Awesome demonstration of design of experiments

The engineering students at South Dakota School of Mines and Technology really do rock. Where else could one present a class on statistics until 8:30 pm on a Friday night and continue it less than 12 hours later – early on a Saturday morning?

Our workshop on design of experiments (DOE) finished with a spirited competition of paper helicopters.* The winner was Team Awesome: Kayla Rithmiller, MacKenzie Trask and Samantha Johnson (pictured from left to right). They scored highest on the basis of flight time and accuracy. You can see their ‘copter spinning to another precise landing in their confirmation run.

Congratulations to Team Awesome and all the SDSM&T students who devoted their free time to learning DOE and demonstrating this newly-gained knowledge via well-planned experiments on the helicopter exercise. I predict that they all will go far!

*See details on this DOE exercise in the September 2004 Stat-Teaser article on Playing with Paper Helicopters.

Technology facilitates building a stronger database on blood pressure and other medical measurements

Some years ago my wife was diagnosed with high blood pressure (hypertension). This necessitated regular measurements with an instrument called a sphygmomanometer, which took me a long while to master for spelling and pronunciation. Being a chemical engineer helped – we used manometers to track barometric pressure. The hard part is the “sphygmo” – a Greek word meaning to throb or pulse. However, it works nicely for blood pressure!

Blood pressure measurements via the mercury gravity sphygmomanometer are still considered to be “gold standard.” Nevertheless, electronic devices are far easier to use and affordable for home use. To help my wife keep track of blood pressure, I bought one made by Panasonic. This came in handy when I developed heart problems of my own – chronicled in my article “How DOE Saved My Life and Made it Worth Living” in the June 2008, Stat-Teaser.

This week’s CRNtech brought news of a Digital Blood Pressure Check via an inexpensive (less than $100) device that connects via USB to a PC for capturing results. This data can then be uploaded to Microsoft’s HeathVault. From there you can enable care givers to watch for statistical trends.

My guess is that by repeated measurements over time, facilitated by this do-it-yourself system, medical professionals would get a far more precise assessment of hypertension. This may be the answer to Blood Pressure Variability: The Challenge of Variation – an issue recognized in this recent publication of the American Journal of Hypertension (2008, 21 3–4).

“It is therefore practically impossible for a clinician to know whether he is changing a drug or dose in response to chance variation in blood pressure or true changes in the underlying mean blood pressure.”
-- Tom P Marshall, Department of Public Health and Epidemiology, University of Birmingham

TV detectives stumble over odds of matching birthdays

Ever since his glory days as the laid-back Hawaiian detective “Magnum PI” I’ve always been a fan of actor Tom Selleck. Now he’s back on television as a moody police chief named Jesse Stone – a character based on a series of mystery novels written by Robert Parker. In the latest installment of the TV franchise (the first one not based directly on one of Parker’s books) Stone searches for a stolen baby thought to be living with the thief in his small Massachusetts’ town. All they know is the birthday and approximate age. One child comes up as a match, but the deputy cautions that it only takes 22 people to get two with the same birthday.

This birthday paradox provides some fun for teachers of statistics who have large enough classes to make a match likely: Simulate the possible outcomes with this fun applet by Stanford Professor Susan Holmes. However, the odds of matching an exact birthday are far lower – it takes 252 to achieve a 50% probability. These statistics are detailed by this Wikipedia article -- see the graphical comparison of the cumulative probabilities.

So I think the odds were fairly high that Chief Stone's hunch about the baby-snatcher was a good one -- simply based on the birthday of the child being a match. In any case, amazing coincidences are standard for novels, movies and television. The writers operate in a world where chance takes a back seat to drama. Thank goodness for that -- real statistics tend to be a bit boring for entertainment purposes.

PS. The photo is one of my all-time favorites from the family album -- it's my son Hank, who helps me with this blog. The Anderson clan now is up to 9 counting those who've married in. So far none of us share a birthday.

The science of “guesstimation”

The latest National Geographic Science column on Mind Games shows a jar of jelly beans (presumably provided by the Easter bunny) and it offers a formula for estimating the number:

1. Count the jars radius (r) in beans. (This is hard to see due to the angle of the picture, but let’s say r equals 5.)
2. Estimate the height (h) in beans. (I can count this fairly easily from the photo – h equals 35.)
3. The volume (V) in beans is: V = 3 h r^2, where the constant 3 is a round-off on the circular constant pi. (So I estimate the beans in the National Geographic jar number 3x35x5^2, or 3x35x25 – the product of which is 2,625.)

The scientific, calculated estimate I made (2,625) for the count of jelly beans came a lot closer than my initial guess of ten thousand: The answer is 4,466. Going to all this effort might be worth it if you come across a bean-counting contest with a prize worth taxing your math skills.

Meanwhile, two professors at Old Dominion University in Virginia, one a mathematician (John Adam) and the other a physicist (Lawrence Weinstein), have teamed up to provide a primer on Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin. As the publisher Princeton University Press says: “The ability to estimate is an important skill in daily life.”

As the father of five, I frequently was asked to help with math problems. First I’d ask that the student (my kid) work out a bottom-line number. Then I’d suggest they do a “reality check” by estimating the answer to at least the order of magnitude. That often sent them back to the beginning of the problem due to their first answer being so obviously wrong. The way facts and figures get thrown around the airwaves and internet nowadays it’s more important than ever to do reality checks.

I’ll bet this new book will be very helpful to equip reality checkers with the tools they need to achieve more accuracy. I learned about Guesstimation from its review in the March 31st New York Times. The Times article provides an interesting test of estimating ability: How many times does the American teenager say “like”? I heard this much more from my three daughters than my two sons, thus I hypothesize that there’s a gender bias. I’d hear this so word so over-used –- at least, like, once per sentence –- that I’d start counting them aloud, thus creating a great deal of aggravation for my teenager. I suppose the work “like” might come out ten times a minute and one hundred times per conversation. So I’m going to say a thousand “likes” per day could be in the realm of possibility. However, some teenagers are not afflicted by this word termite. My guess is ten thousand “likes” per year per teenager. To learn the answer, take this eight-question test of your estimation abilities.