Stats Made Easy

I’ve just capped off two weeks in Great Britain by touring Dewar’s
World of Whiskey at their Aberfeldy Distillery in Scotland. They
let me taste their famed White Label blended brand, which
according to Dewar’s “Never Varies.” I must say that I could not
tell the difference of it versus their Aberfeldy Single Highland
Malt or the 12 year old Special Reserve — they all burned me
through and through (I do not normally drink hard liquor). This
lack of subject matter knowledge may explain why I flunked Dewar’s
computerized blending challenge and prompted the software to say
that my whiskey would be good for “stripping paint” and that “a
monkey could do better and would probably be easier to train!” If
only I had brought my computer along to use Design-Expert
software’s marvelous statistical mixture design features. It
would have helped me match White Label with the correct blend of
the six components: Highland earthy malt, Island salty malt, Islay
peaty malt, Lowland malt, Speyside sweet malt and the spirit base
— raw grain whiskey. I wonder how long it would take a monkey to
uncap a beer — I think I could top it at this task. Anyways,
after this debacle trying my hand at blending whiskey, I may have
a brew or two.

Joke: Why is 6 afraid of 7? Because 7 ate 9! You don’t get this? Perhaps you suffer from dyscalculia — a learning disability that creates severe difficulty in understanding and using functions or symbols needed for success in mathematics. (Or maybe this joke is very stupid!) Like dyslexia, which affects reading ability, dyscalculia can be caused by a visual perceptual deficit. The UK government’s Department for Education and Skills includes this numeracy problem in its leaflet on Guidance to support pupils with dsylexia and dyscalculia. What brought this to my mind was hearing someone at my household this weekend complain that the DVD burning process was only “5/3rds” done! Maybe fractions should be put in a special category — they really are terribly hard to fathom. I thought I had fractions mastered until the time I traveled into the hinterlands of western Wisconsin into a chain of lakes peppered with cabins. The one I wanted was on 178&23/32nd street. It challenged me to calculate that I ought to keep on going past 178&1/2, 178&5/8th and 178&11/16th streets.

The May 15 issue of Sports Illustrated magazine passes along a prediction by statisticians that the Minnesota Twins have virtually no hope of winning this season, even though they’ve only played about one-fifth of the games. The team started the year with a 2 to 1 shot at achieving the playoffs in Major League Baseball, but after their 13-18 start, the odds are now 200 to 1 against this. These probabilities come from a Monte Carlo simulation done by Clay Davenport — a statistician specializing on baseball, also known as a “sabermetrician”. His latest stats can be seen in the Baseball Prospectus Odds Report, which touts that its analyses stem from “Playing the rest of the season a million times.” Evidently the Minnesota Twins management read this report because local sports writers have been spreading rumors that the team will divest itself of highly-paid stars Tori Hunter and Shannon Stewart. Due to a rash of injuries, the New York Yankees need outfielders as soon as possible and they have the money and prospects to entice the small market Twins into giving up their season. As a Minnesota fan, I say that these statistics be damned!

When you are faced with something dreadful, like a final exam in statistics class, do you just want to get it over with as quickly as possible? If so, you are acting irrationally because it makes more sense to delay something unpleasant as long as possible. However, according to a new study in Science magazine reported by Sandra Blakeslee in the New York Times, some people are extreme “dreaders” who prefer more pain if it gets things over with, sooner. The research by Dr. Gregory S. Berns, a professor of psychiatry and behavioral sciences at Emory University, was literally shocking: His team of scientists applied voltage to their subjects’ feet at levels and delays of their choosing. Berns found that when it comes to dread the waiting time makes it more intense. That must be what makes a college course on statistics so dreadful — waiting the whole semester for the final exam! It seems to me that the certainty of something scary like this is also a key. For example, at the moment, the avian flu is creating great dread because it seems likely to become an epidemic and create many deaths. However, if this likelihood abates with time and/or medical preparations advance to a more comforting level, our dread will drop off. Unfortunately, it is hard getting around a final exam!

PS. According to Schachter & McCauley, authors of “When Your Child is Afraid,” an adult’s most common fears, in order of magnitude, are: public speaking, making mistakes, failure, disapproval, rejection, angry people, being alone, darkness, dentists, injections, hospitals, taking tests, open wounds, blood, police, dogs, spiders, deformed people.

It was my pleasure yesterday to teach design of experiments (DOE) at the Ohio State University’s Fisher College of Business for their Web-Leveraged Six Sigma Black Belt program. It turned out that one of the participants, Dennis Dubose — a statistician with Sumco USA, teaches DOE also, so we compared notes. He shared a nice explanation of the difference between simply repeating measures versus performing a true replication of the system setup for purposes of estimating error. Imagine you flip a coin and it comes up heads. You ask a colleague to look at it and call out the result. Then another colleague is asked to observe the coin and state which side came up. This is a repeated measure. A true replication is accomplished only by re-flipping the coin.

In response to studies that demonstrated chronic release of mercury vapor from amalgam fillings during chewing and brushing, the National Institute of Dental and Craniofacial Research (NIDCR) sponsored the Children’s Amalgam Trial (CAT). Today’s issue of Journal of American Medical Association (JAMA) unveiled the results of CAT, which is summarized by this intriguing quote from the lead author:

“The studies indicate that on average we probably don’t have much to worry about…”
(David Bellinger, Harvard Medical School)

In my prior career as a quality professional I’d heard that positive word-of-mouth about a company’s products and services may be passed along to three people, whereas bad news transmits much further — to at least twice as many individuals. This is a powerful inducement for businesses to go all out to avoid bad will. A new study, done in part by the prestigious Wharton School, adds a great deal of insult to the injury caused by customer complaints: As reported in the April 17th Business Week magazine and previously by CBC News, the stories about bad products and/or service become magnified with each re-telling, so that people down the line are up to 5 times as likely to avoid the business in question as the original unhappy customer. Evidently Hollywood is well aware of this phenomenon, because when they know a major movie will be a bomb, they roll it out to as many theaters as possible to maximize revenue the first weekend before the bad buzz can kill it.

While teaching mixture design for optimal formulation at two chemical companies the last two weeks, I was surprised to see that they still specify ingredients as pounds per hundred (pph)– bsed on their main component. This is really old-fashioned, not only for the use of English units of measures,* but because it does not account for the dilution effect. For example, a Stat-Ease client making a construction caulk ran a central composite design, a response surface method (RSM), that varied the filler from 100 to 250 pph and plasticizer from 50 to 100 pph based on 100 pounds of polymer. They kept the other 57 pounds in their recipe constant in terms of relative proportions for the ingredients. We did some simple calculations with a spreadsheet to make the bargraph shown on a 100 percent weight basis. Seeing how everything (depicted by colored segments) varied by concentration (not just the two ingredients they intended to change), it now became clear to the client that they would best re-design their experiment as a mixture.

*(Hired into the petroleum industry as chemical engineer in 1975, I quickly learned that there are 42 gallons in a barrel. Further research into English units of volume revealed that some number of firkins would fit into hogshead — I forget now. Just this last week I discovered a new measure of volume at a brew pub — they sold a “growler” of beer (64 fluid ounces) — a grrrreat deal!)

Having had enough of statistical tea-testing (inside joke), I bought two brands of beer this week — Summit Grand “pilsener” (Bohemian style) and Schell “pilsener” — for an impromptu test of my wife’s tasting abilities. She comes from 100 percent German stock consider beer as dear as mother’s milk. Thus, I was not surprised she got every one of these four combinations correct (“her answer in quotes”), even though I revealed nothing about the sources, saying there may be from one to four beers:
– Grand vs Grand “same”
– Grand vs Schell “different, but I don’t prefer one or the other”
– Schell vs Grand “different, but I don’t prefer one or the other”
– Schell vs Schell “same”.
The Grand beer is clearer, less expensive and offers a twist-off cap, so my wife and I will stay with this brand made in my home town of Saint Paul, Minnesota (Schell is made in New Ulm — a German settlement in the southwest of the State).

I would appreciate other ideas for a simple, but scientifically valid (?) taste-off like this for beverages or foods. My very cursory internet search brought up an article by James Fallows in the e-zine “Slate” titled Booze You Can Use, Getting the best beer for your money, but I do not necessarily advocate its methodology. I do happen to like Sam Adams a lot, which the Microsoft employees doing the tasting rated as best. Well before 1984, when Jim Koch founded The Boston Beer Company and the idea of a microbrewery, a chemist friend of mine snobbishly proclaimed that he only drank the “champagne of bottled beer,” Miller, and not the much cheaper (at that time) Old Milwaukee brand. I’d just taken a marketing class for my MBA that revealed that beers of this era (late 1970’s) were all essentially the same, but advertisers duped drinkers into paying more for “premium” brews. The chemist refused to believe this, so two of us chemical engineers set up a beer-tasting contest for a Super Bowl party. First we all sipped 10 brands of beer straight out of the bottle (perhaps a bit too much!). The chemist rated Miller top and “Old Swill-waukee” bottom. Then we repeated the test with beers poured blind to the tasters. The chemist unknowingly declared Old Milwaukee his favorite and, you guessed it, Miller the worst tasting. Of course by then he was good and drunk, but the point was made. Anyways, we sure had a lot of fun pretending to have a taste for beer!