Issue: Volume 3, Number 4
Date: April 2003
From: Mark J. Anderson, Stat-Ease, Inc.
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, click on the links below. Feel free to forward this newsletter to your colleagues. They can subscribe by going to http://www.statease.com/doealertreg.html.
I start off this Alert on a personal note with a few science-related tidbits tossed in. I just returned from a fun family vacation in Colonial Williamsburg, Virginia -- a hotbed of American history ranging from the first settlement in nearby Jamestown (1607) through the Revolutionary War period, culminating just down the road at Yorktown where Lord Cornwallis surrendered to combined forces of the US and French. Four-score years later Civil War battles raged in defense of the Confederate capital of Richmond -- only an hour away by car. At one of our stops, a costumed interpreter talked about the role of gunpowder and asked if anyone knew which American first developed a product deemed superior to that made by Europeans. See http://footguards.tripod.com/06ARTICLES/ART28_blackpowder.htm for the answer, plus details on centuries of experimentation on chemistry and processing to get the proper powdering. Before heading home, we stopped in Petersburg, Virginia to see "The Crater" battlefield where Union miners blew 4 tons of gunpowder under Confederate lines in the Civil War (for the story, see http://www.wikipedia.org/wiki/Battle_of_the_Crater). Needless to say, with all the conflict going on in the world today, I found this history on American wars and gunpowder very unsettling, but fascinating.
Here's what I cover in the body text
of this DOE FAQ Alert (topics that delve into statistical detail are designated
1. Info alert: The March issue of the Stat-Teaser (a link is provided) features a DOE that helped "Miracle Flowers SurviveIn Spite of Shari!"
2. Reader feedback (Stat-Teaser): Gardeners respond to Shari's experiments on flowers
3. FAQ: How to maintain model hierarchy when three-factor interactions are selected as effects from a two-level factorial design
4. Reader feedback (DOE FAQ Alert): A suggested link for details on fun and somewhat disgusting experiments to try at home with your children
5. Events alert: Stat-Ease is giving talks and exhibiting at quality conferences in Minneapolis and Kansas City
6. Workshop alert: A full slate of workshops is presented in Minneapolisthis is a great time to learn statistics and visit Minnesota
PS. Quote for the month: Ancient alchemist, Paraclesus, provides advice on experimentation
1 - Info alert: The March issue of the Stat-Teaser (a link is provided) features a DOE that helps "Miracle Flowers SurviveIn Spite of Shari!"
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 March issue at http://www.statease.com/news/news0303.pdf.
The feature article, "Miracle Flowers SurviveIn Spite of Shari!" describes how Shari Kraber tortured her Verbenas with varying amounts of fertilizer and the like. She had a few mishaps along the way but managed to salvage some good results from her DOE.
The other story in the Stat-Teaser
describes an exciting new joint venture of Stat-Ease with Beckman-Coulter that
provides a synergistic interaction of DOE education with training on their automated
assay system. This is truly high technology!
2 - Reader feedback (Stat-Teaser): Gardeners respond to Shari's experiments on flowers
----- Original Message -----
"I appreciated your article "Miracle Flowers Survive". Since I was planning to do a similar project in the next couple weeks, you saved me the trouble. In your study, you noted that water fertilizer and pot size were the significant factors along with the pot size/pinch off interaction. I would be interested to see the graphs for the other interactions and factors. With all the advertising that Miracle-Gro does, I'm surprised that soil type took a back seat role. By the way, what was your water fertilizer and secondary soil type? Although your experiment was with verbena, I wonder if your findings are applicable to other plants? Anything you can share would be appreciated. Thanks and happy gardening to you, too."
Answer (from Shari Kraber):
"Thank you for your comments about my Flower DOE. Since the other factors and interactions were not statistically significant, they will be fairly flat lines when plotted. Design-Expert® only provides graphs of the statistically significant factors that are placed in the model so that people do not get misled by non-significant graphs.
Since I did this experiment last summer, I don't know what the other soil type was. It was simply a regular outdoor potting soil with nothing special added to it. I think I purchased it at WalMart. I will admit to inconsistency in the fertilizer I used. I had both a Miracle Gro brand and an unknown brand from a nursery. I used both of these throughout the summer, grabbing whichever was more convenient. This is certainly poor practice in a DOE!
My assumption is that the results can be extrapolated to other typical plants in containers.
Good luck in your experiments!"
"Finally, a good, simple DOE example, with missing data, no less. After several of your seminars, after numerous Stat-Teasers, you have provided an example I can use to promote DOE. After trying to decide why it stood above the rest, I finally figured it out on the way to work this morning. You have used an easy-to-measure, objective response.
Answer (from Shari Kraber):
"Thank you for your comments. I actually had a couple other responses (Height and Width) that didn't analyze as well. So, due to lack of space in the newsletter, I chose not to even comment about them."
3 - FAQ: How to maintain model hierarchy when three-factor interactions are selected as effects from a two-level factorial design
"I am analyzing a DOE with 4 factorsa full factorial, completely replicated for a total of 32 runs. Based on the p-value and engineering judgment I ended up with the following model: A, B, C, D, AB, AC, BD, ABC, & ACD. However, your Design-Ease® software suggests I make the model hierarchical by adding terms AD, BC, and CD. If I pick ABC for my model, isn't AB, C sufficient enough? What about ACD: Wouldn't AC & CD be sufficient to maintain hierarchy?
A side-note: I am also interested in writing a DOE to be published, but would like to disguise the factors, please advise."
Answer (side-note first):
I encourage you to pursue publication of a technical article featuring your use of design of experiments. The tools of DOE make it easy for you to disguise factors by simply labeling them alphabetically as you've done in this e-mail. Furthermore, if you want to show a table of your inputs and outputs, consider showing the factors in coded form, which can be done easily with Design-Ease (the software you used) or Design-Expert via the Display Options feature on the main menu. You do need to report the actual response values so the analysis can be reproduced. If you'd like some help putting your article together, let me know. I can help you with the statistics and put you in touch with a technical writer who can help you put everything together and placed in an appropriate publication.
The DOE you sent me may be a good
candidate for publication. The good news is that you have a number of highly-significant
effects, but the bad news is that possibly one or more of them are three-factor
interactions (3fi). These 3fi's should be supported hierarchically by not only
their main parent terms, but also all 2fi's involving the three factors. (To
see more details on this, go to your Design-Ease Help system, search on "hierarchy"
and look for the topic entitled "model hierarchy check", which I am
reprinting below.) For example, ABC needs A, B, C, AB, BC and AC to make a proper
predictive model. However, I think in your case, all this bother can be avoided
by not selecting any 3fi's for your
model. I see that these are very slight in relation to your main effects and a few 2fi's falling off the lineup of effects near zero.
Stat-Ease Software Help Topic
"Model Hierarchy Check"
"Design-Ease [and Design-Expert] checks the model hierarchy before you can run an ANOVA. Model hierarchy maintains the relationships between main effects, two-factor interactions, three-factor interactions, etc.
For example, if an interaction, such as BD, is a significant term, then the model should also include the main effects B and D, even if the main effects do not appear to be statistically significant on their own. Consider the coefficient for the interaction term to be a correction to the coefficients to the parent terms. A well-formulated model should include all main effects present in the interactions. A model that does not contain the main effects may not remain stable if the method of coding is changed.
Also, the actual models will be incorrect if they have been derived from non-hierarchical coded models and are not reported.
Bottom Line: If the model
fails the hierarchy check (meaning that the lower order (parent) terms haven't
been included in the model), you will be warned and offered a chance to correct
this problem. Just say Yes to correct the model hierarchy, and the additional
parent terms will then be selected in the current view.
For additional details on model hierarchy see:
1."A Property of Well-Formulated Polynomial Regression Models", Julio Piexoto, The American Statistician, Feb 1990, Vol.44, No.1.
2."The Selection of Terms in Response Surface Models - How Strong is the Weak Heredity Principle", John A. Nelder, The American Statistician, Nov 1998, V52, No.4.
User Tip: Always say "YES" to the hierarchy question.
Information in this Help System is subject to change without notice and does not represent a commitment on the part of Stat-Ease, Inc. The software described in this Help System is furnished under a license agreement. The software may be used or copied only in accordance with the terms of this agreement. No part of this Help System may be reproduced, transmitted, stored in a retrieval system, or translated into any language in any form by any means without the permission of Stat-Ease, Inc."
(Learn more about analyzing factorial
designs by attending the 3-day computer-intensive workshop "Experiment
Design Made Easy." See http://www.statease.com/clasedme.html
for a complete description . Link from this page to the course outline and schedule.
Then, if you like, enroll online.)
4 - Reader feedback (DOE FAQ Alert): A suggested link for details on fun and somewhat disgusting experiments to try at home with your children
----- Original Message -----
From: Al Starshak, Dunwoody College of Technology, Minneapolis
"In response to your request for case studies, see: http://www.amstat.org/publications/jse/v2n1/mackisack.supp.html."
Al has been a fan of Stat-Ease as long as I can remember. His suggested link offers several fun "DOE-it-yourself" projects. I might try the squash ball project but with one of my racquet balls instead. The meat-ant experiment might be a good one for my fellow consultant Shari to work on with her two young boys next summer. They'd love it but I don't think their mother will appreciate the results!
Al goes on to say:
"By the way, do you have any case study examples of building construction or architecture? The construction could be various ways of strengthening flooring or routing electrical wires. The architecture could be something else that I cannot think of."
I could not come up with any examples for this application. If any of you have anything to offer, let me know and I will pass it along to Al.
5 - Events alert: Stat-Ease is giving talks and exhibiting at quality conferences in Minneapolis and Kansas City
Click http://www.statease.com/events.html for a listing of where Stat-Ease consultants will be giving talks and doing DOE demos. We hope to see you sometime in the near future!
Stat-Ease consultant Shari Kraber will present a talk entitled "Drive Six Sigma Success with DOE" at the Minnesota Quality Conference/Biomedical Focus, which will be held in Bloomington, MN on April 14-16, 2003. See her and Marketing Director Heidi Hansel at Booth #14.
Mark your calendars and make plans
to come to the American Society of Quality's (ASQ) 57th Annual Quality Congress
(AQC) in Kansas City for talk T310, "How to Use Graphs to Diagnose and
Deal with Bad Experimental Data", presented by me on Tuesday May 20 from
2:00 PM - 03:15 PM. The material, co-authored by fellow Stat-Ease consultant
and Principal Pat Whitcomb, is rated "Basic." See
http://www.statease.com/pubs/baddata.pdf for content. Stop by our booth (#115) to talk with me and other representatives
of Stat-Ease. We'd like to see you! Go to http://aqc.asq.org/
for details on how to register for the exhibit and conference.
Also, we've been asked to pass along an alert for the Conference on New Directions in Experimental Design to be held in Chicago, Illinois on May 14-17, 2003. The focus of the conference will be on design of experiments in the pharmaceutical and related industries. See http://www.math.uic.edu/~kjryan/dae2003.html for more details.
6 - Workshop alert: Full slate of workshops presented in Minneapolis -- a great time to learn statistics and visit Minnesota
for 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
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.
I hope you learned something from this issue. Address your questions and comments to me at:
Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc. (http://www.statease.com)
Minneapolis, Minnesota USA
PS. Quote for the monthadvice
"I admonish you not to reject the method of experiment, but according as your power permits, to follow it without prejudice. For every experiment is like a weapon which must be used according to its own peculiar power."
- Paraclesus (16th century alchemist)
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.
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 (see above)