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Vol: 10 | No: 11 | Nov 2010
Stat-Ease
The DOE FAQ Alert
     
 
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, click here.

Feel free to forward this newsletter to your colleagues. They can subscribe by going to this registration page.

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.

Also, Stat-Ease offers an interactive website—The Support Forum for Experiment Design. 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 to Design-Ease® and Design-Expert® software. Check it out and search for answers. Also, this being a forum, we encourage you to weigh in!
 
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This months topics:

 
     
  If this newsletter prompts you to ask your own questions about DOE, please address them via e-mail to: stathelp@statease.com.

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Topics in the body text of this DOE FAQ Alert are headlined below:

(The expert ones, if any, delve into statistical details).
1:  FAQ: Can we convert the p-value to a percent confidence?
2:  FAQ: Which is the best response surface methods (RSM) design: Central Composite, or Box-Behnken?
3:  Expert-FAQ: Expert-FAQ: How do the coded-model coefficients relate to the effects from a minimum-run resolution V (MR5) design?
4:  Info alert: Whirley Pop DOE Part II
5:  Webinar Alert: DOE Made Easy and More Powerful via Design-Expert Software, Part 3—Mixture Design for Optimal Formulation
6:  Events Alert: Life Science Alley Conference & Expo
7:  Workshop Alert: See when and where to learn about DOE
8:  Heads-up on DOE FAQ Alert format: HTML version in the works
 
 
PS. Quote for the month:
The downside of statistical modeling—using it to entice more e-commerce from gift buyers this holiday season—one consumer's poetic (emphasis on Poe) pushback.

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1: FAQ: Can we convert the p-value to a percent confidence?

Original Question:

From A Coatings Technologist:
"I often read with interest the DOE FAQ Alert and find many tips for (attempting) to explain some of the concepts of experimental design and statistics to non-statisticians. I am an inexperienced (but very willing) student of these things myself, and I was compelled to ask the following question: If the p-value represents the probability that any difference we detect between a value and the population is real, can we convert the p-value to a % significance? For example if calculating a p-value of 0.05, can we say we are 95% confident that there is a difference? Similarly, when we calculate any p-value, can we convert it to percentage, e.g. p-value of 0.12 = 88% significance?"

Answer:

From Stat-Ease Consultant Shari Kraber:
"Yes, we often interpret a p-value of 0.05 (which means that there is a 5% chance that when we declare that there has been a change, we are wrong) to be a 95% confidence that we are right. This still leaves a 1 in 20 chance that we are wrong! I'm comfortable with making confidence statements down to the 90% (p-value .10) area. Beyond that, saying to a general audience that you have, say, 80% confidence may lead people to think that is 'good enough' when they forget that now you are at a 1 in 5 chance of being wrong, which is pretty big! So, yes, you can flip the interpretation to a confidence, just be careful how that is interpreted by others."

(Learn more about p-values by attending the two-day computer-intensive workshop "Experiment Design Made Easy." Click on the title 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 is the best response surface methods (RSM) design: Central Composite, or Box-Behnken?

Original Question:

From a Material Science Engineer:
"We need to optimize our process to put it in the 'sweet spot.' There are 5 key factors. What would be the best approach DOE or RSM? If RSM, which design should I use—Central Composite or Box-Behnken?"

Answer:

From Stat-Ease Consultant Brooks Henderson:
"The goal of design of experiments (DOE), of which response surface methods (RSM) are a subset, is to create a predictive model for the response based on the controllable input factors (parameters). With that model, you can find the 'sweet spot' you seek, be it maximizing the response, minimizing it, or shooting for a target value. You can also go for the best tradeoffs between multiple responses.

Whether you use a two-level factorial or an RSM design depends on your situation. If you still need to identify which factors have the biggest influence on the response and this is your first DOE on the process, you would most likely use a factorial design. If you already have a good idea as to what factors affect the response the most and what region the optimum is likely to be in, you can use an RSM design.

A nice, economical factorial design for five factors would be the design on the factorial tab of Design-Expert labeled 25-1, which is 5 factors in 16 runs. This would help you determine which of the 5 parameters have a significant effect on the response and guide you as to which direction the optimum might be (assuming it might not be in the ranges you studied). You would have enough data to fit a 2-factor interaction (2FI) model (i.e. a tilted or twisted plane). You can also add 4 center points to this design to check for curvature which would let you know if the 2FI model you have is adequate or an RSM is needed. If a higher order model is need, you can then augment this design to a central composite design (CCD).

A good response surface design for 5 factors would take more runs. A CCD would be 50 and a Box-Behnken design (BBD) would be 46, but you could fit higher order models, such as a quadratic model. The choice of a design comes down to where you are at in the knowledge of the process, what your goals are, and what budget you have for the number of runs."

PS. I am partial to face-centered central composite designs (FCD). This reduces the number of levels to 3 for each factor (versus 5 for the standard CCD). A Box-Behnken design (BBD) also features 3 levels only, but it does not provide the extreme vertices of the cuboidal spaces. (I tend to be a bit aggressive in my explorations!). For everything you ever wanted to know about CCDs (vs BBD), refer to "RSM Simplified"—detailed here and from there available for purchase.

PPS. Stat-Ease Consultant Pat Whitcomb warns that for more than 5 factors the FCD exhibits high variance inflation factors (VIFs) relative to the BBD. For these larger designs, a good compromise between FCD and the standard CCD is provided by the "practical alpha" choice in Design-Expert. The alpha value is the 4th root of the number of factors. This has been shown to produce axial values that can practically be run, and yet the design still has sound statistical properties.

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

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3: Expert-FAQ: How do the coded-model coefficients relate to the effects from a minimum-run resolution V (MR5) design?

Original Question:

From a PhD in Industrial Engineering and Operations Research:
"I have a copy of Design-Expert® software ("DX"), which I use in teaching my short course on DOE for simulation modeling. I have a question about minimum-run resolution V designs (MR5), which I think are potentially quite useful. However, I would like to understand what is really going on. I put my response data into DX and got estimates of the coded-variable coefficients. (I also put the data into Excel and fit a regression equation, and the coefficients were the same as those from DE.) I also noticed that the effect estimates in Design-Expert were half of the corresponding coefficients. I knew that this relationship was true for 2k designs. Is it also true for ALL two-level factorial designs, such as minimum-run resolution V designs?

What I really don't understand is the following. Let's say for definiteness that I have a normal 2(6-1) resolution VI design. Then I can estimate directly the main effect for a particular factor by multiplying its column of signs in the design matrix by the column of responses, row-by-row, and taking the resulting sum and dividing it by 16n (n = number of replicates). Is there a comparable approach for a MR5? I can't find anything obvious that works."

Answer:

From Stat-Ease Consultant Wayne Adams:
"The effects should be twice the coefficient estimates if you are using the coded values in the matrix for a balanced orthogonal design or the experiment has zero error. The MR5 designs do not maintain an orthogonal matrix therefore the coefficients are not necessarily half the effect. They approach that behavior, but are not exactly half. With the MR5 design, which does not have an orthogonal matrix, the coefficients generated depend on all the terms being included in the model. Once the decision has been made as to which terms are pooled into error (versus those terms that explain the changes), an X matrix containing a column for each explanatory term and the over-all intercept is formed. Straight forward, least-squares regression is then used to relate the given model to the response."

(Learn more about MR designs by attending the two-day computer-intensive workshop "Experiment Design Made Easy." Click on the title 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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4: Info alert: Whirley Pop DOE Part II

Design Product News published follow up studies by Stat-Ease Consultant Brooks Henderson for optimization for Whirley-Pop™ popcorn. See via this link how he augmented his original factorial design to a response surface methods (RSM) design. Brooks concludes by saying that "After these experiments, I'm sure my wife and I will never look upon our Whirley Pop popper quite the same way again." Read into that what you like. ;)

Whirley-Pop™ is a trademark of Wabash Valley Farms.

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5: Webinar alert: DOE Made Easy and More Powerful via Design-Expert Software, Part 3—Mixture Design for Optimal Formulation

Keeping it simple and making it fun, Stat-Ease is introducing an array of statistical methods for design of experiments (DOE) made easy and more powerful via version 8 of Design-Expert software:
—Two-level factorials for process screening, characterization
and verification
—Response surface methods (RSM) for process optimization
—Multicomponent mixture design for optimal formulation.

I will present the third of this series of free webinars by working through case studies on mixture experiments on Wednesday, December 15 at 2 PM USA Central Time* (CT). I will repeat this presentation on Thursday, December 16 at 8 AM. Stat-Ease webinars vary somewhat in length depending on the presenter and the particular session—mainly due to breaks for questions. Plan for 45 minutes to 1.5 hours, with 1 hour being the target median.

When developing these one-hour educational sessions, our presenters often draw valuable material from Stat-Ease DOE workshops. Attendance may be limited, so sign up soon by contacting our Communications Specialist, Karen Dulski, via karen@statease.com. If you can be accommodated, she will provide immediate confirmation and, in timely fashion, the link with instructions for our new web-conferencing vendor: GotoWebinar.

*(To determine the time in your zone of the world, try using this link. We are based in Minneapolis, which appears on the city list that you must manipulate to calculate the time correctly. Evidently, correlating the clock on international communications is even more complicated than statistics! Good luck!)

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6: Events alert: Life Science Alley Conference & Expo

If you make it to the Life Science Alley Conference & Expo in Minneapolis on December 8th, please stop by the Stat-Ease booth (#305) for a chat about DOE and what we have done or can do for you. To register go here. Click this link for a list of upcoming 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, national, or even international levels? If so, contact me. It may not cost you anything if Stat-Ease has a consultant close by, or if a web conference will be suitable. However, for presentations involving travel, we appreciate reimbursement for travel expenses. In any case, it never hurts to ask Stat-Ease for a speaker on this topic.

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7: Workshop Alert: See when and where to learn about DOE

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! Also, take advantage of up to a $395 discount when you take two complementary workshops that are offered on consecutive days.

All classes listed below will be held at the Stat-Ease training center in Minneapolis unless otherwise noted.

* Take both EDME and RSM to earn $395 off the combined tuition!
** Attend both SDOE and DELS to save $295 in overall cost!
*** Take both MIX and MIX2 to earn $395 off the combined tuition!

See this link to listing of upcoming classes for complete schedule and site information on all Stat-Ease workshops open to the public. To enroll, click the "register online" link on our website 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 workshops@statease.com.

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8: Heads-up on DOE FAQ Alert format: HTML version in the worksI put the final touches to an HTML version of the DOE FAQ Alert, which for over a decade now (first issue April 2000) has gone out in text only. I suppose some folks like me who resist change may struggle a bit with the new look. If so, let me know. However, I'm not likely to look back—it's full steam ahead!

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  Please do not send me requests to subscribe or unsubscribe—follow the instructions at the very end of this message. 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.

PS. Quote for the month—the downside of statistical modeling—using it to entice more e-commerce from gift buyers this holiday season—one consumer's poetic (emphasis on Poe) pushback:

"
Stop, I cried, I'm going crazy!
E-merchants have turned so darn lazy!
They make such lame connections through their online store!
With database and freakish theory, a pile of crock they offer freely;
A statistical correlation, of others' random purchases before,
Twisted so perversely, with random orders of before.
I've had enough! Nevermore!"

—Seen in 9/22/10 Saint Paul Pioneer Press "Bulletin Board"

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, Wayne Adams and Brooks Henderson
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert
Stat-Ease programmers led by Neal Vaughn and Tryg Helseth
—Heidi Hansel Wolfe, Stat-Ease marketing director, Karen Dulski,
and all the remaining staff that provide such supreme support!

DOE FAQ Alert ©2010 Stat-Ease, Inc.
All rights reserved

 
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