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Vol: 12 | No: 2 | Mar/Apr'12
The DOE FAQ Alert

Heads-up (below!)
Free white paper* details how to achieve quality by design via newly developed methods *“Using DOE with Tolerance Intervals to Verify Specifications”

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.

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 this registration page.

Also, Stat-Ease offers an interactive web site—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 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 with answers! The following Support Forum topic provides a sampling of threads that developed since my last Alert:

  • Area: Design Selection, Topic: Use "New factorial method for 2-level” option, Question: “Can you provide some references on the 'new factorial method for 2-level' option available in the Graph Preferences?”

To open yet another avenue of communications with fellow DOE aficionados, sign up for The Stat-Ease Professional Network on Linked In and start or participate in discussions with other software users. A recent thread features How to find the effect of various factors using Plackett Burman?

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Topics discussed since the last issue of the DOE FAQ Alert (latest one first):

Also see the new comments about my 12/22/12 blog on “Why you should be very leery of forecasts.” Please do not be shy about adding your take about any news or views you see in StatsMadeEasy.  Thanks for paying attention.

By the way, an anonymous professor said in regard to my post about Repeated measure versus true replication that “I'm giving a lecture on DOE, and found your example to be extremely useful. It is simple and relatable. Thanks for sharing.”  This accolade floated in through a back door (an older blog-host) so it does not appear at the page linked above.  Please check it out and comment if it inspires you to do so.

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


Topics in the body text of this DOE FAQ Alert are headlined below (the expert ones, if any, delve into statistical details):

1:  FAQ: Fold-over on resolution IV fractional two-level factorial did not de-alias interactions
2:  FAQ: Why the lack-of-fit test does not appear in my statistical analysis
3:  Expert-FAQ: When results hit the upper limit (or lower limit) bound in the logit transformation what value for the correction “k” do you recommend I enter?
4:  Info alert: White paper on QbD, tutorial on mixture-process experiments, inspirational article on using DOE for coatings development
5:  Reader testimonial: DOE Simplified used to teach experiment design in high school
6:  Webinar alert: Overview of Robust Design, Propagation of Error, and Tolerance Analysis
7:  Conference Alert: 4th European DOE User Meeting June 26-28 in Vienna
8:  Events alert: Pharma QbD (in India!), Biotechnology, Quality & Productivity
9:  Workshop alert: See when and where to learn about DOE
PS. Quote for the month: A Nobel Prize-winning philosopher/mathematician provides pithy comments on testing assertions with observational data and listening to data when they speak.
(Page down to the end of this e-zine to enjoy the actual quote.)


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1: FAQ: Fold-over on resolution IV fractional two-level factorial did not de-alias interactions

Original Question:

From a Lean Six Sigma specialist:
“My original design was a 24-1 [8-run half-fraction on four factors at two levels each].  Confounded 2FIs could not be resolved [a resolution IV design].  We augmented the design with a full fold-over and ran the new runs as block 2 per Design-Expert® and entered the data.  I’m wondering why the fold-over is still a res IV.  Did I miss something?”


From Stat-Ease Consultant Wayne Adams:
“Picture a cube to represent the possible design combinations for three factors.  An orthogonal resolution IV design chooses opposite corners of the cube.  A full fold-over merely reverses the signs of all the factor settings, which ends up just running the opposite corners thus replicating the design.”

Further comments:
Wayne helped this user get back on track.  However, just so you know, the default choice presented by Design-Expert software for a res IV design augmentation is not the full fold-over, but rather a ‘semifold’ (see the screen shot below).

Recommended augmentation for a resolution IV design

The semifold will clear up the resolution problem.  For more details, see our white paper showing How To Save Runs, Yet Reveal Breakthrough Interactions, By Doing Only A Semifoldover On Medium-Resolution Screening Designs.  —Mark

(Learn more about two-level factorial design 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: Why the lack-of-fit test does not appear in my statistical analysis

Original Question:

From a Malaysian chemical-engineering graduate student:
“I just want to know why the lack-of-fit test does not appear in my statistical analysis from central composite designs (CCDs) that I perform for response surface method (RSM) optimizations.  I've tried many times, but it seems helpless.  Please guide me.”


From Stat-Ease Consultant Shari Kraber:
“You do not have a lack-of-fit (LOF) test because you removed the replicates of the center points.  The LOF computation requires an estimate of pure error.  Therefore, replicates of some kind are required—at the center and/or other factor combinations in the experiment.

Replication of the center point, specifically, provides another advantage—it brings down the error associated with predictions throughout the middle of the design space for the CCD.  Look at the standard error of prediction plot below. You can see the big ‘mountain’ in the middle which represents the standard error.

Prediction Plot

Standard error plot for CCD with center points removed

In future experiments, we strongly advise staying with the software defaults advised by Design-Expert, which in this case of three factors, calls for 6 center points.”

PS. At a post-conference workshop on RSM, I once watched DOE guru Doug Montgomery display the standard error plot on a CCD built according to the specification of its inventors (Box & Wilson, 1951).  Doug expressed a great deal of enthusiasm (as only he would for such esoteric matters!) for the way this structure (with center points replicated!) created a flat-bottomed bowl on the standard error plot.  Until then I had no idea how great this really was.  —Mark

(Learn more about RSM designs 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: When results hit the upper limit (or lower limit) bound in the logit transformation what value for the correction “k” do you recommend I enter?

Original Question:

From a industrial statistician working on coatings:
“Some of our responses are scored on a scale which ranges between 0 and 10.  In the analysis we treat it as a continuous response.  When we analyze such a response using Design-Expert, we start off with no transformation, build the model, check diagnostics, etc. and then investigate how the factors affect the response under Model Graphs.  Sometimes predictions go above the upper limit of our scale, which does not make sense, of course.  However, if it is slightly above the upper limit, we do not consider it to be an issue.  But when we get a prediction of 12 or higher, we then impose the upper (and lower) limit of our scale by applying the logit transformation.

Screen shot of logit transformation option

Screen shot of logit transformation option

This works very well and makes much more sense from a practical standpoint even though the model properties generally get slightly worse.  However, it often occurs that the upper limit (or lower limit) of our scale is one of the scores in the experiment, and so we cannot enter those as upper limit (or lower limit) in the logit transformation.  What I typically do is add 0.05 to the upper limit of our scale (or subtract 0.05 from our lower limit of the scale) and that works fine.  One my colleagues showed that it can make quite a difference what value you add (the 0.05 or something else) in regards to R-squared and other model attributes.  So the question is what should I add (or subtract) from theoretical bounds on the upper (or lower) for logit transformation—given these extenuating circumstances?


From Stat-Ease Consultant Pat Whitcomb:
“The idea behind the logit is that the data is bounded—the limits (relative to the minimum and maximum values) define the difficulty in approaching the boundaries.  For an ordinal scale of 1 to 10 let’s look at the logit transformation using adjustment differences (Delta or 'd') of 0.01, 0.10 and 0.5 where the limits are 1-d and 10+d.

Here are the results (table below):

Series: 1 2 3 4
Delta: 0 0.01 0.1 0.5
1 -4.5 -6.8035 -4.5109 -2.9444
2 -3.5 -2.0707 -1.9966 -1.7346
3 -2.5 -1.2492 -1.2182 -1.0986
4 -1.5 -0.6915 -0.6769 -0.6190
5 -0.5 -0.2226 -0.2183 -0.2007
6 0.5 0.2226 0.2183 0.2007
7 1.5 0.6915 0.6769 0.6190
8 2.5 1.2492 1.2182 1.0986
9 3.5 2.0707 1.9966 1.7346
10 4.5 6.8035 4.5109 2.9444

Table of logit transformations with a series of increasing deltas

To simplify the comparison I centered the ordinal scale of 1 to 10 on zero by subtracting 5.5 from each value (series 1).  Series 2, 3 and 4 are the logit transform with ds of 0.01, 0.1 and 0.5:

Graph of logit transformations with a series of increasing deltas

Graph of logit transformations with a series of increasing deltas

As can be seen in the above graph smaller values of d translate into the boundaries being more difficult to approach.  One way to choose d is to base it on the expected response behavior:  If it is exponentially difficult to approach the boundaries, then use a small d (e.g. 0.01).  If the approach is more linear, then use a larger value (e.g. 0.5).”

PS. Here's what I get from this intriguing answer by Pat:

  • If bounds represent near impossible achievements, such as 100 percent yield, then use a delta of 0.01, for example.
  • When bounds are subjective, such as sensory, then apply a larger value-say 0.5 delta.
Beyond that I think the delta must be kept within a reasonable range.  For example, for the case presented above, one would not use a delta of 3.  But if the response ranged 0 to 1000, than 3 might be good delta.  If you have other ideas, please reply directly.  —Mark

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4: Info Alert: White paper on QbD, tutorial on mixture-process experiments, inspirational article on using DOE for coatings development

Check out the white Paper posted on “Using DOE with Tolerance Intervals to Verify Specifications” posted here.  It’s based on a talk given by Pat Whitcomb to the 11th annual meeting of the European Network for Business and Industrial Statistics (ENBIS) at the University of Coimbra (Portugal) last September.  The tools are geared to the Quality by Design (QbD) initiative by the U.S. Food and Drug Administration (FDA).  However, they can just as well be applied to transform how any products are discovered, developed, and manufactured.

If you formulate products, take a look at this “Tutorial for mixture-process experiments with an industrial application” by Luiz Bello and Antonio Vieira published in Pesquisa Operacional (Operations Research), Vol.31 No.3 Rio de Janeiro Sept./Dec. 2011.  They present a case study of a three-component mixture used in the delay mechanism for starting a rocket engine.  Two process factors are considered as well.

Rick Caldwell emailed Stat-Ease an alert about publishing this article on “Applying Statistical Design of Experiments to VAE-Based Coatings Development A Formulator’s Perspective” in PCI Magazine.  He aimed this at chemists—advising them of the advantages for using DoE instead of one factor at a time (OFAT).

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5: Reader Testimonial: DOE Simplified used to teach experiment design in high school

“My daughter’s high school teaches statistics. Most schools cannot afford the full license to your software. I passed along the DOE Simplified flyer to the stats teacher. He was ecstatic to see this economical book including a 180-day license to Design-Ease software. Teachers can get such budgeting through their administration and thus use the program in lessons.”
—Dan Doe, Senior Research Chemist, ITW Plexus, Product Development Group, Performance Polymers Div., Danvers, MA

(Fitting coming from a fellow named “Doe”! —Mark)

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6: Webinar Alert: Overview of Robust Design, Propagation of Error, and Tolerance Analysis

Response Surface Methods (RSM) can lead you to the peak of process performance.  In this advanced-level webinar presented on Wednesday, May 23 at 2:00 PM CT,* Stat-Ease Consultant Pat Whitcomb will discuss robust design, propagation of error, and tolerance analysis.  Propagation of error (POE) accounts for variation transmitted from deviations in factor levels.  It finds the flats—high plateaus or broad valleys of response, whichever direction one wants to go—maximum or minimum; respectively.  Tolerance analysis drills down to the variation of individual units, thus facilitating improvement of process capability.

If you are working to make your system more robust, this webinar is for you!  It will be especially valuable to those involved in Design for Six Sigma (DFSS).

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  If you can be accommodated, she will provide immediate confirmation and, in timely fashion, the link with instructions from our 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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7: Conference Alert: 4th European DOE Meeting June 26-28 in Vienna

You are invited to participate in our Fourth European Design of Experiments (DOE) User Meeting in Vienna, Austria.  Find all the details here.

The meeting will focus on DOE, with a special emphasis on Design-Expert software.  Both the theoretical and practical aspects of DOE will be addressed, including the latest developments in the field.  The two meeting days will include lectures by DOE experts, case study presentations by DOE practitioners, and an opportunity to consult with the experts about your DOE applications.  Optional pre-meeting workshops will be presented to sharpen these powerful statistical tools.  Oh, and let’s not overlook the opportunity for breaking away to spend time in Vienna—a magnificent city of world culture.

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8: Events Alert: Pharma QbD (in India!), Biotechnology, Quality & Productivity

Pat Whitcomb jets halfway around the world to present a one-day workshop on DOE for QbD to pharma researchers in India.  See all the details here.

Stat-Ease will exhibit at the 2012 American Association of Pharmaceutical Scientists (AAPS) National Biotechnology Conference in San Diego, CA, on May 21-23 (Booth N313).  Shari Kraber will provide a lecture for the post-conference short course on Practical Essentials of Design of Experiments (DoE) toward Robust Bioanalysis on May 24.  See the details here.

See Stat-Ease also at the 29th Quality and Productivity Research Conference in Long Beach, CA, June 4-7.  Wayne Adams will provide a demo of Design-Expert software on June 6th, 3-4 pm.

Click here 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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9: 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 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 in February to earn $395 off the combined tuition!

** Take both MIX and MIX2 to earn $395 off the combined tuition!

See this web page 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

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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 Nobel Prize-winning philosopher/mathematician provides pithy comments on testing assertions with observational data and listening to data when they speak:

Aristotle could have avoided the mistake of thinking that women have fewer teeth than men by the simple device of asking Mrs. Aristotle to open her mouth.”

“The mark of a truly civilized human being is the ability to read a column of numbers and then weep.”

—Bertrand Russell

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
—Heidi Hansel Wolfe, Stat-Ease marketing director, Karen Dulski, and all the remaining staff that provide such supreme support!

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DOE FAQ Alert ©2012 Stat-Ease, Inc.
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