Stats Made Easy

Practical Tools for Effective Experimentation

Saturday, March 29, 2008

Box seminar from 1996 remains visionary

While cleaning out files this week, I found my long-forgotten notes from “Design of Experiments for Discovery, Improvement and Robustness” co-presented by DOE guru George Box in March of 1996 – over a dozen years ago. The first thing I noticed was the photo roster showing how huge my spectacles and others were in that era.* The ones I have now are so narrow I cannot see, but at least they are fashionable! (There is an added factor: In 1996 I did not need progressively-lensed bifocals, although they would have benefited from the goggly glasses of that time.)

However, even more enjoyable than the chuckle over obsolete fashions were Box’s timeless anecdotes, which I recorded religiously. For example, Professor Box mentioned how his father would comment on trivial differences: “A blind man would be glad to see it.” This drove home a point Box wanted to make on how being statistically significant did not necessarily lead to anything of practical importance. In fact, while working as a statistician at Imperial Chemical Industries (ICI), he banned the use of p-values by their industrial experimenters! (Box advocated the use of confidence intervals, instead.)

In my webinar last month on “10 Ways to Mess Up an Experiment & 8 Ways to Clean it Up”. I made this point (statistical significance versus practical importance) in a slide similar to that shown here. It accomplishes little to achieve a low p value for a change that is so small that it produces nothing of any practical importance. In today's age of robotic experimentation this happens more-and-more often due to the large number of runs -- in the hundreds or even thousands. On the other hand, plenty of experiments are still done in situations where runs are dear and not many can be performed. Then a big difference may be seen that fails the pre-ordained threshold level for p. In that case it often pays to investigate further.

“Even if the probability was 6% of not finding a crock of gold behind the next tree, wouldn’t you go and look?”

-- Quote from “An appendix featuring quaquaversal quotes … that embellish key concepts and enliven the learning process” presented by George E. P. Box, J. Stuart Hunter, and the late William G. Hunter in the second edition of the classic book Statistics for Experimenters: Design, Innovation and Discovery.

*You have to see this web site, at least the goofy glasses shown on the rotating eye-catcher, on spectacles through the ages.

Friday, March 21, 2008

Thomas Edison and Henry Ford would have loved the new hybrid cars

By the luck of the Irish from the Russell clan on my dearly departed grandmother’s side, Hertz issued me a Toyota Prius last weekend for my Spring break in Florida (commencing on the three-day Saint Paddy’s Day weekend). This innovative hybrid vehicle drove like a dream from Miami to our lodging in Fort Myers Beach – averaging over 50 miles per gallon of gasoline. At low speeds it evidently runs on battery, because it made so little noise that we could hear the Little Blue Herons cackling along the Ding Darling Wildlife Refuge drive on nearby Sanibel Island.

In Fort Myers, my wife and I visited the Edison Winter Estate where, with funding from Ford and Harvey Firestone, the elderly inventor Thomas Edison developed a substitute for rubber made from Goldenrod after abandoning the Banyon tree as a source of latex. (The one pictured with the statue of the great inventor has grown to enormous proportions.) As noted on this timeline history of electric cars, Edison originally had greater aspirations for automobile technology, but he never could achieve the level of battery technology needed to make electric cars economically feasible.

The idea of combining battery and engine power is a stroke of genius, in my opinion, and the niftiest touch may be the regenerative braking that recoups power during stopping. However, I wonder about the durability of hybrid cars, especially their battery. I hope they last longer than the ones in laptop computers, cell phones and other portable electrical devices. Furthermore, I have had many a car battery die in the dead of a Minnesota winter when temperatures fall far below zero F. So, although I’ve enjoyed tooling around Florida in my rented Prius, I remain skeptical (but hopeful!) about its long-term viability.

Sunday, March 16, 2008

How to explain a statistical interval confidently

My youngest daughter, being a glutton for punishment like her father, is struggling on the stretch run of her senior year in high school with three AP (advanced placement) college-level classes, one of which is Statistics. That means more fun for me trying to answer questions she has about her homework, many of which are very tricky.

Possibly the most perplexing thing to learn is how one should express a confidence interval. For example, this month’s issue (#49) of Stats, “the magazine for students of statistics,” states this common misconception: “After you compute a 95% confidence interval for the mean, you can say the probability is 95% that it contains the population mean.” *

I confess that after learning statistics on the job as chemical engineer in the 1970s, I would have agreed with this statement. It wasn’t until the advent of applets allowing one to simulate any number of random samples taken from a normal population and generating confidence intervals that I literally saw how they really worked.

For example, see the screen shot taken the tenth time I took one-hundred random samples of 5 using an applet programmed by my oldest son.** I got lucky on this run by missing the true mean of 50 only the expected 5 times out of one hundred (the red intervals). However, the total of 954 successes on the total of one thousand trials reflects the nature of statistics nearly always being a bit off true kilter. The varying results, albeit somewhat unnerving like any natural variations (deterministic outcomes being much more comforting!), are very instructive for statistical concepts like confidence intervals.

For a great discussion on how to properly describe a confidence interval see this thread posted at the Math Forum of Drexel University by Doctor Wilko (aka Dr. Math). It may help you from falling into this particular trap, one of many as noted in the Stats article, that riddle the field of statistics. Be careful out there!

*(Jessica Utts interview with Jackie Miller titled “Busting Statistical Myths,” page 10.)

**(Stat-Ease provides this applet and others to students of its Statistics for Technical Professionals workshop.)

Sunday, March 09, 2008

Random thoughts on taxing calculations

Yesterday I made my weekly Saturday morning trek to our local bank to deposit checks. Yes, I know this is old-fashioned, but I enjoy the exercise, talking with the tellers and keeping my calculating skills sharpened. However, I always warn that my bottom line should not be banked upon –- somehow, despite being an engineer with an MBA, I fall short of being confident at the level required for such endeavors (one hopes one-hundred percent!).

Do not get me wrong: I like calculators. I remember dealing with chemical engineering problems when I was an undergraduate at University of Minnesota. Many could be handled by my K&E slide rule,* but round-off error bothered me, especially for performing anti-logs, which magnify discrepancies. That’s why I might wait an hour or more to use the one Wang calculator provided for use by students in U-of-M’s Institute of Technology. They kept it in a windowless, darkened cubicle where the red numbers glowed all-knowingly to 10 significant digits. Awesome!

Now, of course, calculators have become virtual by way of the personal computer. You will likely find just the one needed for a particular problem at MARTINDALE'S CALCULATORS ON-LINE CENTER. One that I found interesting is the Research Randomizer provided freely by the Social Psychology Network ("SPN"). Although it looks quite easy and appears effective for laying out experiments in random order or choosing samples, the developers of this calculator (Geoffrey C. Urbaniak and Scott Plous) admit that more genuine results are produced via radioactive decay, as can be seen (and heard with annoying effect) at a web site by Fourmilab Switzerland called HotBits.

As you can see from the picture, I am working on taxes today for my two remaining dependents who both earned enough money to buy their own movie tickets and lots of things at the local shopping malls. I wonder... if I enter a few calculation errors in these small fry, will the IRS be distracted from the bigger fish like me? However, I fear they apply a random sampling component to counteract any selection bias. A macabre (but not random) thought arises to end this blog: Which would be worse? Being subjected to a tax audit? Or running the risk of exposure to radioactivity for very brief, but possibly hazardous, time?

*For a fascinating look at the old-fashioned ‘slip stick’, see this web site by the International Slide Rule Museum.