Stats Made Easy

Practical Tools for Effective Experimentation

Monday, February 26, 2007

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!

Sunday, February 18, 2007

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.

Monday, February 12, 2007

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

Saturday, February 03, 2007

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!