Issue: Volume 2, Number 6
Date: June 2002
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, go to 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 offer the following link as an appetizer: http://www1.umn.edu/systemwide/enews/05-16-02.html. You will see the May 16th issue of the University of Minnesota's "E-News." It features a professor who uses "superhero science" to teach critical thinking in an imaginative freshman seminar. Pick up some trivia on the forces involved in Spider-Man's web antics - featured in the current blockbuster movie. Also, learn why Superman's home planet of Krypton exploded. It's a bird; it's a plane; no, it's an impossibility based on physical principles.
Here's what I cover in the body text of this DOE FAQ Alert (topics that delve into statistical detail are rated "X"):
1. Info alert: We
have a new home page - check it out! Also, try using the search feature to look
for answers to your questions on DOE.
2. FAQ: How to quantitatively compare effects from a two-level factorial design
3. User feedback: Changing the default data directory for Design-Expert® or Design-Ease® software
4. Events alert: Stat-Ease software is on exhibit at Quality Expo in Detroit
5. Workshop alert: Stat-Ease holds its first class in its new, computer-intensive training facility. More are coming!
PS. Quote for the month - DOE
books are advised as sleep aids
1 - Info alert: We have a new
home page - check it out! Also, try using the search feature to look for answers
to your questions on DOE.
If you have not gone to http://www.statease.com within the last week or two, do so now to see our new home page. This spearheads a more comprehensive makeover of the Stat-Ease site undertaken by our Marketing Director, Heidi Hansel. The goal is to improve functionality while modernizing the look.
Did you know that answers to your
statistical questions can be quickly found via a search of the Stat-Ease site?
For example, after getting an FAQ on Plackett-Burman designs, I surfed to http://www.statease.com/search.html
and entered "Plackett-Burman" in the search field. It quickly found
relevant material from past DOE FAQ Alerts plus references in software manuals,
newsletters, technical articles, etc. Give this a try!
2 - FAQ: How to compare effects
from a two-level factorial design
"I recently ran a "run of the mill" 2-level, 3-factor DOE and was asked which factor had the most influence. It was easy to state which factors are significant, but I had a hard time quantifying the relative effects (i.e. factor A has twice the effect as factor B or AB). I would think you could look at the sum of squares to give qualitative results, but I don't know how to give any quantitative results. Thanks in advance for your help. I have really enjoyed using your software."
[If you're not familiar with the
term "sum of squares" see: http://www.curvefit.com/sum_of_squares.htm
(brief definition) and/or http://www.uwsp.edu/psych/stat/13/anova-2w.htm
(a comprehensive review on two-way analysis of variance (ANOVA), incorporating
details on sum of squares, written by Dr. M. Plonsky (Psychology Dept., University
of Wisconsin,Stevens Point). It includes a simple, but fascinating, two-level
factorial case study on young versus old rats whose mothers drank either chocolate
milk or White Russians (an alcoholic drink).) MJA]
Your first instincts are good: Use sum of squares as one way to quantify the variation in response due to the effects from a two-level factorial design. (Things get more complicated for designs that include factors with more than two levels.) For example, let's look at a 2-level, 5-factor design on starting the engine on a weed whacker.* Here's the effects list, with the numbers rounded, that you get from our Design-Ease or Design-Expert software by clicking on the Effects button and selecting View, Effects List:
Notice that we made it very easy to compare the contribution of the effects in terms of sum of squares by translating it to percentages (see "% Contribution" column). This is calculated by simply dividing the sum of squares for each term by the total sum of squares. In this case it becomes obvious that the main effects of C (gas during full choke phase) and E (gas for starting phase) predominate. On an absolute scale, the effect of E exceeds that of C by a ratio of 2.25 to 1.75 (see "Effect" column). Varying factor E from its low level to its high level accounts for 40.7% of the total variation about the mean, versus 24.62% for B. All other effects contribute little in comparison.
When making comparisons like this, you should always qualify any statements by noting what ranges you varied within for each factor. What if some factors are very tightly controlled relative to others? Then comparing effects may be misleading.
Comparing sums of squares works nicely when only main effects predominate, but things get complicated when interactions emerge. For example, here's the effects list for taste from a study of microwave popcorn**:
Notice that not only do the main effects of B (power level) and C (time) stand out, but also their interaction. Therefore, it would not be proper to compare the main effects independently.
As I mentioned parenthetically at the outset of my answer, all of these ideas for comparing effects go out the window if you vary any factors over more than two levels. Then it becomes necessary to look at mean squares rather than the raw sums of squares. Let's not worry about this, at least for now!
PS from Professor Gary Oehlert, statistical advisor for Stat-Ease: "...in a [two-level] design, it is also true that the ratios of sums of squares for terms are equal to the ratios of squared effects for terms. No big surprise there, but your readers may not know.
Your points about range of the actual factor levels and interpretation in the presence of interaction are very important."
*"DOE Simplified" (see
http://www.statease.com/doe_simp.html for reference)
**"DOE Simplified" page 43.
(Learn more about analyzing results
from two-level factorial designs by attending the 3-day computer-intensive workshop
"Experiment Design Made Easy." For a description, see http://www.statease.com/clasedme.html.
Link from this page to the course outline and schedule. Sign up on-line if you'd
like to attend.)
3 - User FAQ: Changing the default
data directory for Design-Expert or Design-Ease software
program is stored in the C:\Program Files directory. By default, the data directory
is thus C:\Program Files\DX6\Data. However, I have created my own data directory
on the D:\directory. Each time when I start the program and click on "File
open", the software points to the default directory C:\Program Files\DX6\Data
directory. How can I change the default to D:\Data?"
Answer (from Tryg Helseth, programmer
and Principal of Stat-Ease):
"If you are using Windows 95 or 98 or NT 4.0, you can change the default folder by right clicking on the shortcut icon to Design-Expert and changing the "Start In" folder to the directory of your choice. Windows 2000 and XP will always go to the folder where the last document you opened or saved resides."
4 - Events alert: Stat-Ease software
is on exhibit at Quality Expo in Detroit
Stat-Ease software will be displayed
in Detroit on June 12-13 for the Quality Expo. Click http://www.statease.com/events.html
for links to this exhibition and a listing of other venues where Stat-Ease consultants
will be giving talks and doing DOE demos. We hope to see you sometime in the
5 - Workshop alert: Stat-Ease
holds its first class in its new, computer-intensive training facility. More
Stat-Ease hosted a full house (16+) of students this week for its "Experiment Design Made Easy" workshop. This was the inaugural class at our new computer-intensive training facility. We've posted a digital photograph of the class at http://www.statease.com/trainingpics.html . Take a look.
for schedule and site information on upcoming Stat-Ease workshops at its Minneapolis
training facility and elsewhere around the country. To enroll, click the "register
online" link at 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 month - DOE books
are advised as sleep aids.
"Most people ... have heard of designed experiments, but found the insides of [their] eyelids more pleasant to look at than the books devoted to the topic."
- C.J. Keller and Richard Scranton
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 (see above)