Stats Made Easy

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

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.

Recently the Wall Street Journal reported that a Study Questions Evidence Behind Heart Therapies — specifically by this alarming statistic: “Just 11% of more than 2,700 recommendations approved by cardiologists for treating heart patients are supported by high-quality scientific testing.” It seems that the vast majority of prescribed treatments remain unratified by multiple randomized clinical trials – the highest level of evidence according to guidelines issued jointly by the American College of Cardiology and the American Heart Association.

I am caught up in this personally due to having had one heart attack some years ago. Ever since then I’ve been working hard to avoid a second one. My daily aspirin is strongly supported by scientific study, but it’s not very sure that I should be keeping on with the platelet inhibitor Clodiprogel (Plavix™, Bristol-Meyers Squibb/Sanofi Pharmaceuticals) prescribed after getting my clogged artery stented. I have to credit my cardiologist though – he is utterly impartial on the Clodiprogel – I cannot get any signal – pro or con. What can he say? As pointed out in this related article by US News & World Report no clinical trials exist beyond about one year (even that time is a bit vague!) of the heart surgery.

So as not to let all this cause me too much stress (possibly bad for the heart, but not strongly supported by solid scientific study) I picked up on this promising therapy – waltzing as a form of cardio-exercise. Evidently this works as well as trudging the treadmill and the dancing leads to a better quality of life as measured by the Minnesota Living With Heart Failure Questionnaire.* I note that the subjects were selected at random – that’s good, but “the study was not blinded, neither to the investigators nor to the patients.” Obviously it would not do to waltz blindly along, no matter how blissful that might be – until one hits the wall!

*I’d be skeptical if this weren’t based on Minnesota standards, that is, bitter cold, biting insects and so forth. 😉

Tonight the NCAA filled out their 65-team* bracket for their annual Division I basketball championship. The quality of basketball will no doubt be better than ever, at least since 1995 when Kevin Garnett broke barriers by jumping directly from high school to the Minnesota Timberwolves. That really provides no excuse though for what Larry Wright, and adjunct professor of statistics at Columbia, says is a “mind boggling” lack of improvement in the rate at which college players make free throws. In this article by the New York Times, John Branch reports that in 1965 NCAA teams shot 69 percent. This year they cashed in from the 15 foot charity stripe at a rate of only 68.8 percent.

Some athletic endeavors leap ahead due to an innovation in technique, such as the Fosbury Flop in high jumping or skating on cross country skis. I wonder why more players don’t throw up free throws underhanded like Rick Barry did as depicted by this NBA website on The Art of the Free Throw. His 90 percent rate set the NBA bar when he retired.

I saw an interesting shooting variation at the halftime of a Timberwolves game a few weeks ago. They gave a fan one shot from half court to win a million dollars. The contestant was an older fellow who seemingly had no chance throw a basketball that far. However, he succeeded on distance by flinging it backward over his head, an approach used by this more accurate fan who won a car by sinking the 47-foot shot shown here.

It would be interesting to experiment with an accomplished basketball player to see how their shooting percentage would vary facing forward versus backward from the free-throw line. Surely the success rate would fall precipitously.** Actually, that might make things a lot more interesting – even the seemingly static 69 percent rate is too boringly accurate.

*One aspect of this “March Madness” is that it commences with a “play-in” game that makes one team the absolute loser!

**An exception might be 41 percent free thrower Ben Wallace seen missing the iron completely in this video . He should do the same as the fans watching him at the line — don’t look.

My son Hank, ‘blogmeister’ of StatsMadeEasy, just forwarded me this cartoon from Randall Munroe’s blog xkcd. It dovetails nicely with my presentation to the ASQ Lean Six Sigma Conference this week titled “Friend or Foe? How to Use Graphical Diagnostics for Scoping Out Discrepant Data.”*

As I am wont to do, I started my talk with a humorous anecdote on the topic. This is a story on seeking something out using visual clues. It’s a matter of being on guard for something unusual like Nassim Taleb’s Black Swan but being a Minnesotan my thinking differs a bit on what’s distinctive.

“A fellow borrowed a neighbor’s fishing car** to sneak in some last-minute anniversary gift shopping at Mall of America (MOA) without his wife knowing. After wandering the vast hallways of MOA for a long period of time, he found just the thing. However, by then he’d forgotten where the car was and even what it looked like. All he could think of to tell the security staff was that the front right tire did not have a hub cap. After a thorough search the car was located. However, it would have been easier for the MOA staff if the fellow had thought to mention that the car had a red canoe strapped to the roof! “

*For the basis of my talk, see this manuscript.
**Fyi Minnesotans generally keep two spare automobiles — a ‘winter beater’ that stands up to all the snow and road slop, plus an old ‘fishing car’ that can be kept at the ready with rods and all (and allowed to get stinky with fish and bait).

“Armed with a bevy of State testing data” our local school district’s Superintendent dispelled the notion that Minnesota charter schools provide a superior education. Charter schools are publicly funded, but they are run by independent boards. Their enrollment has doubled in the last 5 years, thus inciting battles of statistics like the one presented by the Superintendent this week. His main point was that published assessments do not account for the impact of special education, “at-risk” and other students that do not attend the particular charter school in our area. (To be fair to the ideal of charter schools, some actually provide for students with particular needs that would otherwise get lost in the shuffle.)

In the interest of helping the general public sort out the endless conflict of statistics by opposing groups like this, the Union College Academy for Lifelong Learning (UCALL) in Schenectady, New York invited an illustrious faculty, including Gerald Hahn – formerly statistician emeritus from General Electric, to teach a course “Numbers in Life.” This 10 hour presentation was really all about statistical literacy, but ironically the course coordinator advised that the word “statistics” in the course title would be a turn-off. That tells it all: How can people be educated a on a subject that must not be named (like the evildoer in Harry Potter)?

To the everlasting credit of Hahn and his fellow teachers, they gave “Numbers in Everyday Life” the old college try. Here are some of the course take-aways published in the February AmStat News (the parenthetical comments are my own):
— Always ask who is taking/reporting the numbers and how they obtained.
— Be wary of advocate’s numbers (such as a glowing report on a drug study sponsored by the manufacturer).
— Remember that the news media seek surprising numbers.
— Appreciate limitations of observational studies and differentiate correlation from causation.
— Controlled experimentation (the forte of my company Stat-Ease) is the gold standard.

By the way, you’d best be wary of how I cherry-picked these take-aways to support the cause for design of experiments. Actually, this was one of the take-aways that I conveniently omitted (“cherry-picking”). 😉 See the entire AmStat story posted via the YUDU epublishing initiative.

“One of the greatest contributions of statistical thinking… is design of experiments.” – Gerald Hahn