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Vol: 15 | No: 3 | May/Jun '15
The DOE FAQ Alert

Stat-Ease Statistical Group

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.

To open another avenue of communications with fellow DOE and Stat-Ease fans, sign up for The Stat-Ease Professional Network on Linked in. A recent posting features a discussion on DOE analysis with non-normal residuals.

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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:  Software alert: Version 9.0.5 of Design-Expert® software released (free update for licensed users of v9)
2:  FAQ: Prediction versus confidence intervals
3:  FAQ: Why do unimportant factor effects fall on a straight line in the half-normal probability plot?
4: Events alert: From Philadelphia to Prague
5:  Workshop alert: Coming to the East Coast!

PS. Quote for the month: Addicted to “DX” (Design-Expert)

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1: Software alert: Version 9.0.5 of Design-Expert software released (free update for licensed users of v9)

Newly-released version 9.0.5 of Design-Expert software is posted at this download site for free trial evaluation.  To update older licensed versions of 9.0, simply download the update from within the program, or download the full installation and reinstall it.  The release primarily provides maintenance of existing features.  However, it does add as a user preference the option for enhanced line placement on half and full normal plots of effects.  This makes it far easier to see which effects, if any, ought to be selected.  Check it out!

View the Read Me file for details on this update, installation tips, known ‘bugs,’ change history, and FAQs.

PS. Reminder: If you want to receive notice when an update becomes available, go to Edit on the main menu of your program, select Preferences and, within the default General tab, turn on (if not already on by default) the “Check for updates on program start” option.

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2: FAQ: Prediction versus confidence intervals

Original question from a Quality Consultant:
“Please clarify the meaning of the prediction interval provided by Design-Expert. I understand that that the confidence interval relates to the mean response for a given value of the predictor variable, and the prediction interval relates to individual values at the specified predictor level, but what range of individual values are we talking about?

For example, presumably we are not talking about the whole 100% population of individual values. We must be talking about some limited range of the population of the individual values.

I have some recollection from the past that the prediction interval indicates the range of values within which we would expect a result to fall from another experiment at the specified value of the predictor, but I can’t now find the reference.

Suppose we have a 95% prediction interval—what is included in that?”

Answer from Stat-Ease Consultant Wayne Adams:
“The confidence interval (CI) is for the true population average. Data from a sample only provides an estimate of that population. If an infinite number of samples from the same population are used to generate 95% confidence intervals, then 95% of those intervals will contain the true average.

Prediction intervals (PI) are for the average of a future sample rather than the whole population. This is usually presented as a future sample of size 1, and taken to mean the next observation. Again, if an infinite number of 95% confident prediction intervals are generated, then 95% of the PIs will contain the average of a future sample from that population. The interval width is widest for a sample size of 1. It approaches the confidence interval as the sample size approaches infinity.

Tolerance intervals (TI) are the intervals used for the whole population. These intervals have two parameters, the customary confidence, and the proportion of the population contained by the interval. They are usually set up as 95% confident that 99% of the population will be inside the tolerance interval bounds.”

P.S. For Wayne covered this before in FAQ 1 of the Nov/Dec ’12 Alert. Check it out! —Mark

(Learn more about prediction versus confidence intervals by attending the two-day computer-intensive workshop Response Surface Methods 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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3: FAQ: Why do unimportant factor effects fall on a straight line in the half-normal probability plot?

Original question from a School of Engineering PhD Candidate:

“I have been a user of Design-Expert for almost a year. Could you please explain why unimportant factor effects fall on a straight line in a half-normal probability plot? I am totally fine with using the half-normal plot features and the method. But, I need to know the theory behind it that shows a normal distribution for insignificant effects. Unfortunately, I could not find an answer in DOE reference books.”

Answer from Stat-Ease Consultant Brooks Henderson:
“There are very simple matter-of-fact explanations in the textbooks, as you may have seen. The fundamental reference is the “Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments” by Cuthbert Daniel published in Technometrics, Vol. 1, No. 4, pp. 311-314 in November 1959. For a simpler explanation see this detailing in the NIST/SEMATECH e-Handbook of Statistical Methods.

What we’re looking for on the plot are the nonzero effects. We need some rule for whether an effect is significantly non-zero or not. That’s where the half-normal plot comes into play. The effects that are normally distributed and centered on zero will follow the straight line. These represent normal process variation. The Central Limit Theorem (CLT) asserts that a distribution of averages, such as null factorial effects, follow a normal distribution. Search the internet on ‘CLT’ for more details. The effects that are not centered on zero will stand off to the right. They are created by special cause rather than common cause (normal) variation.”

P.S. For a picture of a half-normal plot and thoughts on this from Consultant Shari Kraber, see FAQ 2 in the Nov/Dec ’13 Alert —Mark

(Learn more about half-normal effect plots 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: Events alert: From Philadelphia to Prague At the Society for Industrial Microbiology & Biotechnology August 2-6 Annual Meeting in Philadelphia, PA, I will present a talk on “Strategy of Experimentation for Fermentation Process and Product Development” and exhibit our software in Booth 20. Register here.

Consultant Pat Whitcomb will provide guidance on “Confirmation—The Final DOE Step” for the Annual Conference of the European Network for Business and Industrial Statistics in Prague, Czech Republic held September 6-10. Click this link for all the details.

Click here for a list of upcoming appearances by Stat-Ease professionals. We hope to see you sometime in the near future!

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5: Workshop alert: Coming to the East Coast!

All classes listed below will be held at the Stat-Ease training center in Minneapolis unless otherwise noted.  If possible, enroll at least 4 weeks prior to the date so your place can be assured.  Also, take advantage of a $400 discount when you take two complementary two-day workshops that are offered on consecutive days.

*Take both EDME and RSM to earn $400 off the combined tuition!

** Take both MIX and MIX2 to earn $400 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, scroll down to the workshop of your choice and click on it, or call Rachel Pollack 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:

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


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

PS. Quote for the month—Addicted to “DX” (Design-Expert):

"Your computer's on, you're data's in
Your mind is lost amidst the din
Your palms sweat, your keyboard shakes
Another transform is what it takes
You can't sleep, you can't eat
You have runs you must repeat
You squeeze the mouse, it starts to squeak
A new analysis will look less bleak
Whoa, you like to think that you're immune to the stats, oh yeah
It's closer to the truth to say you need your fix
You know you're gonna have to face it, you're addicted to Dee Ex.”

—Design-Expert software user named Sammy (with apologies to Robert Palmer)

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

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