Archive for category design of experiments
I’ve been watching with interest the trend for ‘flipping’ classrooms; that is, using time together for working on homework and leaving the teaching to web-based and other materials (books, still!) for students to teach themselves on their own time. At the college level this new educational approach for is gaining momentum via massive open online courses, called MOOCS.
For example University of Minnesota chemistry professor Chris Cramer will teach this 9-week MOOC on Statistical Molecular Thermodynamics starting next month. Follow the link and watch him demonstrate a thermite reaction. If anyone can make statistical molecular thermodynamics interesting, it will be him, I think, so I enrolled. It’s free, thus there’s nothing to lose. Also, I still feel guilty about getting an A grade in the stat thermo class I took 30 years ago—the reason being it was graded on a curve and thus my abysmal final score of 15 out of 100 got rated highly as the second highest in my class. As you can infer, it was not taught very well!
P.S. I recently unveiled a distance-based lecture series on design of experiments called the DOE Launch Pad. It augments my book (co-authored by Pat Whitcomb) on DOE Simplified. Contact me at mark @ statease .com to sign up. It’s free for now while in pilot stage.
George Box passed away this week at 94. Having a rare combination of numerical and communication skills along with an abundance of common sense, this fellow made incredible contributions to the cause of industrial experimenters. For more about George, see this wonderful tribute by John Hunter.
My memorable stories about Box both relate to his way with words that cut directly to a point:
- In 1989 at the Annual Quality Congress in Toronto seeing him open his debate with competing guru Genichi Taguchi by throwing two words on an overhead projector–”Obscurity” and “Profundity”, and then after a dramatic pause, adding the not-equal sign between them. This caused Taguchi’s son Shin to leap up from the front row and defend his father. This cause the largest crowd I have ever seen at a technical conference to produce a collective gasp that one only rarely experiences.
- In 1996 at a DOE workshop in Madison, Wisconsin enjoying his comeback to a very irritating disciple of Taguchi who kept interrupting the lecture: “If you are going to do something, you may as well do it right.”
Lest this give the impression that Box was mean-spirited see this well-reasoned white paper that provides a fair balance of praise and criticism of Taguchi, who created a huge push forward for the cause of planned experimentation for quality improvement.
The body of work by George Box in his field is monumental. It provides the foundation for all that we do at Stat-Ease. Thank you George, may you rest in peace!
The latest issue of Wired magazine provides a great heads-up on random numbers by Jonathan Keats. Scrambling the order of runs is a key to good design of experiments (DOE)—this counteracts the influence of lurking variables, such as changing ambient conditions.
Designing an experiment is like gambling with the devil: only a random strategy can defeat all his betting systems.
– R.A. Fisher
Along those lines, I watched with interest when weather forecasts put Tampa at the bulls-eye of the projected track for Hurricane Isaac. My perverse thought was this might the best place to be, at least early on when the cone of uncertainty is widest.
In any case, one does best by expecting the unexpected. That gets me back to the topic of randomization, which turns out to be surprisingly hard to do considering the natural capriciousness of weather and life in general. When I first got going on DOE, I pulled numbered slips of paper out of my hard hat. Then a statistician suggested I go to a phone book and cull numbers from the last 4 digits from whatever page opened up haphazardly. Later I graduated to a table of random numbers (an oxymoron?). Nowadays I let my DOE software lay out the run order.
Check out how Conjuring Truly Random Numbers Just Got Easier, including the background by Keats on pioneering work in this field by British (1927) and American (1947) statisticians. Now the Australians have leap-frogged (kangarooed?) everyone, evidently, with a method that produces 5.7 billion “truly random” (how do they know?) values per second. Rad mon!
Tia Ghose of The Scientist provides a thought-provoking “Q&A” with biostatistician Peter Bacchetti on “Why small is beautiful” in her June 15th column seen here. Peter’s message is that you can learn from a small study even though it may not provide the holy grail of at least 80 percent power.* The rule-of-thumb I worked from as a process development engineer is not to put more than 25% of your budget into the first experiment, thus allowing the chance to adapt as you work through the project (or abandon it altogether). Furthermore, a good strategy of experimentation is to proceed in three stages:
- Screening the vital few factors (typically 20%) from the trivial many (80%)
- Characterizing main effects and interactions
- Optimizing (typically via response surface methods).
For a great overview of this “SCO” path for successful design of experiments (DOE) see this detailing on “Implementing Quality by Design” by Ronald D. Snee in Pharm Pro Magazine, March 23, 2010.
Of course, at the very end, one must not overlook one last step: confirmation and/or verification.
* I am loathe to abandon the 80% power “rule”** but, rather, increase the size of effect that you screen for in the first stage, that is, do not use too fine a mesh.
** For a primer on power in the context of industrial experimentation via two-level factorial design, see these webinar slides posted by Stat-Ease.
Stat-Ease Consultant Brooks Henderson produced this video — it’s quite impressive!
For background on the paper helicopter experiment, see this previous StatsMadeEasy post.
The Stat-Ease training center here at our world headquarters in Minneapolis features a wonderful single-cup brewing system that you can see demoed here. When we are not holding a workshop, I sometimes sneak in to steal a cup late in the day. By then I am reaching my limit, so I brew a “half-calf” at the half-cup setting. Being a chemical engineer, I calculate that, in this case, half of half makes a whole, that is, coffee with the normal concentration of caffeine. Does that make sense?
Making a tasty and effective cup of coffee is a huge deal for knowledge workers who need to keep their heads in gear from start to finish of every single day. One of our workshop students, a PhD, has been picking my brain about testing coffee blends on her staff of scientists. She proposes to do a mixture design such as I did on varying types of beers (see Mixture Design Brews Up New Beer Cocktail—Black & Blue Moon).
Obviously overall liking on a sensory basis should be first and foremost for such an experiment on coffee – a 5 to 9-point scale works well for this.* However, the tricky part is assessing the impact of coffee for accelerating information processing and general problem-solving, which I hypothesize depends on level of caffeine. I wonder if an online “brain training” service, such as this one developed by neuroscientists at Stanford and UCSF, might provide a valid measure.
The down side of doing a proper test on whether coffee improves cognitive skills will be the necessity of reverting to the base line, that is, every morning getting up and trying to function without the first cup.
“A mathematician is a machine for turning coffee into theorems.”
– Alfréd Rényi
*Turn your volume down (to not hear the advert) and see this primer on sensory evaluation by S-Cool– a UK educational site for teenagers.
This add by Target got my attention. It reminded me of my futile attempt to get my oldest daughter interested in math. For her the last straw was my overly-enthusiastic reaction to her questioning me why anyone would care about quadratic equations. Perhaps I over-reacted and lectured on a bit too long about this being a very useful approximating function for response surface methods, blah, blah, blah…
I am learning a lot this week at the Third European DOE User meeting in Lucerne, which features many excellent applications of DOE to industrial problems. Here’s an interesting observation from Pavel Nesladek, a technical expert from the Advanced Mask Technology Center of Dresden, Germany. He encounters severe pressure to find answers in minimal time at the least possible cost. Pavel found that whatever number of runs he asked to do for a given design of experiment, his manager would press for fewer. However, he learned that by asking for a prime number, these questions would be preempted, presumably because this seemed to be so precise that it must not be tampered with! For example, Pavel really needed to complete 20 runs for adequate power and resolution in a troubleshooting experiment, so he asked for 23 and got it. Tricky! Perhaps you stats-savvy readers who need a certain sample size to accomplish your objective might try this approach. Prima!
PB&J please, but hold the jelly (and margarine) and put it on toast – a mixture design combined with a categorical factor
My colleague Pat Whitcomb just completed the first teach of Advanced Formulations: Combining Mixture & Process Variables. It inspired me to develop a virtual experiment for optimizing my perfect peanut butter and jelly (PB&J) sandwich. This was a staple for me and my six siblings when we were growing up. Unfortunately, so far as I was concerned, my mother generously slathered margarine on the bread (always white in those days – no whole grains) and then thick layers of peanut butter and jelly (always grape). As you see* in the response surfaces for overall liking [ 1-9 ], I prefer that none of the mixture ingredients (A: Peanut butter, B: Margarine, C: Jelly) be mixed, and I like the bread toasted. This analysis was produced using the Combined design tab from Design-Expert® software version 8 released by Stat-Ease earlier this year. I’d be happy to provide the data set, especially for anyone that may be hosting me for a PB&J dinner party.
*Click to enlarge the plots so you can see the legend, etc.
I am a fan of classical music – it soothes my mind and lifts my spirits. Maybe I’m deluded, but I swear there’s a Mozart effect* on my brain. However, a big monkey wrench comes flying in on my blissful state when my stereo speaker (always only one of the two) suddenly goes into a hissy fit. I’ve tried a number of things on a hit-or-miss basis and failed to find the culprit. At this point I think it’s most likely the receiver itself – a Yamaha RX496. However, before spending the money to replace it, I’d like to rule out a number of other factors:
- Speaker set: A vs B
- Speaker wire: Thin vs Thick.
- Source: CD vs FM-Radio
- Speaker: Left vs Right.
It’s very possible that an interaction of two or more factors may be causing the problem, so to cover all bases I need to do all 16 possible combinations (2^4). But, aside from the work this involves for all the switching around of parts and settings, I am stymied by the failure being so sporadic.
Anyways, I feel better now having vented this to my blog while listening to some soothing Sunday choir music by the Dale Warland Singers on the local classical radio station. I’m taking no chances: It’s playing on my backup Panasonic SA-EN25 bookshelf system.
*Vastly over-rated according to this report by the Skeptic’s Dictionary.