Wrong more often than right but never in doubt
Posted by mark in Consumer behavior, Uncategorized on October 23, 2011
The New York Times Magazine provided a great readout on the “Surety of Fools”* in today’s issue. The author, psychologist Daniel Kahneman, starts by providing a real-life example of WYSIATI – “What you see is all there is.” Read his story to learn more about this, but basically it means that many times what you observe does not provide any meaningful information for predicting future behavior. Cocky Wall Street brokers are hit very hard, especially the males, who “act on their useless ideas significantly more often than women.” Ouch!
Kahneman examined the illusion of skill in a group of investment advisors who competed for annual performance bonuses. He found zero correlation on year-to-year rankings, thus the firm was simply rewarding luck. What I find most interesting is his observation that even when confronted with irrefutable evidence of misplaced confidence in one’s own ability to prognosticate, most people just carry on with the same level of self-assurance.
The bottom line is that you shouldn’t swallow everything said by assertive and confident people who advise on highly-variable systems such as financial markets. Heeding what an experienced physician suggests is one thing, but going with the most boastful money manager is another.
“True intuitive expertise is learned from prolonged experience with good feedback on mistakes.”
— Daniel Kahneman
“It’s what you learn after you know it all that counts.”
— John Wooden
* Posted earlier under a different title here.
Trouble with math & stats? Blame it on dyscalculia.
Posted by mark in Basic stats & math, Uncategorized on October 16, 2011
According to this article in Journal of Child Neurology “dyscalculia is a specific learning disability affecting the normal acquisition of arithmetic skills, which may stem from a brain-based disorder. Are people born with this inability to do math in particular, but otherwise mentally capable – for example in reading and writing? Up until now it’s been difficult to measure. For example, my wife, who has taught preschool for several decades, observes that some of her children progress much more slowly than other. However, she sees no differential in math versus reading – these attributes seem to be completely correlated. The true picture may finally emerge now that Michèle M. M. Mazzocco et al published this paper on how Preschoolers’ Precision of the Approximate Number System Predicts Later School Mathematics Performance.
Certainly many great minds, particularly authors, abhor math and stats, even though they many not suffer from dyscalculia (only numerophobia). The renowned essayist Hillaire Belloc said*
Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death.
I wonder how he liked balancing his checkbook.
Meanwhile, public figures such as television newscasters and politicians, who appear to be intelligent otherwise (debatable!) say the silliest things when it comes to math and stats. For example a U.S. governor, speaking on his state’s pension fund said that “when they were set up, life expectancy was only 58, so hardly anyone lived long enough to get any money.”** One finds this figure of 58, the life expectancy of men in 1930 when Social Security began, cited often by pundits discussing the problems of retirement funds. Of course this was the life expectancy at birth, in times when infant mortality remained a much higher levels than today. According to this fact sheet by the Social Security Administration (SSA), 6.7 million Americans were aged 65 or older in 1930. This number exhibits an alarming increase. The SSA also provides interesting statistics on Average Remaining Life Expectancy for Those Surviving to Age 65, which show surprisingly slow gains over the decades. I leave it to those of you who are not numerophobic (nor a sufferer of dyscalculia) to reconcile these seemingly contradictory statistical tables.
*From “On Statistics”, The Silence of the Sea, Glendalough Press, 2008 (originally published 1941).
**From “Real world Economics / Errors in economics coverage spread misunderstandings” by Edward Lotterman.
Clickers allow students to vote on which answer is right for math questions
Posted by mark in Basic stats & math on October 12, 2011
Yesterday I attended a fun webinar on Interactive Statistics Education by Dale Berger of Claremont Graduate University. Because I was multitasking (aka “continuous partial attention” — ha ha) at work while attending this webinar my report provides just the highlights. However, you can figure out for yourself what they (the stats dept at Claremont) have to offer by going to this web page offering WISE (Web Interface for Statistics Education) tutorials and applets.*
After the presentation a number of educators brainstormed on interactive stats. David Lane of Rice U (author of many stat applets) suggested the use of “interactive clickers” – see this short (< 2 min.) newscast, for example. I wonder what happen when a majority vote for the wrong answer? For some teachers it might be easiest just to declare the most popular response as the correct answer. That would be consistent with the way things seem to be going in politics nowadays. ; )
*Just for fun try the Investigating the Central Limit Theorem (CLT) applet (click the link from the page referenced above or simply click here). This would be a good applet to provide when illustrating CLT using dice (such as is done in this in-class exercise developed by two professors from De Anza College). In this case, pick the uniform Population and sample size 2. Then Draw a Sample repeatedly, and, finally, just Draw 100 samples. Repeat this exercise with sample size 5 a la the game of Yahtzee (a favorite in my youth). Notice how as n goes up the distribution of averages becomes more normal and narrower. That’s the power of averaging.
Speed of light exceeded (astounding!)? Or was it measurement error?
This morning I read this NY Times news that European physicists measured neutrinos at 0.0025 percent above the speed of light. If so, it may be only a matter of time before you can send yourself a telegram to not do whatever you did that you’ve always regretted and, by the way, to please invest a thousand dollars in Microsoft, Facebook or the like (depending on the timing).
Years ago I visited Mount Wilson Observatory in California with my son Hank. See me pictured by their two domes that house 60 and 100 inch telescopes; respectively. This was the center for landmark experiments on the speed of light as detailed in this Wikipedia article. Obviously measurement error made this a very difficult.
Being a skeptic, and seeing that a similar experiment* found neutrinos whizzing about at the speed of light, but not beyond that, I was going to advise caution. However, Hank gave me the heads up to today’s xkcd cartoon (click the image to make it bigger and more readable). I think this guy has got a better idea.
*Done with a group at the Soudan Underground Laboratory here in Minnesota. They first did physics experiments there, in an abandoned iron mine, in 1980. I featured this in a retro young-adult techno/adventure/mystery/thriller called The Secret of the Wolf Ring (Amazon, Kindle Edition).
Blended learning for math & stats
Posted by mark in Basic stats & math on September 18, 2011
Check out this intriguing YouTube video by Khan Academy proving the Pythagorean Theorem:
Now imagine grade schoolers being lectured like this at home and then spending their time in class following up one-on-one or in small group sessions with the teacher. See this report from a 7th grade math teacher in California who takes advantage of this “blended learning” approach. As face-to-face time with educators becomes ever-more expensive, expect more-and-more use of asynchronous web-based training like this. That’s what I foresee. Don’t you?
Proofing Blackbeard’s rum
Posted by mark in pop, Uncategorized on September 11, 2011
Being only about a week from this year’s Talk Like a Pirate Day this Atlantic Monthly article (read belatedly from a backlog of magazines) about Gunpowder on the Rocks caught my eye. I like the idea of setting a drink on fire and then drinking it, as Blackbeard did to impress his pirate crew.
It turns out that this is a practical test of rum to ensure it hasn’t been watered down by a ne’er-do-well hornswoggler, as you can see in this video by experimental archaeologist Jeff Lindow. After watching this, I decided not to try this at home as it would no doubt shiver my timbers. However, if it gets cold enough this winter, I might consider a swig of this gunpowder-infused Man O’War rum. Yo ho ho!
It may pay to make your product less than perfect!
Posted by mark in Consumer behavior, Uncategorized on September 4, 2011
I once analyzed data from a designed experiment that quantified consumer distaste for flaws in chocolate-covered cherries. This was a very rewarding project – lots of free candy! It also produced a counter-intuitive result: People preferred boxes with a few upside-down morsels. I figure this is akin to a beauty mark adding to the enticement of a model or actor. This article on “When Blemishing Leads to Blossoming”, published online by the Journal of Consumer Research confirms that under specific circumstances, a flaw makes a product more attractive. For example, in one experiment (highlighted in the July 16 issue of Wall Street Journal) the researchers (Danit Ein-Gar, Baba Shiv, Zakary L. Tormala) offered either perfect or slightly flawed chocolate bars to several hundred relaxed (strolling around) or stressed (rushing to exams) college students. I searched out the results and reproduced them in this interaction graph from Design-Expert® software. It seems to me that this surprising effect, presuming it’s real, provides yet another devious opportunity for marketing mavens to make us buy stuff. One thing I might advise is that you never buy anything when you are in a hurry.
Mind-reading fish know I am out to catch them
Last week I enjoyed a relaxing sojourn up in the north woods of Wisconsin. The resort encompasses its own pristine pine-ringed lake featuring a 26-foot fishing hole. Just before I headed off for my vacation I read this Scientific American report on The Mind-Reading Salmon: The True Meaning of Statistical Significance
. Although I think they meant to be disrespectful of p-values in this case, my feeling, based on empirical evidence from a large sample size – hundreds of unsuccessful casts of my lure around the shore and over the hole, is that some fish living in isolated areas have developed mental telepathy. How else do they avoid being caught?
PS. Here’s a picture of me in happier days at a different lake last summer. My brother-in-law insisted that the first one to catch a crappie would have to kiss it. Evidently this fish thought it might be fun to try, knowing I’d then release it back into the lake.
The chaotic, yet regular sounds of weeping waters and lapping waves inside Lake Superior sea caves
Earlier this month I enjoyed a wonderful sail out of Cornucopia, Wisconsin to Lake Superior’s Mawikwe Sea Caves — described nicely here in a pictorial blog by the Howder family.
Mawikwe means “weeping woman” in Ojibwe. Due to heavy rains in the days leading up to our voyage, the caves were weeping steadily, as you can see and hear in my video. I was fascinated by the cacophony of dripping water combined with the galumphing of the waves into the baby caves at water level. It provided a pleasing mix of randomness and rhythm. Turn up your volume and listen for yourself.
PS. By the way, I learned that by yelling into a sea cave you can (pun intended!) duet yourself.
A Santa Claus machine
Someone just sent me this amazing video of a 3D printer copying a crescent wrench – moving parts and all. The company featured, Z-Corp, is a Stat-Ease client. See this case study showing how their engineers used response surface methods (RSM) to discover a small window of operability.
Another client of Stat-Ease, Stratasys, also offers rapid-prototyping machines, but they make use of another technology called fused deposition modeling (FDM) – explained nicely by this schematic from Ferris State University. I’ve seen these machines at work. They run from plastic line similar to what’s used in a weed whacker. Based on a computerized blueprint, this material (suitable for functional parts, not just prototypes) is melted layer-by-layer into complex shapes. Check out this full-scale turboprop engine produced by FDM.
The next step will be the development of machines that can make whatever you need out of whatever you happen to have nearby that can be shoveled in the hopper. Then people who really want to get away from the crowds can rocket off to any old unoccupied planetismal and set themselves up with house and home.
“It’s possible to imagine a machine that could scoop up material – rocks from the Moon or rocks from asteroids – process them inside and produce just about any product: washing machines or teacups or automobiles or starships. Once such a machine exists it could gather sunlight and materials that it’s sitting on, and produce on call whatever product anybody wants to name, as long as somebody knows how to make it and those instructions can be given to the machine. I think the name Santa Claus Machine for such a device is appropriate.”
– Physicist Theodore Taylor (1978)