Stats Made Easy

Many experimenters are plagued by variation. Physicists cite Heisenberg for uncertainty in their measurements. However, most engineers prefer to blame their troubles on the devilish Murphy or elusive gremlins.

Those of us in the computer business swear by, or rather – at, bugs as the culprit for anything that does not go as planned:
“Things were going badly; …Finally, someone located the trouble spot and, using ordinary tweezers, removed the problem, a two-inch moth. From then on, when anything went wrong with a computer, we said it had bugs in it.”
— Admiral Grace Murray Hopper, pioneer computer scientist

PS. The Admiral lived her life at ‘full steam’ as evidenced by this quote : “It’s easier to ask forgiveness than it is to get permission.” (I advise extreme caution if you ever feel compelled to take action on this basis!)

This week sadly marks the demise of Whamo co-founder Richard Knerr – the company who popularized Fred Morrison’s Pluto Platter, re-branded as the “Frisbee.” Plastics were the thing back in those halcyon days of my youth in the 1960’s (the one word advised by the business man in the film The Graduate). However, Whamo’s Hula Hoop failed to ignite my interest, whereas the Frisbee kept me running for hours on end. The older fellows up the hill would float it far down our street for me to happily retrieve.

Throughout my life I’ve kept these plastic discs at hand for impromptu flings. I always brought several along on family camping trips we took throughout Minnesota in the 1980’s. I would designate a tree down the State park’s lane as flag number one and challenge my two boys to hit it before me. When they bonked the bark first, it was the winner’s prerogative to choose the next destination.

Evidently this proved to be a hit with my oldest son Ben, because he became an avid disc golfer. I’ve accompanied him on occasion and been privileged to see Ben make two aces, that is, the first toss going directly into the basket. These typically feature chain link ‘catchers’ that provide a very satisfactory ‘kachink’ when hit straight-on by the flying lid. By dint of keeping my throws short and accurate, I sometimes enjoy this sensational sussuration before my long-tossing offspring, but not often.

The week before last I enjoyed a great buddy trip with Ben doing some disc golfing in Southern California. We stayed with my aunt and her son (my first cousin) at their homes in Corona Del Mar. She found it amusing that grown men would play “Disco” golf, perhaps imagining a Travola-like stroll down the fairway to the tune of the BeeGee’s Stayin’ Alive. For me it was more of a good walk soiled by my ultimately successful attempt at retrieving a disk before if floated away on a muddy pond (pictured above) at Emerald Isle Golf Course outside Oceanside, CA. Ben ran into problems at another disc golf course in La Mirada’s Regional Park. I think it was hole 22 where his ‘driver’ floated over the fence into a back yard guarded two dogs – a little yapper and an ominously silent pit bull. I hope they enjoyed their new toy.

Like the more traditional golfing with balls, one must learn to move on from lost or irretrievable disks and remain mellow. To me, that’s what Frisbee was all about, so it really is an end of an era now that Whamo’s co-founder has passed on — to greener pastures, I hope.

PS. My daughters all enjoy doing the “disko” too. For example, Katie and her cousin did an experiment on a variety of brands and configurations, such as rings, which I documented in a Stat-Teaser article titled Sixth-Graders Experiment with Flying Disks. It generated a surprising number of responses, including:

– Support for the girls’ hypothesis that color might create an effect (an expert on plastics pointed out that pigments vary by weight)*

– A picture sent by University of Nevada Las Vegas Professor D. W. Pepper of a 10-foot wide disc made by an engineering student who purportedly threw it 1000 feet outside Reno, which generated reports of UFOs.** (I would enjoy the look of the La Mirada pit bull seeing this sky-blotting saucer sail over the fence!)

*See item #5 in my October 2002 DOE FAQ Alert

**Details reported in #6 of November 2002 DOE FAQ Alert

Earlier this month,* Newsweek’s “Health Matters” columnist Jerry More resolved that
“I will not report on any amazing new treatments for anything, unless they were tested in large, randomized, placebo-controlled, double-blind clinical trials published in high-quality peer-reviewed medical journals.”

He was “shamed” into this by biostatistician R. Barker Bausell’s book Snake Oil Science. Based on observations of his own loved ones, Bausell explains how immensely powerful placebo effects make almost any medical treatment appear to work, even though they are often caused by faith alone. Those who feel the benefits, whether it be placebo or physical (double-blind verified), usually do not care how this comes to pass. However, Bausell makes the case that placebo effects tend to be mild and temporary.

In an ironic twist of Jerry More’s resolution, Bausell advises that those afflicted with chronic health problems seek a promising remedy from an enthusiastic promoter and take the plunge with no reservations, thus maximizing any placebo effect!

Obviously one must be extremely cautious about side effects from any such purported therapy or substance. For example, some years ago my wife and I hosted a weight-obsessed exchange 16-year-old student from Mexico who harbored strong faith in alternative medicines (an oxymoron?) for curbing appetite. One day while shopping at a local mall, she got away from me and made a bee line to a health-food store. I found her at the counter with half a dozen bottles of very potent natural (?) substances that the teenage clerk recommended to her. I hustled us out of there without making that purchase.

Blind faith just does not work well for me. I like the double-blind approach much better.

* A Big Dose of Skepticism

In the November issue of The American Statistician the Editor published this comment by David J. Finney, Professor Emeritus of Statistics at the University of Edinburgh: “On a day in 1919 or 1920…I murmured silently to myself: ‘David, you are becoming a clever boy…you have learnt to stand on one leg. What next?’…I showed creditable numerical ability in saying to myself ‘2-1-0.’ I willed myself to make…an effort to lift the foot. I rapidly became aware of a sore bottom…I never tried again but memory of the pain has given me a prejudice against any form of extrapolation from particular to general.”

In 1798, Thomas Malthus created one of the most controversial extrapolations in history in An Essay on the Principle of Population. Based on the sketchy statistics of the time, he assumed that population grows geometrically (exponential), whereas food supplies increase at an arithmetic rate (linear). No wonder he became known as “Gloomy” Malthus! Fortunately, due to development of new agricultural regions and improvements in productivity from these lands, the mass misery of his projections did not happen…yet.

In 1972, I read a book called Limits to Growth by the Club of Rome think tank. They presented a series of Malthusian projections with consumption increasing exponentially relative to linear expansion of resources. I found it terribly depressing. It seemed certain to me from all the graphs that mankind would not last beyond 2000. As subsequent developments averted what seemed sure disaster, I became ever more wary of extrapolation, especially ones that predict doom and gloom.

“Human history becomes more and more a race between education and catastrophe.”
— H. G. Wells

On the other hand, I’ve seen forecasts fizzle and become forgotten that turned out true — albeit much delayed. For example, in the spring of 1989 I co-taught a DOE class in the San Francisco Bay Area. One night my top-floor room shook so hard that it woke me up – it was an earthquake that registered a bit above 5 on the Richter scale. The next morning another earthquake rocked our training room – built on stilts just off shore on the Bay. It measured near 6. That led to a forecast that by week end there was a 20 percent probability of a really major quake. It did not materialize. However, in October, San Francisco suffered the devastating Loma Prieta earthquake – nearly 7 points on the Richter scale.

So, whereas little Finney took a fall from misguided extrapolation, Bay Area residents found themselves floored from what turned out to be a prophetically forecasted tremblor. I suppose one way of dealing with scenarios for the future is to expect, and plan, for the worst, but hope for the best, that is, hedge your bets. For example, try to keep two feet on the ground as often as possible, keep a hold on the bannister and look before you leap.

This Fall at a statistical conference I attended a stimulating talk on improving communications. The speaker recommended a book called Made to Stick. The authors, brothers Chip and Don Heath, provide six principles for making messages memorable: simplicity, unexpectedness, concreteness, credibility, emotions and stories (SUCCESs). This article by News and World Report provides more details on the tricks to Making it Stick.

Our company’s mission statement, Statistics Made Easy®, has proven to be very sticky. It is simple, very unexpected, concrete and emotional (statistics are scary!). However, the never-ending challenge for Stat-Ease is to make its slogan credible.

The Heaths provide an enlightening discussion on how to convey statistics better. They provide, for example, the challenge of being the publicity director for a group committed to saving sharks. A statistician might say that on average only 0.4 Americans die per year from shark attacks (that seems very macabre!), whereas in 2000 alone, 12 died while swimming off lifeguard-protected beaches. These stats do not stick nearly as well as this alternative: Which wild animal is more like to kill you – a shark or a deer? Answer: A deer is 300 times more likely to be the death of you. Oh dear!

“Statistics are rarely meaningful in and of themselves…It’s more important for people to remember the relationship than the number.”
– Chip and Dan Heath

A former colleague of mine, Jim Mork, sent me the ‘heads up’ to this blog by Mark Chu-Carroll, a PhD computer scientist who works for Google. He and others* mocked the Wall Street Journal (WSJ) for a poorly fitted curve of tax revenues versus percentage of gross domestic product (GDP) by country. They claim that it confirms the Laffer curve, which quantifies the diminishing returns that a government gains by going beyond a certain level of taxation.

“It should be known that at the beginning of the dynasty, taxation yields a large revenue from small assessments. At the end of the dynasty, taxation yields a small revenue from large assessments.”
— Ibn Khaldun (14th century)

The WSJ curve starts from the origin at 0 percent corporate taxes for United Arab Emirates (UAE), which obviously contributes 0 to their treasury (presumably their money comes from a general sheikh down). The WSJ graphic designer then took the curve all the way up to Norway at 10 percent on the y (upper) axis, ignoring the dozen countries below this in the mid-range of rate of taxation on corporations. This is a case or providing one point (Norway) an extreme leverage in curve-fitting.

I searched out comparable Organisation for Economic Co-operation and Development (OECD) figures from a few years earlier (2002) than those upon which WSJ based their analysis. My curve-fit, done in with Design-Expert® software, does show a characteristic Laffer peak at 29 percent corporate rate, thus supporting the argument for reducing our USA rate of 35 percent. However, as one can see from the very broad 95 percent confidence band, this finding is not one that government officials ought bank on.

*Kevin Drum of the Washington Monthly