization.
Low raw R^2 values are not necessarily a show-stopper: This just indicates that there is a lot of noise relative to the signal in our design space. Whenever you need to add runs to increase power or precision due to a low signal (delta) to noise (sigma) ratio, then you should anticipate seeing low R^2 values. For example, if you are sizing to have an 80% chance of detecting a delta-to-sigma of 1 to 2, then expect (approximately): R^2 = delta^2/(delta+sigma)^2 = (1)^2/(1+2)^2 = 0.11.
That is not a very high value for R^2. However, by performing a sufficient number of experimental runs to provide power, one can adequately model the mean in the presence of a lot of noise. Nevertheless; knowing the location of the mean doesn't reduce the variation of the distribution about that mean; so you get low R^2 values."
—Pat
(Learn more about RSM by attending the two-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.)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4. Book Giveaway: Three classics seeking owners who appreciate statistical tools for process and quality improvement
(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 December 13 if you'd like (free!) one of three books that Stat-Ease no longer stocks.
1 "Response Surface Methodology," 2nd edition, by Raymond H. Myers and Douglas C. Montgomery, 2002. This RSM textbook achieved third edition this year.
2 "Statistical Intervals: A Guide for Practitioners," by Gerald J. Hahn and William Q. Meeker, 1991. Although we no longer resell this textbook, its recommended reading for students of our Statistics for Technical Professionals workshop.*
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.
*(See details on the two-day Statistics for Technical Professionals workshop, offered on-site only (no public classes), at http://www.statease.com/clas_stp.html. Link from this page to the course outline. Contact our Workshop Coordinator, Elicia, at 612.746.2038 if you'd like a quote for a private class.)
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5. Info Alert: A gold mine on mixture design for formulators
In a feature for the August/September issue of Scientific Computing World titled "Analysis is the mother of invention," Felix Grant explores the role of statistical analysis. Here he talks about mixture design" — quoting a publication by me:
"In many areas, directed invention at some point boils down to seeking the optimum mixture of ingredients to maximize an identified beneficial effect. Those ingredients may be as disparate as metals in an alloy, capital instruments affecting economic performance, or chemical agents in a pain relief tablet, but all of them rely on multivariate analysis of response to inputs. I choose the metal alloy example deliberately, because A primer on mixture design[9], by Mark Anderson of Stat-Ease, uses it as an illustrative example, which made me think about the nature of a live project on which I am currently consulting. Anderson’s example invites the reader to consider the invention of gold solder by ancient goldsmiths through adulteration of pure gold with small quantities of copper, to lower the melting point and assist fine filigree work."
See Grant's article here: http://preview.tinyurl.com/mf7tux. To view "A Primer on Mixture Design: What’s In It for Formulators?" go to the Stat-Ease home page (http://www.statease.com) and follow the "I'm a formulator" link.
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6. Events Alert: International Aerospace Sciences Meeting
See several talks on DOE at The International Aerospace Sciences Meeting (ASM) January 4 - 7 in Orlando. Stop by to visit with a Stat-Ease representative at the DOES booth. For details, see http://www.aiaa.org/content.cfm?pageid=230&lumeetingid=1812.
(SECOND NOTICE) Stat-Ease will exhibit new software developments and answer questions about experiment design at the Life Science Alley Conference & Expo in Minneapolis on December 9. This event engages the medical device, health care, pharmaceutical, biopharma, biotechnology, and food and nutrition sectors. See http://www.lifesciencealleyconference.org/ for details.
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!
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7. Workshop Alert: Last chance to sharpen tools before 2010 via dynamic duo of DOE-RSM workshops — save $395 by attending both
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)
> December 8-9,* (Minneapolis, MN)
> February 9-10, 2010 (Minneapolis)
—> Response Surface Methods for Process Optimization (RSM)
(http://www.statease.com/clas_rsm.html)
> December 10-11,* (Minneapolis)
> April 29-30, 2010 (Minneapolis)
**Save $395 by attending December EDME-RSM back-to-back**
—> Mixture Design for Optimal Formulations (MIX)
(http://www.statease.com/clas_mix.html)
> January 26-27 (Minneapolis) **ADDED DUE TO POPULAR DEMAND**
> March 2-3, 2010 (Minneapolis)
—> Designed Experiments for Life Sciences (DELS)
(http://www.statease.com/clas_dels.html)
> February 23-24, 2010 (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 [email protected].
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I hope you learned something from this
issue. Address your general questions and comments to me at: [email protected].
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—An apple fell on his head, causing Newton to realize that no great discovery was ever made without what? Answer provided below:
"No great discovery was ever made without a bold guess."
—Isaac Newton
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, led by Neal Vaughn and Tryg Helseth
(http://www.statease.com/pgmstaff.html)
—Heidi Hansel Wolfe, Stat-Ease sales and marketing director, and all the remaining
staff that provide such supreme support!
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