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 firstname.lastname@example.org.
Here's an appetizer to get this Alert off to a good startan experiment to see if people swim faster in guar-thickened water! In my days at General Mills I traveled the world, primarily in India, buying beans of this natural thickener which you often see listed as an ingredient in foods such as salad dressing. The instigator of this bizarre experiment, Ed Cussler, is a professor at my alma materthe University of Minnesota department of chemical engineering and material science. With the aid of powdered guar, he created a gummed-up pool of slime and somehow induced several people (mainly his students!) to actually swim in it. See if they went faster or slower (or could not tell the difference) by viewing http://makeashorterlink.com/?I472518A5. Decide for yourself whether guar should be added as an ingredient in Olympic swimming pools. It may not be a good idea for the high divers!
Here's what I cover in the body text of
this DOE FAQ Alert (topics that delve into statistical detail are
1. Info alert: The September issue of
the Stat-Teaser (a link is provided)
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/news0309.pdf.
The feature article, "Messing with Medieval Missile Machines (Part 2)" is a followup to my previous report on a simulated trebuchet. This time I got my hands on the real thinga sizable scale model made by the South Dakota School of Mines and Technology (SDSMT). I successfully applied response surface methods (RSM) to zero in on a backyard target. For enlightenment on this powerful optimization tool (and some amusement), read about my experiments on the SDMST 'treb'.
The other stories in the Stat-Teaser, authored by consultant Shari Kraber, provide details on RSM designs and training.
(Learn more about RSM designs by attending
the "Response Surface Methods for Process Optimization"
workshop. For a description, see http://www.statease.com/clas_rsm.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.)
2. FAQ: Rule-of-thumb
for assessing outliers
The outlier t, more properly described as the "externally studentized residual" in statistical terms, is a type of "deletion diagnostic". The idea is to measure influence of each response after deleting it from the data set. The "outlier t" requires that each response be set aside, the model re-fitted and residual error calculated, and finally, plotted on a standard deviation scale. This requires re-fitting the model to what remains and making it the benchmark. The end result looks much like a control chart with data plotted in run order and limits imposed to prevent tampering with the process.
As a general rule, the upper and lower control
limits should be placed at plus-or-minus 3.5 to be conservative. Any
individual runs that fall outside the limits should be investigated
for special causes, such as typographical errors or mechanical breakdowns.
In such cases, it may be prudent to ignore the result and re-analyze
the remainder of the data. Results that fall within the control limits
should be considered as common-cause variation. Removing any of this
data would likely bias the outcome of your
OK, now where did we get the value of 3.5? (I am finally getting to your question!) The answer can be found in an elegant book by Weisberg called "Applied Linear Regression", 2nd ed. New York: John Wiley and Sons, 1985. On page 116 he provides the formula for the externally studentized residual (outlier t) and then provides guidelines on determining critical values. His technique is based on the Bonferroni inequality which is described in the NIST/Sematech "Engineering Statistics Handbook at http://www.itl.nist.gov/div898/handbook/prc/section4/prc473.htm. Weisberg presents a table of the critical values for the outlier test. We used the one for a risk (alpha) of 0.05. The table is laid out as a function of n, the number of runs in the experiment, and p, the parameters in the model. It turns out that for n's from 16 to 32 the value of p makes little difference: Critical t's stabilize at 3.5 or so. That's why we use this value for the red lines on the outlier t plots in our software. (Learn more about diagnostic plots and other statistical tools 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.)
3. Events alert: See us at the Fall Technical
Conference (a forum for both statistics and quality) plus the Medical
Design and Manufacturing Show
Click on http://www.statease.com/events.html
for a list of where Stat-Ease professionals will be giving talks and
doing DOE demos. Next month we set up shop at:
We hope to see you sometime in the near future!
4. Workshop alert: See when
and where to learn about DOEconsider advanced training (Six
Sigma Black Belt +)
If you are already well-versed in design of experiments (having mastered RSM*) and want to make a move to the next level, attend our Robust Design: DOE Tools for Reducing Variability (RDRV) workshop September 16 - 18 (next week!) in the Stat-Ease training center (Minneapolis). This class will be extremely useful for Six Sigma Black Belts who work on improvement of manufacturing processes. Seats remain for this RDRV presentation, but you'd better act fastclick on http://www.statease.com/clasrdrv.html for details and from there link to the online registration.
*(If you lack this knowledge, come to our three-day, computer-intensive Response Surface Methods for Process Optimization workshop (http://www.statease.com/clas_rsm.html). It will be presented October 28-30, 2003 in Minneapolis.)
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 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.
PS. The "Statistics for Technical Professionals" workshop scheduled for October 7-9 has been postponed until February 17-19.
I hope you learned something from this issue. Address your general questions and comments to me at:
Mark J. Anderson, PE, CQE
PS. Quote for the
monthComments applicable to the 'appetizer' provided
(on how a pool of goo affects swim times):
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