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Vol: 17 | No: 4 | Jul/Aug '17
The DOE FAQ Alert

Dear Experimenter,
Here’s another set of frequently asked questions (FAQs) from me and the rest of our StatHelp team about design of experiments (DOE), plus alerts to timely information and free software updates. If you missed the previous DOE FAQ Alert click here.

To open another avenue of communication with fellow DOE and Stat-Ease fans, sign up for The
Stat-Ease Design of Experiments (DOE) Network
on Linkedin. A recent posting features “DOE or Stats in a Hospital Setting.

Stats Made Easy Blog










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

1:  FAQ: If analysis of variance (ANOVA) and adequate precision results look good, but the predicted R-squared is negative, can the model still be useful?
2: Info alert: Quality Progress success story: DOE relieves “Paint Process Pains”
3: Events alert: Stat-Ease Consultants talking up mixture design for optimal formulation and other DOE tools in USA and Europe
4: Workshop alert: Experiment Design Made Easy and beyond

P.S. Quote for the month: Words of wisdom from Isaac Asimov on being open to evidence that goes against prior science.

(Page down to the end of this e-zine to enjoy the actual quote.)

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1: FAQ: If analysis of variance (ANOVA) and adequate precision results look good, but the predicted R-squared is negative, can the model still be useful?

Original question from a Coatings Formulation Scientist:
“I am having some trouble interpreting the ANOVA results. The model is significant, the lack of fit is not significant, the adequate precision is above 4, but I get a negative predicted R-squared [R2pred] value. Does this mean the entire model is no good, or since everything else looks good, I can use it to predict data?”

Answer from Stat-Ease Consultant Martin Bezener:
“Take a look at the Cook's Distance plot in the Diagnostics tab. Notice that nearly every point is highly influential. This is probably what's causing the low R2pred. This suggests the model has too many terms in it.”

This case of over-fitting as indicated by the negative R2pred is illustrated nicely by statistics educator Jim Frost in his April 8th blog on How to Interpret Adjusted R-Squared and Predicted R-Squared in Regression Analysis. He provides a “nearly perfect” example of no relationship in his data on how approval ratings for U.S. presidents predict how historians rank them. I reproduced his cubic-modeling results in Design-Expert (file available on request)—the only difference being that the software Jim used rounds negative R2pred to zero and reports it in percents, whereas ours gives it as-calculated and as a fraction: -0.216. Rounded or not, the low R2pred is very alarming.

You may still be puzzled by R2pred going negative. It’s explained in Chapter 1 of RSM Simplified, 2nd Edition by my co-author Pat Whitcomb and me (pp 14-15). The figure below tells the story by illustrating what happens with a poor model—trying to fit points on a curve with only a straight line. The R2pred relates directly to the predicted residual sum of squares (PRESS), which accumulates the discrepancies of each point when fitted with all the others, that is, taken out one at a time. When PRESS exceeds the residual sum of squares, the R2pred goes below zero. Then you know something is not right with the model (in this case it needs to be upgraded from linear to quadratic so it fits the curve).

Cause for Negative Predicted R-Squared
Cause for negative predicted R-squared: Excessive predicted residual sum of squares (PRESS)


P.S. The cause for R2pred going negative, and the possible remedies, cannot be generalized. If you come across this problem on a mission-critical response model, you would do well to get help from a statistician. To pursue consulting services from Stat-Ease, click here.

(Learn more about how to interpret model statistics by attending the three-day computer-intensive workshop on Modern DOE for Process Optimization. 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: Info alert: Quality Progress success story: DOE relieves “Paint Process Pains”

The June issue of Quality Progress features a case study by Design-Expert user Christopher Bertoni who successfully applied DOE to solve paint adherence problems. It is posted here (registration required by the publisher—American Society of Quality).

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3: Events alert: Stat-Ease Consultants talking up mixture design for optimal formulation and other DOE tools in USA and Europe

(Second Notice) Stat-Ease Consultant Martin Bezener will provide a briefing on “Strategies for Mixture-Design Space Augmentation” at the 2017 Joint Statistical Meetings (JSM) July 29 through August 3 in Baltimore. Register for JSM here.

Stat-Ease Consultant Pat Whitcomb will exhibit software and give two talks at the 17th annual meeting of the European Network for Business and Industrial Statistics (ENBIS) in Naples, Italy, on September 10 through 14:

  • “Strategies for Mixture-Design Space Augmentation” and
  • “Sizing Mixture Designs for Precision”.

Details on ENBIS 17 can be found via this link.

Stat-Ease software will be on exhibit at the Fall Technical Conference (FTC) in Philadelphia, PA, October 4 through 6, 2017. This annual forum for statistics and quality is co-sponsored by the Chemical and Process Industries Division (CPID) and Statistics Division of the American Society for Quality (ASQ), and Sections on Physical and Engineering Sciences (SPES) and Quality and Productivity (Q&P) of the American Statistical Association (ASA). Two talks will be presented by our Consultants:

  • Martin: “Strategies for Mixture Design Space Augmentation”
  • Shari: “RSM Split-Plot Designs & Diagnostics Solve Real-World Problems”

Sign up for the Philly FTC here.

Click here for these and other upcoming appearances by Stat-Ease professionals.

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4: Workshop alert: Experiment Design Made Easy and beyondYou can do no better for quickly advancing your DOE skills than attending a Stat-Ease workshop. In these computer-intensive classes, our expert instructors provide you with a lively and extremely informative series of lectures interspersed by valuable hands-on exercises with one-on-one coaching. Enroll at least 6 weeks prior to the date so your place can be assured—plus get a 10% “early-bird” discount.

See this web page for complete schedule and site information on all Stat-Ease workshops open to the public. To enroll, scroll down to the workshop of your choice and click on it, or call our Client Specialist Rachel Pollack, at 612-746-2030. 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:

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Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc.
2021 East Hennepin Avenue, Suite 480
Minneapolis, Minnesota 55413 USA

P.S. Quote for the month:

"I believe in evidence. I believe in observation, measurement, and reasoning, confirmed by independent observers. I'll believe anything, no matter how wild and ridiculous, if there is evidence for it. The wilder and more ridiculous something is, however, the firmer and more solid the evidence will have to be.”

—Isaac Asimov, a professor of biochemistry at Boston University who became famed as a writer of science fact and fiction (quote from The Roving Mind, first published in 1983 by Asimov and reissued in 1997 as a tribute to him after his passing in 1992).

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, Martin Bezener, and Shari Kraber
Stat-Ease programmers Hank Anderson, Neal Vaughn, Joe Carriere and Jon Kraber
—Heidi Hansel Wolfe, Stat-Ease sales and marketing director, and all the remaining staff that provide such supreme support!

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