Issue: Volume 4, Number 1
Date: January 2004
From: Mark J. Anderson, Stat-Ease, Inc. (www.statease.com)

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 previous DOE FAQ Alerts, please click on the links at the bottom of this page. Feel free to forward this newsletter to your colleagues. They can subscribe by going to http://www.statease.com/doealertreg.html. If this newsletter prompts you ask to your own questions about DOE, please address them to stathelp@statease.com.

Here's an appetizer to get this Alert off to a good start: Go to http://www.its.caltech.edu/%7Eatomic/snowcrystals/ for beautiful snowflake pictures and physics of their crystallization.  The site is maintained by Professor Kenneth G. Libbrecht, Chairman of the Physics Department California Institute of Technology (Caltech). He's written a new book called "The Snowflake: Winter's Secret Beauty" that's published by Voyageur Press in my hometown of Stillwater, Minnesota—a place where people appreciate snow, because we see lots of it.  Contacts at the publisher tell me that the snowflake book has been one of their most popular ever.

On the subject of frozen water, I'd always heard that skates melted a thin layer of ice to reduce friction via hydroplaning. Not so according to a professor at Lawrence Berkeley National Laboratory. For details on new ice-skating theories, see http://www.exploratorium.edu/hockey/ice2.html. Also, keep an eye out for a link provided later on in this issue on a DOE done on ice hockey.

The slippery conditions caused by water in its solid state provide a perfect environment for snowmobilers. They have no fears about venturing out in the cold, because if an emergency arises, it's a simple matter to write a message in the snow. For example, see http://makeashorterlink.com/?M41451DD6. (They're Canadians, eh!)

Finally, to finish off these cold appetizers on a royal note, see http://www.2004icepalace.com/ for an architect's drawing of the Saint Paul, Minnesota's 2004 Winter Carnival Ice Palace. It's due to be lit up later this month after piling on tens of thousand of ice blocks totaling tens of millions in pounds. Luckily for the construction crew the weather is cooperating this week with wind chills in the range of 20-30 below zero °F.

Here's what I cover in the body text of this DOE FAQ Alert (topics that delve into statistical detail are designated "Expert"):

1. Newsletter alert: The December issue of the Stat-Teaser features "A DOE for the Sweet Tooth" (watch out for the odd dog)  
2. FAQ: Can analysis of a two-level factorial design be simplified down to one t-test for overall significance?  
3. Info alert: See a DOE on ice hockey by the brother of a professional player (a class project)  
4. Events alert: Link to a schedule of 2004 appearances by Stat-Ease at conferences and shows  
5. Workshop alert: There is a DOE class in San Jose later this month, see details on this and other public presentations by Stat-Ease statistical consultants

PS. Quote for the month: The first golden rule of mathematics.

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1. Newsletter alert: The December issue of the Stat-Teaser features "A DOE for the Sweet Tooth" (watch out for the odd dog)

Many of you by now have received a printed copy of the latest Stat-Teaser, but others, by choice or because you reside outside of North America, will get your first look at the September issue at http://www.statease.com/news/news0312.pdf.

The feature article, "A DOE for the Sweet Tooth," provides a recipe for delicious peanut butter balls resulting from experimentation by Stat-Ease consultant Shari Kraber. She succeeded in making significant taste improvements despite losing a batch of balls to the family dog. (Have you ever fed peanut butter to a pet? It's not a pretty sight!)

The other story in the Stat-Teaser provides details on the "Mixture Design for Optimal Formulation" workshop.  For a description, see http://www.statease.com/clas_mix.html.  Link from this page to the course outline and schedule.  You can enroll online by linking to the Stat-Ease e-commerce page for workshops.

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2. FAQ: Can analysis of a two-level factorial design be simplified down to one t-test for overall significance?

-----Original Question-----
From: California


"I have an engineer who performed as a two-level factorial  experiment.  I've told him to analyze the experiment using ANOVA, but he says he usually does a two-sample t-test and then only if he finds anything suspicious does he bother doing an analysis of variance.  He claims that it's OK to 'project' the factorial experiment into one factor and then only the t-test will be  needed.  Is my engineer correct in simplifying things this way?"

Answer (from Pat Whitcomb, Stat-Ease Statistical Consultant): "To answer your question—orthogonal arrays can be projected into fewer dimensions without changing the effect estimates.  HOWEVER, this does NOT mean you can use the t-test in the projected space.

Let me illustrate by a simple 2^3 example where factors B, C and the BC interaction have an effect.  Factor A, the AB, AC, ABC interactions have no effect and their SS can be used to estimate error.  Here are the data sorted by B:

A B C Y
-1 -1 -1 74
+1 -1 -1 75
-1 -1 +1 81
+1 -1 +1 77
-1 +1 -1 71
+1 +1 -1 80
-1 +1 +1 42
+1 +1 +1 32

If B, C and BC are chosen to model and ANOVA is performed, the effect of factor B is -20.50 (significant at p-value = 0.0043).  Now let's project this design into the B space by deleting the other factor columns (A and C). The data are:

B Y
-1 74
-1 75
-1 81
-1 77
+1 71
+1 80
+1 42
+1 32

Next we perform a t-test. The B effect (the numerator in the t-test) remains at -20.50. But now it's insignificant (p-value = 0.1263) because the error term (the denominator) in our t-test becomes inflated by the C and BC effects.

This design can be projected into the B-C factor space by deleting column A. Since factor A has no effect the ANOVA for the B, C, BC model will not change. In the B-C factor space there are four replicates to estimate error and their sum of squares (SS) is exactly the same as the SS originally obtained by pooling the SS for A, AB, AC and ABC prior to projection.

(Learn more about analyzing two-level factorial designs by attending the three-day computer-intensive workshop "Experiment Design Made Easy." See http://www.statease.com/clas_edme.html 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. Info alert: A DOE on ice hockey by the brother of a professional player (a class project)

See http://www.statease.com/pubs/studenthockey.pdf for a DOE on ice hockey done by Neil, a graduate student at Memorial University of Newfoundland, Canada.  His teacher, Professor Leonard M.Lye, sent it to me with this cover note about his pupil: "He is the older brother of Dan Cleary of the Phoenix Coyotes.  I guess he chose engineering rather than hockey... As a hockey fan, I thought you might enjoy reading it.  Of course Design-Expert® software was used for the analysis."

Making use of DOE may not be a worthy goal (unsporting, pun intended) when it comes to hockey, particularly for a team that competes with the Minnesota Wild!

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4. Events alert: Link to a schedule of appearances by Stat-Ease

Click on http://www.statease.com/events.html for a list of appearances by Stat-Ease professionals.  We hope to see you sometime in the near future!

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5. Workshop alert: There is a DOE class in San Jose later this month, see details on this and other public presentations by Stat-Ease statistical consultants

Later this month (January 20-22) I will head off to San Jose, California to teach the three-day, "Experiment Design Made Easy," workshop.  It's tough for a Minnesotan to tear himself away from home at the coldest time of the year and be subjected to the mild California weather, but someone from Stat-Ease has to do it. Seats remain for this class, so if you need basic training on DOE and don't mind getting it in San Jose, sign up now.

See http://www.statease.com/clas_pub.html for schedule and site information on all Stat-Ease workshops open to the public. To enroll, click on the "register online" link on our web site or call Stat-Ease at 1.612.378.9449.  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.  Call us to get a quote.

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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. (http://www.statease.com)
Minneapolis, Minnesota USA

PS. Quote for the month—the first golden rule of mathematics:

"An approximate answer to the right question is worth a great deal more than a precise answer to the wrong question."
 
- John Tukey*

*For a biography on this great statistician, including a slightly different version of this quotation, see http://www.mrs.umn.edu/~sungurea/introstat/history/w98/Tukey.html

Trademarks: Design-Ease, Design-Expert and Stat-Ease are registered trademarks of Stat-Ease, Inc.

Acknowledgements to contributors:

—Students of Stat-Ease training and users of Stat-Ease software
—Fellow Stat-Ease consultants Pat Whitcomb and Shari Kraber (see http://www.statease.com/consult.html for resumes)
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert (http://www.statease.com/garyoehl.html)
—Stat-Ease programmers, especially Tryg Helseth (http://www.statease.com/pgmstaff.html)
—Heidi Hansel, Stat-Ease marketing director, and all the remaining staff

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#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
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