Statistics reinforce my happy choice for vacation destination
Posted by mark in Uncategorized on April 1, 2007
After enjoying a fun vacation in Puerto Rico, I was not surprised to see this country* topping the list in a worldwide ranking by happiness reported in the April 2007 issue of Minnesota Business. It stems from a study by the World Values Survey that questioned such things as “All things considered, how satisfied are you with your life as a whole these days?” See the combined index of happiness and well-being (positive versus negative) ranked by country (or the original Word doc).
The author of the Minnesota Business article, Tor Dahl, added 2006 per capita income to the mix. This reveals some surprising statistics, such as Mexicans earning less than half the income of Spaniards, yet reporting twice the level of happiness and well-being. However, using Design-Expert® software’s historical regression tools, I find overall a significant (p<0.0001) positive relation of income with happiness and well-being. Luxembourg, which at $65,900 per capita income (’06) exceeds the next richest country (Norway!) by 50 percent, stands out as an extremely high leverage point. If ignored, the non-linear plateauing of happiness and well-being becomes insignificant. In my opinion, though, this makes sense – at some point more money probably cannot buy more happiness. The quest for the secrets of happiness will no doubt continue with little chance of a totally satisfying outcome. Princeton professors Daniel Kahneman and Alan B. Krueger in their Developments in the Measurement of Subjective Well-Being present a list of variables which are correlated with global reports of life satisfaction and happiness, among which is an “unfakeable smile.” Isn’t that wonderful! 🙂
*(I enjoyed a good chuckle calling Earthlink before my vacation in San Juan, Puerto Rico to get their local dial-up accesses for internet. Their representative could not find Puerto Rico on the list. “Is it a United State?” he asked. “Not exactly,” I replied. “Well, then, it must be a country – correct?” “No.” I then tried to briefly explain the status of Puerto Rico as a self-governing commonwealth – possibly even more difficult to explain than why their people seem to be so happy. Anyways, the Earthlink rep pleased me greatly by saying he found two access numbers for San “Chew-on.” Evidently this fellow’s native language was not Spanish, but in a case like this, I do as Bobbie McFerrin says – “Don’t worry, be happy”.)
El Morro’s twisty ternary bastions
Posted by mark in Uncategorized on March 25, 2007
While vacationing in San Juan, Puerto Rico this week, I came across a tricky triangular staircase. It’s in a bastion of the Spanish fort El Morro. Military engineers, evidently well-versed in geometry by the late 16th century when these fortifications were built, favored polygonal designs because the oblique angles resisted cannon balls. Triangular outworks provided fields of fire along adjoining walls. In the jargon of fortress design these are called “demilunes” if inside the surrounding ditch or moat, and a “ravelin” if outside. I think even the 5th graders who outsmarted their adult contestant in knowledge of a trapezoid would be challenged to identify all the shapes in a fort like El Morro.
“Sometimes things happen in the world that we are not capable of understanding.” “Yeah, like geometry.” 3/23/07 comic strip Baldo
It turns out that the only one to successfully take over El Morro was Sir George Clifford, 3rd Earl of Cumberland. His English predecessor Sir Francis Drake failed to defeat the Spanish in San Juan three years earlier. Perhaps Clifford’s solid education in mathematics helped him formulate a successful strategy. However, although he was fearsome on a horse — being one of the top jousters of the age, Sir Clifford struggled on foot. While suited up in his legendary armor, he slipped while bridging a moat and nearly drowned. After traversing the pictured triangular stairway (termed “ternary” as explained in my previous blog), I cannot see how anyone could manage this in full armor. Perhaps by then Sir Clifford had achieved victory and stripped down to his Bermuda shorts to sip on one of San Juan’s famous pina coladas.
For more on El Morro and its place in the battle against pirates of the Caribbean, see this blog by scholar Jon Beasley-Murray.
Pairing foods and beverages to please the palate
Fish is white. Meat is red. That color pairing helps me decide which type of wine to order. It also sums up my interest and ability as a gourmand! For example, today we had a family brunch to celebrate my oldest daughter’s birthday and I ended up with two pitchers, one with grape juice and the other orange. Each had about a third of the juice remaining and the refrigerator could accommodate only one pitcher. Hmmm, what could I do? Eureka, a thought came to me: Mix the grape into the orange juice to combine it all into one container! Unfortunately, the resulting mixture looked so unappetizing that only my son Hank, an engineer like me (him software, me chemical), would drink it. Also, Hank admitted to having one or two beers –maybe more, while watching the Gopher hockey game last night at the corner pub. The Gophers unexpectedly lost, so I’m thinking my son may’ve drowned his sorrows. Therefore, I think that his positive review of my “orangerape” juice must be considered an outlier. 🙁
So far as beers are concerned, I’ve done equally bad, for example, by seeing what would happen if I mixed cream into it (detailed in my 1/14/07 blog “Mixing beers — synergy of zymurgy?”). One thing I never considered pairing with beer is chocolate, but, according to this article by J.M. Hirsch of Associated Press, Boston’s brahmins attend classes on this! An obvious combo is Belgian chocolate with Belgian abbey ale. However, I prefer to continue studying only beer. Any time our chemical engineering society sponsors a brewery tour and tasting, I am there!
My favorite pairing is apples with cinnamon. For example, this applesauce recipe looks very a pealing (pun intended!), in part because it’s so amazingly simple. I once tested my Stat-Ease colleagues by asking them to rate on a 1 (worse) to 10 (best) scale their taste preference of apple, cinnamon and lemon jelly beans and combinations thereof. The results are detailed in DOE Simplified in the chapter on mixture design, but the ternary diagram *, tells the story: Pairing apple with cinnamon creates a taste sensation (over 7 on the tasting scale) –- they are synergistic. However, putting the two fruits together (apple and lemon) created a sour reaction from our sensory testers (rated less than 3 on average) -– these two ingredients interact in an antagonistic manner. The trick when pairing foods and beverages is to avoid antagonism and seek synergism.
“Look for those opposites that attract. For example, sweet and acidity, sweet and spicy, hot and cold, salty and sweet.” David Kamen, chef instructor at the Culinary Institute of America (CIA).
*(Source of primer on ternary diagram: Lynn S. Fichter, Department of Geology and Environmental Science, James Madison University, Harrisonburg, Virginia.)
Do narrower columns hold up better for body of written work?
Pat Whitcomb came across a very intriguing article in the February ’07 issue of Training & Development magazine that says keeping line lengths shorter makes text easier to read and remember.* (Hmmm – did this asterisk cause you to reflexively glance to the footnote and interrupt your train of thought? Sorry about that!) IBM researchers evaluated paragraphs at 40 percent screen width versus 80 with a device that measures eye-gaze tracking. They found that narrow columns were more comprehensible and required less re-reading. However, this came at the cost of “paragraph abandonment,” a shift by readers to skimming completely over segments of text.
What’s telling to me, is that the IBM web page on this research (linked above) displays text in a single, wide column. I like this wider style for displaying text on my computer because I can then scroll line-by-line and not be forced to go back up again as required with two columns side-by-side. For example, see this latest edition of the Minnesota Section ASQ newsletter. Notice how it shifts format from one column to two. Observe how you read these. Which do you prefer?
My preference is to print pieces written in two-column format and then use my finger as a guide to maintain focus on the line of text. I picked this up from a business colleague years ago after he took a speed-reading course.
* “The Long and the Short of Learning” by Peter Orton, David Beymer and Daniel Russell.
Graupeling for words to describe nature’s emanations
Late Friday I took a call from a client in Hawaii. All day long here in Minnesota the weather forecasters had been harping about the dire prospects for over a foot of snow. The Hawaiian sounded skeptical when I told him of my positive view on these developments. Believe it or not, many of us Minnesotans enjoy the opportunity to ski, snowmobile and just revel in the contrast of winter with our other three seasons.
The first round of snow hit that evening. It was quite unusual – pelletized like Dippin Dots or IttiBitz ice cream, created by flash freezing the sugary dairy mix in liquid nitrogen. Something similar must have occurred naturally over my home town of Stillwater. The American Meteorology Society (AMS) describes this frozen phenomenon as graupel. Evidently it’s a cousin of hail, which we see in the summer-time when thunder storms become severe. This graupel was great for shoveling. I’ve got a low-tech, but amazingly effective, snow scooper, which just pushed it out the way and, with a quick twist, dumped it over. The pellets just poured right out.
That was only the first wave of the storm. Over the next 24 hours, another half-foot of snow fell. The neighbor across the street was really fired up about getting his snow blower running for the first time this year and promised to shovel my driveway after all was done with this winter storm. However, it took so long to start the disused engine, that I scooped him.
Getting back to Hawaii (a very attractive thought at the moment), I once visited their namesake “Big Island” and saw lots of lava from Kilauea. There I learned that Hawaiians differentiate flows as “aa” – rough, versus “pahoehoe” – smooth. (See details by volcanologist J. M. Rhodes.)
Having hand-shoveled snow for half a century, I can readily characterize their types. However, I must hand it to the Hawaiians for putting words to what Mother Nature puts in ones path. More snow is forecast later this week for Minnesota. I predict that this may precipitate many Minnesotans to have an “Aa, ha” and book an impromptu getaway to Hawaii or another warm State!
Overreacting to patterns generated at random – Part 2
Professor Gary Oehlert provided this heads-up as a postscript on this topic:
“You might want to look at Diaconsis, Persi, and Fredrick Moesteller, 1989, “Methods for Studying Coincidences” in the Journal of the American Statistical Association, 84:853-61. If you don’t already know, Persi was a professional magician for years before he went back to school (he ran away from the circus to go to school). He is now at Stanford, but he was at Harvard for several years before that.”
I found an interesting writeup on Percy Diaconis and a bedazzling photo of him at Wikipedia. The article by him and Moesteller notes that “Coincidences abound in everyday life. They delight, confound, and amaze us. They are disturbing and annoying. Coincidences can point to new discoveries. They can alter the course of our lives; where we work and at what, whom we live with, and other basic features of daily existence often seem to rest on coincidence.”
However, they conclude that “Once we set aside coincidences having apparent causes, four principles account for large numbers of remaining coincidences: hidden cause; psychology, including memory and perception; multiplicity of endpoints, including the counting of “close” or nearly alike events as if they were identical; and the law of truly large numbers, which says that when enormous numbers of events and people and their interactions cumulate over time, almost any outrageous event is bound to occur. These sources account for much of the force of synchronicity.”
I agree with this skeptical point of view as evidenced by my writing in the May 2004 edition of the Stat-Ease “DOE FAQ Alert” on Littlewood’s Law of Miracles, which prompted Freeman Dyson to say “The paradoxical feature of the laws of probability is that they make unlikely events happen unexpectedly often.“
Overreacting to patterns generated at random — Part 1
My colleague Pat Whitcomb passed along the book Freakonomics to me earlier this month. I read a story there about how Steven D. Levitt, the U Chicago economist featured by the book, used statistical analysis To Catch a Cheat –teachers who improved their students’ answers on a multiple-choice skills assessment (Iowa Test). The book provides evidence in the form of an obvious repeating of certain segments in otherwise apparently-random answer patterns from presumably clueless students.
Coincidentally, the next morning after I read this, Pat told me he discovered a ‘mistake’ in our DX7 user guide by not displaying subplot factor C (Temp) in random run order. The data are on page 12 of this Design-Expert software tutorial on design and analysis of split plots. They begin with 275, 250, 200, 225 and 275, 250, 200, 225 in the first two groupings. Four out the remaining six grouping start with 275. Therefore, at first glance of this number series, I could not disagree with Pat’s contention, but upon further inspection it became clear that the numbers are not orderly. On the other hand, are they truly random? I thought not. My hunch was that the original experimenter simply ordered numbers arbitrarily rather than using a random number generator.*
I asked Stat-Ease advisor Gary Oehlert. He says “There are 4 levels, so 4!=12 possible orders. You have done the random ordering 9 times. From these 9 you have 7 unique ones; two orders are repeated twice. The probability of no repeats is 12!/(3!*12^12). This equates to a less than .00001 probability value. Seven unique patterns, as seen in your case, is about the median number of unique orders.”
Of course, I accept Professor Oehlert’s advice that I should not concern myself with the patterns exhibited in our suspect data. One wonders how much time would be saved by mankind as a whole by worrying less over what really are chance occurrences.
*The National Institute of Standards and Technology (NIST) provides comprehensive guidelines on random number generation and testing– a vital aspect of cryptographic applications.
Weather to be or not to be, that is the question
Last night I got a panicked call from my host for a talk scheduled tomorrow night to a group of quality professionals and their student section at Purdue University. Predictions had just firmed up for a major winter storm that might dump up to a foot of snow in parts of Indiana. Which parts would get snow was hard to forecast, but it seemed likely to be rain south of Indianapolis – my flight destination, icy there and snowy to the north in Lafayette – home of Purdue. Thus, given I’d be driving through the middle of this wintry mess, my host’s bias toward canceling the meeting met with little resistance from me. At the moment, based on tonight’s weather reports, it appears that we made the right decision. However, I’ve seen plenty of dire weather predictions fizzle over the years, particularly for snow and/or ice, which often end up precipitating as relatively benign rain due to unexpected warmth.
North American winter storms can wreak havoc on a grand scale, for example, when ice builds up to a point where power lines come down over broad areas. However, hurricanes like Katrina really strike fear in the hearts of insurance underwriters. Richard Mullins of the “Tampa Tribune” reports* on the use of simulations for predicting the financial scale of disasters like this. According to him, some storm models sell for as much as $10 million! For that price, one would assume the results would be unbiased. However, non-profit and privately-funded researchers interviewed by Mullins agree that results from studies underwritten by insurance companies naturally fall to the high side, whereas ones done for the public interest tend to the low end. The range went from $2 billion to $12 billion for 2005’s Hurricane Wilma!
Things really get wacky when one tries to assess risks of buying a vacation property in Florida to escape the wretched winter weather of the northern USA, from Indiana on up. Where would one be safest in a beach home – a place like Jacksonville that’s experienced no category 4 hurricane in 150 years? Maybe they are ‘due’ for one. A contrarian might take an opposite tack – buy where the most recent horrific hurricane hit, such as the surprisingly robust Wilma that tracked in to Florida after clobbering Cancun.
My idea is to simply rent a haven in Florida during the winter – the season when there are no hurricanes. I would leave at the first sign of snow up north and not go back until it melted. I wonder if any fellow northerners have thought of this?
*“Calculating Disaster,” Sunday, 2/11/07
Nature’s dangerous forces — including cold temperatures
Sadly, tornados devastated central Florida this week, including a church designed to resist a category 4 hurricane. The twister that destroyed this building must have been a 3 on the Fujita scale based on my comparison of its wind speeds with that of the Saffir-Simpson categorization for hurricanes.
Scales like this are popular for devasting forces, such as the Richter for earthquakes and decibels for Rolling Stones (a joke). I’d like to contribute one of my own:Cold Force. My cold force (CF) scale begins at 40 degrees C (104 F) and increases by 1 for each decrease of 10 C. For example, today I experienced a temperature of 6 degrees F (-15 C), which translates to a CF over 5 on the Anderson scale. This measure is a useful predictor for the number of layers a person should wear to maintain body temperature. Notice all the clothes I wore today – not quite enough for prolonged exposure – take my word on that!
I experienced extreme heat, over 100 degrees F, last July at a Baltimore Oriole baseball game in their home field — Camden Yards. Since this correlates to 0 CF, one could comfortably go around in literally nothing, but I recommend at least a bathing suit. At 1 CF (30 C, 86 F), you might consider putting on a t-shirt. Next on the scale comes 20 C or 68 F, at which point (CF 2) a nylon windbreaker would be good – in other words a second layer.
Wind-chill becomes a factor below CF 3 (10 C, 50 F). The Mount Washington Observatory, “Home of the world’s worst weather,” provides the mathematical formula below their chart of temperature versus wind. They also provide a calculator for this purpose. According to Environment Canada , residents of Pelly Bay experienced a wind chill of -91 degrees C on January 28, 1989. That created a freezing force of 13 by my reckoning. However, it would be ridiculous to put on that many layers of clothes. Maybe that’s why last winter while vacationing in Miami during unseasonably cold weather – CF 2, a radio DJ derisively noted that anyone wanting to see Canadians need only drive by the beach. I was decked out in my bathing suit and driving there myself at the time!
Making coffee to the most by taking on the roast
The “Everyday Cheapskate,” Mary Hunt, advised this week that the more you learn about coffee the less, you’ll spend. I went high-tech some years ago with Cuisinart’s Automatic Grind & Brew Thermal ™. It makes great coffee and preserves it well by percolating directly into a stainless steel carafe. I get up early for a fresh-made cup and set the remainder at bed-side for my wife to enjoy as an eye-opener. She was the one who pointed out Hunt’s article to me, which suggested that roasting your own beans makes the brew “infinitely better tasting” at half the price. That is good, because after reading this, I immediately bought a $400 Swissmar Bravi and fired it up this weekend — the distinctive, but not unpleasant, smell of roasted coffee fills my home as I write. (My daughter thought I’d been boiling down maple syrup.)
The Bravi manufacturer leaves nothing to chance. For example, in the coffee roaster’s product guide they begin by saying “Keep the instructions (sic) manual.” The Swissmar engineers then specify that their customers “always use exactly one-half pound (225 g)…no more, no less.”** The machine offers a variety of roasting levels to a maximum of “Espresso,” which “comes very close to the edge of ruin.” Taking no chances, I went far lower than that extreme roast my first time around!
The moment of truth will come tomorrow morning when I make coffee with my home-roasted beans (Sumatra Mandheling). It had better be good, because I figure that, given the $6 per pound savings in beans and assuming a production rate of 40 cups of coffee per pound, the payback period will be two years. If the brew gets a “boo,” that will seem like an eternity to a ‘caffiend’ like me.
*Coffee trees produce a red “cherry” that peels back to the core green-bean
**At Ubersite, which “capitalizes on random, chaotic, unpredictable, flexible, bizarre human behavior,” I found these humorous comments (censored) on whether one ought to bother weighing:
I’m too lazy to actually measure the coffee out, so I just dump some in and try to visually judge how much I’ll need to brew a pot. Each day I stare while it’s brewing, tingling with anticipation… “today it’s going to be perfect.” No matter what, I either get really strong goo, or light brown water. Wouldn’t I be so much happier if I just measured?
The righteous way, and the path to true enlightenment, is to judge for yourself. As you hone your senses and your appreciation of the subtleties of coffee concentration increases, you will journey on a remarkable voyage of self discovery. You will see things that are invisible to the unenlightened eye. This will lead to a greater understanding of being. However, if you are fluctuating between brown water and syrupy goo, then I suggest you measure. You are a dingbat.
No. You will never achieve Zen-like coffee by measuring. The only way is trial and error. I know, I have achieved UberCoffee.