Archive for category Uncategorized
Designed experiment creates egg-splosive results
Posted by mark in design of experiments, Uncategorized on August 20, 2019
Design-Expert® software version 12 (DX12) released this summer with a cool new tool to model binary responses, for example, pass-versus-fail quality-testing. For what it’s worth, the methodology is called “logistic regression”, but suffice it to say that it handles results restricted to only two values, typically 0 or 1. The user deems which level is a success, most often “1”.
During development of DX12 Stat-Ease moved to a penthouse office on a building with a cascade of balconies. So, when our programmers, led by Hank Anderson, considered how to test this feature with an experiment, they came up with the idea of trying various packing on eggs to see if they could be dropped some distance without breaking—a project that high-school science teachers assign their students. However, we figured that our neighboring tenants down below and our new landlord might not be very happy about the mess that this would create. Therefore, Hank and his team took a less problematic tack by testing various factors for microwaving eggs to an edible stage. This experiment (or ‘eggs-periment’ if you like) also was more productive for varying the diet of the programmers from their staple of boiled ramen noodles—the focus of a prior DOE.* If they could achieve consistent success in cooking eggs by microwave, a combination of these with ramen might be the ideal sustenance for awesome coding for new versions of Design-Expert.
The Stat-Ease experiment began with a bang during the range-finding stage with an explosive result. You might say that the yolk was on us—bits of overcooked egg and shell dispersed throughout the chamber of the microwave. The picture below shows the messy aftermath (note the safety glasses).
After this learning experience (‘eggs-perience’?), Hank and his lab technician, Mike Brownson, settled into a safer range of factors, shown below, that kept the contents from reaching the catastrophic breaking point:
- Preheat—0 to 180 seconds
- Cooking time—120 to 420 seconds
- Power—60 to 100 percent
- Salt—0 to 2 teaspoons
- Egg Size —Large or Jumbo
Hank and Mike, with input from Stat-Ease Consultant Martin Bezener, put together an ambitious design with 92 runs using Design-Expert’s custom design builder (i-optimal) for response surface methods. Heads-up: When responses are restricted to just two outcomes (binary), many more runs are required to provide adequate power than would be required for a continuous measure.
The investment of nearly 100 trials for the ‘eggs-periment’ paid off by producing significant results on pass/fail measures of undercooking and overcooking. For example, the 3D graph below shows the probability of eggs being undercooked as a function of time and power for the microwaving. Notice by the corner at the left being cut off that potentially catastrophic combinations of high power and long cooking were excluded via a multifactor constraint. Clever!
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Based on models produced from this experiment, Design-Expert’s multiple-response optimization recommends a most desirable setup for microwaving eggs as follows: Heavily salted jumbos preheated to the maximum level and then cooked for 315 seconds at medium power.
Thanks to the research by Hank, Mike and Martin, our programming staff now is fueled not just by ramen, but also with eggs—a spectacular success for DX12’s new logistic-regression tools!
* “The Optimal Recession-Proof Recipe”, Brooks Henderson, pp 1-2, September 2012 Stat-Teaser, followed up by “Confirming the Optimal Ramen”, p3, January 2013 Stat-Teaser.
Over half of all children have below-average reading skills
Posted by mark in Education, leadership, pop, Uncategorized on June 24, 2019
Yes, you read that right—this statistic was cited by Eugenia Cheng last weekend in her column for the Wall Street Journal on why Averages Aren’t Always What They Seem. In this case, a small number of excellent readers skews the distribution to the right.
But none of this applies to my offspring, them being in the Lake Wobegon region where all the children are above average.
I would never admit it, but deep down I realize that I’ve succumbed to the superiority illusion, aka the Dunning-Kruger effect. As advised in this June 3rd post by Forbes you’d best be careful not to be taken in by individuals who consistently overestimate their competence due to this cognitive bias.
Steve Carell took the superiority illusion to an absurd extreme as the manager Michael Scott in the “The Office” television series. It’s funny unless you are subject to someone like this.
“The knowledge and intelligence that are required to be good at a task are often the same qualities needed to recognize that one is not good at that task—and if one lacks such knowledge and intelligence, one remains ignorant that one is not good at that task.”
— David Dunning, professor of psychology at the University of Michigan
“Stupid people are so stupid they’re unable to grasp the fact that they’re stupid.”
— Letter to Editor of Oroville Mercury Register, 6/23/19
Park in the first open spot or chance one opening much closer?
Posted by mark in pop, Uncategorized on June 6, 2019
Up until a few years ago when going to an event with limited parking, I always took the first opening available. But then one of my buddies told me how he prays for a closer place and one always opens. I thought about that and came to an epiphany that, as a general rule, one may as well try for a parking spot as close as possible to the destination. That’s been working for me ever since.
This strategy is now validated by researchers who evaluated three alternatives: meek, optimistic and prudent. They mathematically disrespect the meek driver parks at the first available spot that is behind the most distant parked car.
“The meek strategy is the most stupid strategy.”
Professor Sidney Redner, Santa Fe Institute—co-author of Simple Parking Strategies, Apr 14, 2019
However, the optimistic driver (like my prayerful friend) who goes for the closest spot, bypassing any gaps before the destination, pays a big penalty if they fail–going all the to the back of the parking line and being late for their even. It is better to be prudent—the middle strategy—by parking at the first gap.
Being methodical and frequently searching for parking at sporting events, I am very appreciative of this analysis. It reinforces my new-found faith (thanks to my friend) that the meek do not inherit the earth, at least not a good place to park your car.
ASA calls for abandoning the declaration of results being “statistically significant”
Posted by mark in Basic stats & math, Uncategorized on May 1, 2019
On March 21 the American Statistical Association (ASA) sent out a shocking email to all members that the lead editorial in a special, open-access issue of The American Statistician calls for abandoning the use of “statistically significant”. With irony evidently intended by their italicization, they proclaimed it “a significant day in the history of the ASA and statistics.
I think the probability of experimenters ignoring ASA’s advice and continuing to say “statistically significant” approaches 100 percent. Out of the myriad of suggestions in the 43 articles of The American Statistician special issue the ones I like best come from statisticians Daniel J. Benjamin and James O. Berger. They propose that, because “p-values are often misinterpreted in ways that lead to overstating the evidence against the null hypothesis”, the threshold for “statistical significance” of novel discoveries require a threshold of 0.005. By their reckoning, a p-value between 0.05 and 0.005 should the be degraded to “suggestive,” rather than “significant.”*
It’s a shame that p-hackers, skewered in this xkcd cartoon, undermined the sound application of statistics for filtering out findings unsupported by the data.
*The American Statistician, 2019, Vol. 73, No. S1, 186–191: Statistical Inference in the 21st Century, “Three Recommendations for Improving the Use of p-Values”.
Money buys happiness unless you get caught up in the Easterlin paradox
Posted by mark in Uncategorized, Wellness on April 23, 2019
The March 23rd issue of The Economist provides an interesting graphic on GDP per person—a measure of wealth—versus self-reported happiness. Overall it shows an upward trend that increases life satisfaction by 0.7 points (on a 10-point scale) as GDP doubles.
China is a prime example of money buying more happiness. Sadly, us citizens of the USA (and many European countries) are subject to the Easterlin paradox, which puts a limit on how satisfied people get as their income rises, beyond which money cannot buy more happiness.
Check out this interactive online version of the happiness vs wealth posted by The Economist. There, if American, you will see with some satisfaction (misery liking company) that Netherlands and several other wealthy countries share our downward trend. However, Germany and Britain remain on the upswing. (I wonder with Britain now in the throes of Brexit if their GDP will shrink and, if so, suspect that their happiness will also fall off.)
So, bottom line, for those of us stuck in the paradox, would you rather be richer or happier? That is a tough question!
Recreational reading off by more than 25%
Posted by mark in pop, Uncategorized on February 24, 2019
I’ve noticed that none of my many offspring or their significant others read newspapers (that I know of), while I and many others of my generation keep up with at least one daily publication. This report by BookRiot bears me out—passing along Bureau of Labor Statistics that Americans 15 years and older spent an average of only 16.8 minutes a day reading non-work (or non-school) materials in 2017—down from 22.8 minutes in 2005. According to BookRiot, we fall far behind India, the world leader, India, who came in at nearly over 90 minutes of reading per day. Given their literacy rate of 60% versus the USA’s 99% level,* that is quite impressive.
The New Yorker points out that the average American reader is reading more. However, this is counteracted by fewer people reading anything at all, falling from 26.3 per cent of the population in 2003 to 19.5 per cent in 2016.** That worries me–over 80% of Americans who, evidently, only watch TV. Read these reports and weep.
“People in the U.S. spend 10 times more time watching TV than reading.”
– Sarah Nicolas, BookRiot
**“Why We Don’t Read, Revisited”, Caleb Crain, June 14, 2018
“Data are profoundly dumb”
Posted by mark in Basic stats & math, Uncategorized on October 22, 2018
This is the controversial view of Judea Pearl and Dana Mackenzie expressed in “Mind over Data”—the lead article in the August issue of Significance. In this excerpt from The Book of Why these co-authors explain “how the founders of modern statistics ‘squandered’ the chance to establish the science of causal inference”. They warn against “falsely believing the answers to all scientific questions reside in the data, to be unveiled through clever data-mining tricks.”
“Lucky is he who has been able to understand the cause of things.”
– Virgil (29 BC)
Pearl and Mackenzie are optimistic that the current “Causal Revolution” will lead to far greater understanding of underlying mechanisms. However, by my reckoning, randomized controlled trials remain the gold standard for establishing cause and effect relationships. Only then can the data speak loud and clear.
Hurricane forecasters getting in the zone with their cone
Posted by mark in Nature, Uncategorized on September 13, 2018
Owning a home in Florida, I keep a close eye on the National Hurricane Center (NHC) forecasts throughout the June-through-November season. I see that Florence is now predicted to make landfall around mid-day tomorrow just south of Wilmington, North Carolina—the gateway to the aptly named Cape Fear. Even though that’s less than 24 hours away, it’s still subject to a broad zone of uncertainty–on the order of 100’s of miles. However, it’s very impressive that the NHC forecast made 48 hours ago remains right on. According to a Wall Street Journal report yesterday their 5-day conical projections have improved by more than 100 nautical miles (115 land miles) in radius over the past decade. That’s even more impressive.
However, WSJ advises we’d best remain very leery of the NHC’s spaghetti plots (an alternative to the cone), because they include very simple forecasts along with those that are state-of-the-art. This can be very disconcerting as I discovered when Irma came along a year ago to graze my place along the west coast of Florida. You can see in this Business Insider report on Irma that, only 3 days beforehand, this hurricane’s predicted landfalls ranged from Louisiana to Massachusetts. The article says that NHC suggests that people not focus on the specific tracks. That seems obvious to me based on the ridiculously high variance. I’d like to see these tracks vary by thickness according to the sophistication of the models—the thinner the weaker.
In any case, let’s hope that Florence fizzles out, after all.
Fascination for pendulums piqued by Foucault’s in France
Posted by mark in science, Uncategorized on June 26, 2018
Earlier this month I visited the Pantheon in Paris where I observed this attendant recalibrating Foucault’s pendulum.
This French scientist’s elegant scientific demonstration of earth’s rotation has delighted observers like me since 1851. For more on this story read this Ask Smithsonian blog. Unfortunately, one morning in 1998, the cable on the 52-foot long pendulum at Smithsonian’s National Museum of Natural History (originally History and Technology when opened in 1964) snapped, nearly ‘clocking’ a staffer with its wayward 240-pound brass bob. This Foucault device being unAmerican and dangerous, it was removed in favor of the Star-Spangled Banner Preservation Project, thus eliminated a favored place for folks to gather.
By the way, I am now reading The Discoverers by The Librarian of Congress, Daniel Boorstin—the first in his wonderful Knowledge Trilogy. There, coincidentally, I learned that Galileo—only 19-years old at the time (1583) and bored by a church service in Pisa—became distracted by the swinging of a chandelier. By timing his pulse, he observed the time of a pendulum being independent of its arc length—an important discovery of a property called isochronism. This simple discovery, as pointed out by Boorstin, began a new age where science developed from observation and measurement rather than pure speculation.
Are you one of the elite 10% who can work out this test of logic?
Posted by mark in pop, Uncategorized on May 2, 2018
Four cards are laid out before you, each with a letter on one side and a number on the other. You see E, 2, 5 and F. Which cards should you turn over that will prove the following rule: If there is an E on one side, the number on the other side must be a 5? See the answer by Manil Suri, Professor at University of Maryland, in this April 15 New York Times article that asks “Does Math Make You Smarter?”.
As to whether math really does make you smarter, the answer remains unclear. However, those who do well with numbers make far more money. That is not surprising, but the multiplier may be. See this U.S. News report (or not if you failed the test above) for the statistics.