Issue: Volume 8, Number 9
Date: September 2008
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 If this newsletter prompts you to ask your own questions about DOE, please address them via mail

For an assortment of appetizers to get this Alert off to a good start, see these new blogs at (beginning with the most recent one):

— How to be alerted to new StatsMadeEasy blogs (like this one!)
— Putting a snap into your presentation
— Arriba for Tequila Sangria
— Careful for the eye beams

Topics in the body text of this DOE FAQ Alert are headlined below. Given a plenitude of things worth alerting you too, I slacked off on FAQs and their answers. My excuse is taking some summer vacation that coincides with celebrating Independence. (Do you suppose I am referring to the separation of the United States from England; or could it be that I am celebrating the statistical assumption that one observation be independent of every other? Flip a coin!)

1. Newsletter Alert: September issue of the Stat-Teaser features new fraction of design space (FDS) graph — a handy tool for assessing precision (as an alternative to power)
2. FAQ: Does a low R-squared invalidate all my results?
3. Expert-FAQ: Choosing sequential vs classical vs partial sum of squares (SS) for the analysis of variance (ANOVA) types
4. Book Giveaway: Winners announced
5. Info Alert: DOE optimizes pharmaceutical coating process
6. Webinar Alert: How to Plan and Analyze a Verification DOE
7. StatsMadeEasy Reader Response: Inverse transformation puts mileage comparisons on track
8. DOE FAQ Alert Reader Response: Is it good to delete an insignificant factor?
9. Event Alert: For those who say "statistics are Greek to me" and mean that as a good thing!
10. Workshop Alert: Do not miss our DOE class in Philadelphia!

P.S. Quote for the month: The difference between scientists versus engineers.


1. Newsletter Alert: September issue of the Stat-Teaser features new fraction of design space (FDS) graph — a handy tool for assessing precision (as an alternative to power)

Many of you will soon receive a printed copy of the latest Stat-Teaser, but others, by choice or because you reside outside of North America, will get your only view of the September issue at It features an article by Stat-Ease Consultant Pat Whitcomb on "FDS — A Power Tool for Designers of Optimization Experiments." Our latest version of Design-Expert® software* features this very useful tool for assessing the capability of response surface method (RSM) and mixture designs.

Also, this issue of the Stat-Teaser profiles our Workshop Coordinator Elicia Bechard. Check out her puppy Kaylee — an adorable white lab that looks angelic but behaves devilishly (or so I am told by Elicia!).

Thank you for reading our Stat-Teaser newsletter. If you do get the hard copy, but find it just as convenient to read what we post to the Internet, consider contacting us to be taken off our mailing list, thus conserving resources. However, we do appreciate you passing around hard copies of the Stat-Teaser, so do not feel obliged to forego this.

*Download a free, fully-functional trial of Design-Expert v7.1.5 (our most current), from


2. FAQ: Does a low R-squared invalidate all my results?

-----Original Question-----
From: Medical device engineer
"My experiment produced an R-squared below 0.6: Does such a low result for this statistic invalidate all my results?"

It depends. (I've been associating with master statisticians for so long now that I've finally learned The answer!) Seriously though, the best answer I've seen yet to this very frequently asked question came from Consultant Pat Whitcomb in his illustrated 1997 (September) Stat-Teaser article titled "Don't Let R^2 Fool You," which can be seen on page 2 of the newsletter posted at

(Learn more about interpreting statistical analysis of experimental data by attending the three-day computer-intensive workshop "Experiment Design Made Easy." For a description of this class, see and then link from this page to the course outline and schedule. Then, if you like, enroll online.)


3. Expert-FAQ: Choosing sequential vs classical vs partial sum of squares (SS) for the analysis of variance (ANOVA) types

-----Original Question-----
From: French semiconductor engineer
"I have problems with the meaning of the three methods of computing the sum of squares (SS): Sequential, Classical or Partial. Could you advise a reference, easily readable by a non-statistician, that explains these different types of SS? What I find in the Stat-Ease program Help is rather short:

>The ANOVA can be calculated using either partial sums of squares, sequential sums of squares, or a classical sum of squares... definable under Edit, Preferences, Math. Partial SS is sometimes referred to as Type III sum of squares. This calculates the SS for a term after correcting for all other terms in the model. This is normally the desired form of sums of squares. A disadvantage is that for a non-orthogonal design, the term SS may not add up to the total SS. Sequential SS is sometimes referred to as Type I sum of squares. This calculates sums of squares in sequence. The SS for a term is corrected only for terms above it on the term list. The term SS will add up to the total SS, but they are order dependent.<"

Answer (from Stat-Ease Consultant Wayne Adams):
See Wayne's answer via, which links to a posting by him, our Statistics Moderator, to a new Forum that we are nearly ready to unveil — watch for a 'heads-up' coming soon (I hope!) in an upcoming DOE FAQ Alert.

The best explanation I can find in print on this topic is by Professor Gary W. Oehlert (Statistical Advisor to Stat-Ease) in his book "A First Course in Design and Analysis of Experiments" (link to publisher's web site: — see section 10.1.1 "Sums of squares in unbalanced data."

Not being a statistician by profession, I struggle with distinctions such as these, but I can see how the sequential approach could be very tricky in programs that require you to specify the order of model terms in a different order. For example, in an unbalanced design such as Oehlert presents for a case study, the sum of squares differ for these two model specifications: (A, B, C, AB, BC, AC) versus (A, B, AB, C, AC, BC)! This Type I approach to SS is not used by default in Stat-Ease software, although it is available via an editing of preferences. I am glad of that.

To see exactly what can happen with the options for SS types, I went back to a study on ACT college placement scores done earlier this year by my daughter for her high school statistics class. I
reported her results in my StatsMadeEasy blog of June 1: When you look this over, please bear in mind the source. (You might be surprised how unkind people can be. This provides a suitably ugly example of regression modeling that one sees rarely when working with controlled experiments on industrial processes. Here are the breakdowns of sequential (Type I) sums of squares for the two factors — number of AP (advanced placement) college-level courses taken by these high-schoolers and their GPA (grade point average). The p-values are shown in brackets:

AP first
AP: 242.1 SS (p < 0.0001)
GPA: 4.9 SS (p = 0.4596)

GPA first
GPA: 107.4 SS (p = 0.0013)
AP: 139.6 SS (p = 0.0003)

The way I interpret this is that after first accounting for the variance due to AP, nothing much remains for GPA, so it cannot become significant statistically. However, by putting GPA first, it accounts for a significant amount of SS and there's still enough left over for AP that it remains significant as well. Now don't worry over this particular situation — let's leave this to social scientists and remain focused on industrial experimentation — machines are so much easier to deal with than people! The point is that the sequential method (Type I) for computing sums of squares in analysis of variance should be used only with great caution by those who can justify putting one term ahead of another in their predictive modeling.

*(Learn more about the basics of ANOVA by enrolling in the web-based "PreDOE" course at — You can assess your abilities by first taking the free self-assessment questionnaire, which is available as a pre-test within the PreDOE course. )


4. Book Giveaway: Winner announced

This lucky reader was drawn at random from 42 entrants to a drawing* for a first edition of "Empirical Model-Building and Response Surfaces" by Box & Draper:

-> Dusty Vaughn, Project Engineer, Aerospace Testing Alliance, Arnold AFB, Tennessee

Congratulations to Dusty and condolences to the others who entered into this drawing. Keep watching for more great books to be given away in the future.

*(Sorry, due to the high cost of shipping, this offer applied only to residents of the United States and Canada.)


5. Info Alert: DOE optimizes pharmaceutical coating process

See how Sarah Betterman, Scientist for Upsher-Smith, used design of experiments (DOE) to determine how key fluidized-bed coating parameters affected dissolution of their pharmaceutical product by reading this original manuscript posted at Sarah
made use of a Box-Behnken design, a response surface method (RSM*) well suited to the goal of process optimization.

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


6. Webinar Alert: How to Plan and Analyze a Verification DOE

You are invited to attend a free web conference by Stat-Ease Consultant Shari Kraber, who will show "How to Plan and Analyze a Verification DOE." This free conference, which Shari will keep at an intermediate level statistically, will be broadcast on Wednesday, October 29 at 12 PM noon USA Central Daylight Time (CDT), which is 17:00 in Coordinated Universal Time (UTC). (We are at UTC -5 under CDT.) She will repeat her webinar at 8 PM that evening (01:00 UTC October 30). The talk will be offered one last time on Thursday, October 30 at 8 AM (13:00 UTC).

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 as soon as you see your way clear by contacting our Communications Specialist, Karen, via If you can be accommodated, she will send you the link for the WebConnect and dial-in for ConferenceNow voice via telephone (toll-free access extends worldwide, but not to all countries).


7. StatsMadeEasy Reader Response: Inverse transformation puts mileage comparisons on track

-----Original Message-----
Reed Wahlberg
"The timing of your blog article "Inverse transformation puts mileage comparisons on track" last month was perfect (see I really enjoyed it. For a day or so I had been toying with trading in my Honda Civic (consistently high 30's mpg, record=42) for a Prius. That would have meant giving up on my goal of driving this great car for 20 years. Then I read your article. I had not worked the numbers on potential savings in gasoline. I have since shared the example you provided with a number of other people. Your efforts are appreciated!

You are welcome. It really is interesting how something as simple as an inverse can transform how one views things (other than just looking at things upside down!). I really like the idea of being logical about the cost versus benefit and so assessing what one pays for fuel per ten thousand miles — about a year for city commuters to only 6 months for outliers like me — makes a lot of sense to me. Nonetheless, as I noted in another blog (see, I really like the Prius and if I did not have two kids in college at present, I would buy one to replace the '98 Grand Voyager that my wife drives. As it is, that van works great for moving these college students back and forth from home to school.


8. DOE FAQ Alert Reader Response: Is it good to delete an insignificant factor?

-----Original Message-----
Senior biotechnologist
"In one of the courses that I attended at Stat-Ease, someone talked about 'design projection' where you could delete a non-significant factor or two in a design (a larger design I presume) and increase the degrees of freedom and gain some statistical power. Is the answer to last month's FAQ on deleting factors* in conflict with this?

*(See FAQ 1 at

Answer (from Consultant Pat Whitcomb):
"I think of projection in this way: when a factor is not included in a model it is as if the design was projected down in that dimension. For example, here is an evaluation of a 2^4 full factorial for A, B and C (not D):

-> Degrees of Freedom: Model 3, Residuals 12, Lack of Fit 12, Pure Error 0
-> Power at 5% to detect a 1 Std. Dev. signal/noise ratio: A 95.6%, B 95.6%, C 95.6%

After deleting factor D, here are the results:

->DF: Model 3, Residuals 12, Lack of Fit 4, Pure Error 8
->Power: A 95.6%, B 95.6%, C 95.6%

Deleting factor D produces absolutely no power gain! This is the beauty of orthogonal design). By deleting all factor D effects (instead of simply leaving then unselected when modeling), you are saying the D effects are zero. Now all the eight D effects (D, AD, BD, CD, ABD, ACD, BCD, ABCD) are treated as pure error. However, we know D was varied so how can this error estimate be pure? Since the zero effects cannot be proved why make this assumption when there is no gain? Therefore, I prefer to have a design reflect what was actually run and not delete factors."


9. Events Alert: For those who say "statistics are Greek to me" and mean that as a good thing!

ENBIS — the European Network for Business and Industrial Statistics will hold their annual conference in Athens, Greece on September 22-24. For conference details, go to Stat-Ease Founder Pat Whitcomb will be there to provide a tabletop display and talk about "Graphical Selection of Effects in General Factorials" (see abstract at Pat will follow up with another European appearance at Planet xMAP in Amsterdam on October 9 to present "A Factorial Design Planning Process" to this symposium for life scientists and clinical diagnosticians hosted by Luminex. For details, see

Back here in Minneapolis, Consultant Shari Kraber will be at the Stat-Ease booth for the annual Operational Excellence Conference and Expo of the Institute of Industrial Engineers on October 1 and 2. See for all the details. Click for a list of upcoming appearances by Stat-Ease professionals. We hope to see you sometime in the near future!


10. Workshop Alert: Do not miss our DOE class in Philadelphia!

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
> September 30 through October 2 (Philadelphia, PA)

—> Response Surface Methods for Process Optimization (RSM)
> September 23-25 (Minneapolis, MN) — SOLD OUT*
*(Contact Elicia for possible overflow class late in 2008.)

—> Mixture Design for Optimal Formulations (MIX)
> October 21-23 (Minneapolis)

—> DOE for DFSS: Variation by Design (DDFSS)
> November 11-12 (Minneapolis)

—> Designed Experiments for Life Sciences (DELS)
> November 18-20 (Minneapolis)

See 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


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 —The difference between scientists

"The scientist seeks to understand what is;
the engineer seeks to create what never was."

—Theodore von Karman (aerodynamicist)

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 for resumes)
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert (
—Stat-Ease programmers, especially Tryg Helseth and Neal Vaughn (
—Heidi Hansel, Stat-Ease marketing director, and all the remaining staff


Interested in previous FAQ DOE Alert e-mail newsletters?
To view a past issue, choose it below.

#1 Mar 01, #2 Apr 01, #3 May 01, #4 Jun 01, #5 Jul 01 , #6 Aug 01, #7 Sep 01, #8 Oct 01, #9 Nov 01, #10 Dec 01, #2-1 Jan 02, #2-2 Feb 02, #2-3 Mar 02, #2-4 Apr 02, #2-5 May 02, #2-6 Jun 02, #2-7 Jul 02, #2-8 Aug 02, #2-9 Sep 02, #2-10 Oct 02, #2-11 Nov 02, #2-12 Dec 02, #3-1 Jan 03, #3-2 Feb 03, #3-3 Mar 03, #3-4 Apr 03, #3-5 May 03, #3-6 Jun 03, #3-7 Jul 03, #3-8 Aug 03, #3-9 Sep 03 #3-10 Oct 03, #3-11 Nov 03, #3-12 Dec 03, #4-1 Jan 04, #4-2 Feb 04, #4-3 Mar 04, #4-4 Apr 04, #4-5 May 04, #4-6 Jun 04, #4-7 Jul 04, #4-8 Aug 04, #4-9 Sep 04, #4-10 Oct 04, #4-11 Nov 04, #4-12 Dec 04, #5-1 Jan 05, #5-2 Feb 05, #5-3 Mar 05, #5-4 Apr 05, #5-5 May 05, #5-6 Jun 05, #5-7 Jul 05, #5-8 Aug 05, #5-9 Sep 05, #5-10 Oct 05, #5-11 Nov 05, #5-12 Dec 05, #6-01 Jan 06, #6-02 Feb 06, #6-03 Mar 06, #6-4 Apr 06, #6-5 May 06, #6-6 Jun 06, #6-7 Jul 06, #6-8 Aug 06, #6-9 Sep 06, #6-10 Oct 06, #6-11 Nov 06, #6-12 Dec 06, #7-1 Jan 07, #7-2 Feb 07, #7-3 Mar 07, #7-4 Apr 07, #7-5 May 07, #7-6 Jun 07, #7-7 Jul 07, #7-8 Aug 07, #7-9 Sep 07, #7-10 Oct 07, #7-11 Nov 07, #7-12 Dec 07, #8-1 Jan 08, #8-2 Feb 08, #8-3 Mar 08, #8-4 Apr 08, #8-5 May 08, #8-6 June 08, #8-7 July 08, #8-8 Aug 08, #8-9 Sep 08 (see above)

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