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. If you have a question that needs answering, click the Search tab and enter the key words. This finds not only answers from previous Alerts, but also other documents posted to the Stat-Ease web site.
This month's 'appetizer' relates to tools I taught at a session of "Statistics for Technical Professionals"* presented last week on-site for a pharmaceutical client of Stat-Ease. Among other things, we discussed how to construct confidence and tolerance intervals for binomial responses, such as the proportion of products that fail to pass manufacturing specifications. In 1873, Francis Galton devised an ingenious machine he called the "Quicunx" that demonstrates how the binomial distribution becomes approximately normal. For a virtual reconstruction of Galton's Quincunx, see an applet by John Carroll University posted at http://www.jcu.edu/math/isep/Quincunx/Quincunx.html. Warning: you may be mesmerized by the balls falling through the pins, which in Galton's original machine were laid out in patterns of five, hence the name "Quicunx."
*(See http://www.statease.com/clas_stp.html for a course description of "Statistics for Technical Professionals," a two-day computer-intensive workshop.)
Here's what I cover in the body text of this DOE FAQ Alert (topics
that delve into statistical detail are designated "Expert"):
1. FAQ: The use of factorial design for market research
"Conjoint analysis presents choice alternatives between products/services defined by sets of attributes. This is illustrated by the following choice: Would you prefer a flight with regular seats, that costs $400 and takes 5 hours, or a flight which costs $700, has extra-wide seats and takes 3 hours? Extending this, we see that if seat comfort, price and duration are the only relevant attributes, there are potentially eight flight choices:
Choice: Seat-Comfort, Price, Duration
Unfortunately no responses are given for this 'thought' experiment, but my choice would be to get a free, frequent-flyer upgrade to the extra-wide seat in first class!
2. Expert-FAQ: Why power statistics look so poor for mixtures
For mixtures power calculations are further clouded by collinearity among the coefficients. Recall that in a factorial design the coefficients are orthogonal, i.e., the size of each coefficient is the same regardless of what other coefficients are present in the model. In a mixture this is far from the case, depending on the constraints there is usually extreme dependence. Therefore the power to resolve individual effects is very low, while the ability of the design to adequately model the type of behavior (linear, quadratic, etc.) designed for is high. Unfortunately no one knows how to measure this ability directly.
Thus, power for mixture designs is at best a relative measure for comparing designs over the same mixture space. Even for these direct comparisons the standard error of the coefficients, leverages, determinate and trace are more useful than power."
Pat is working on a technical article that will detail the inherent deficiencies in power for mixture designs. I took the liberty of excerpting key portions of Pat's pending paper and posting it at: http://www.statease.com/pubs/powerinmixsimp.pdf.
(Learn more about power by attending the
three-day computer-intensive workshop "Experiment Design Made
Easy." See http://www.statease.com/clas_edme.html for
a course description. Link from this page to the course outline
and schedule. Then, if you like, enroll online.)
3. Info alert: Stat-Ease featured in cover of "Advance"—a publication for medical laboratory professionals
See the cover of the June 28 issue of "Advance" magazine at: http://makeashorterlink.com/?Z31323AB8. It features an article titled "How Experimental Design Optimizes Assay Automation," co-authored by Stat-Ease consultant Shari Kraber, which describes how "an innovative blend of hardware, software and the right training in statistical know-how supercharges research automation" provided by Beckman Coulter. An unedited version of this article is posted at http://www.statease.com/pubs/optimizeassays.pdf.
4. Book alert: Recommended summertime reading on statistics
Here's some good summertime reading recommended by Bill Risk—a student of mine at the recent "Experiment Design Made Easy" workshop in San Jose (what a great name for someone interested in statistics for experimenters!): "The Lady Tasting Tea, How Statistics Revolutionized Science in the Twentieth Century." This soft-cover book by David Salsburg is available for purchase at http://makeashorterlink.com/?T11721398. I already had the title story, which was originally told by Sir Ronald Fisher.* As he told it a Lady claims to have the ability to tell which went into her cup first—the tea or the milk. Fisher devised a test whereupon the Lady is presented eight cups in random order, four of which are made one way (tea first) and four the other (milk first). He calculates the odds of correct identification as 1 right way out of 70 possible selections, which falls below the standard 5% probability value generally accepted for statistical significance. Salsburg reveals on good authority (H. Fairfield Smith--a colleague of Fisher) that the Lady identified all eight cups correctly!
Here's another interesting anecdote from Salsburg:
*("Mathematics of a Lady Tasting Tea" in Newman’s "The World of Mathematics," Vol. 3, Dover Press, available from http://store.yahoo.com/doverpublications/0486411516.html in paperback.)
PS. A book I recommended last summer, "A Short History of Nearly Everything" by Bill Bryson, just won the Aventis Prize for best science book. The 2004 winner for children's science is a book called "Really Rotten Experiments." That sounds fun! The press releases on these two prize winners and others that won honorable mention are posted at http://news.bbc.co.uk/2/hi/science/nature/3806375.stm.
5. Reader reply: Coke versus Pepsi test in the Stat-Teaser
To preface my story, I want to say that, personally, I prefer my soft drinks cold and over ice. I drink them fairly rapidly to keep dilution to a minimum. I also prefer Coke to Pepsi, though I will drink whatever is on sale, my preference for cash overriding the minor preference for taste difference (it is not fine wine we are discussing).
I can tell the difference between Coke and Pepsi, and can also tell "other brands" though I am not always "accurate" in estimation of what the other brand is (RC Cola, Sam's Choice, etc). My kids have taken me up and done blind tests and they haven't stumped me yet on telling the difference between Coke and Pepsi. ("New Coke", really an other, was miscalled as Pepsi on occasion, though I never considered New Coke to be Coke).
I was at the mall a number of years back, when they were doing the "Pepsi Challenge", and I was going to do it and put in my vote for Coke (which is indeed my preference). They put out the two identical cups and I tasted and I noticed that the Coke was (at least to me) noticeably warmer than the Pepsi. I asked: "why is the Coke warmer than the Pepsi?" (My hypothesis being that perhaps this biases the testing, most people I know preferring colder beverages), but they would not answer, they only wanted a response as to what I preferred.
In actuality, I did prefer the cold(er) Pepsi to the cold (yet warmer) Coke (though I would have preferred a cold Coke over a cold Pepsi), but I lied and still chose the Coke over the Pepsi.
I don't know if it was part of the design
of the challenge (I would not put it past the designers of the
test, since they were trying to get people to "choose Pepsi"),
but I did notice it and thought that you might be interested. I
could see how this could be a "built-in confounding" to
help push a preference to the
I thank you for the sharing of your excellent DOE "experiences". I really like to see the examples of more "everyday" testing that is done as a way of educating. Keep up the good work."
PS. I am biased to RC Cola because my grandmother always gave it to me and my cousins (our mothers sisters—forbade any soda pop in our respective homes, but they were over-ruled by their mother—our grandmother when on these visits).
6. Events alert: A talk in Toronto at the Joint Statistical Meetings; also questions about a previous presentation on screening
If you make it to the 2004 Joint Statistical Meetings (JSM) in Toronto, Canada in August, stop and visit Stat-Ease at booth #405. Also, sign up for the JSM RoundTable Discussion on Wednesday, August 11th on "Design of Experiments Trials and Tribulations." Stat-Ease consultant Shari Kraber will be the moderator. She says "Participate in a lively discussion of the trials and tribulations of planning and running designed experiments. Plan to share your experiences and learn from the experiences of others. Discuss the most common pitfalls that experimenters encounter and learn how to avoid them. Explore problems with fractional factorials, mixtures, missing data, pass/fail data, etc."
I received this question on my talk titled "Screening
Process Factors In The Presence of Interactions," which
I presented recently for the Annual Quality Congress
Stat-Ease will present "Experiment Design
Made Easy" on
August 17-19 in Philadelphia. See http://www.statease.com/clas_pub.html for schedule and site information on this and all other Stat-Ease
Mark J. Anderson, PE, CQE
PS. Quote for the month—why the normal distribution is normal:
"Whenever a large sample of chaotic elements are taken in hand... an unsuspected and most beautiful form of regularity proves to have been latent all along."
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Acknowledgements to contributors:
DOE FAQ Alert—Copyright 2004
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