Common confusion about probability can be a life or death matter
Posted by mark in Basic stats & math on June 3, 2024
As a certified quality engineer (CQE), I often focused on the defect rates of manufactured products. They either passed or failed—a binary outcome.
I learned quickly that even a small probability of failure would build up quickly when applying a series of operations. For example, I worked as chief CQE on a chemical plant startup that involved several unit operations in the process line—all to a scale never attempted before. It did not go well. By my reckoning afterwards, each of the steps probably had about a 80/20 chance of succeeding. That led to optimism by the engineers in the company who design our plant. Unfortunately, though, multiplying 0.8 repeatedly is not a winning strategy for process improvement (or gambling!).
As we approach the 80th anniversary of D-Day this diabolic nature of binary outcomes takes on a deadly aspect when you consider how many times our warriors were sent into harms way. The odds continually waver as technology ratchets forward on the offense versus defense. This can be assessed statistically with specialized software such a that provided by Stat-Ease with its logistic regression tools. For example, see this harrowing tutorial on surface-to-air missile (SAM) antiaircraft firing.
Thanks to a heads up from statistician Nathan Yau in one of his daily Flowing Data newsletters, I became aware that many people, even highly educated scientists, get confused about a series of unfortunate or fortunate events (to borrow a phrase from Lemony Snicket).
Yau reports that a noted podcaster with a PhD in neuroscience suggested that chances could be summed, thus if your chance of getting pregnant was 20%, you should see a doctor if not successful after 5 tries. It seems that this should be 100% correct (5 x 20), but not so. By my more productive math (lame pun—taking the product, not summation), the probability of pregnancy comes to 67%. The trick is to multiply the chance of not getting pregnant—0.8—5 times over, subtracting this from 1 and then times 100.
If you remain unconvinced, check out the odds via Yau’s entertaining and enlightening simulation for probability of success for repeated attempts at a binomial process.
Enjoy!
A solution for saving migrating birds from disorienting light pollution
Posted by mark in Education, Nature, science, Uncategorized on May 3, 2024
My grandson Archer and his class of sixth graders at Stillwater Middle School advanced to last week’s national Solve for Tomorrow competition in Washington, DC–an amazing accomplishment at their age. The event, sponsored by Samsung, empowers students in grades 6–12 to leverage the power of STEM (science, technology, engineering and math) to create innovative solutions addressing critical issues in their local communities.
Archer and his classmates focused their attention on reducing the impact of light on bird migration patterns in the St. Croix Valley. They developed a very inventive plan that featured bioluminescence; sensors to reduce unnecessary light and a flower-petaled, controllable cover for directing streetlights downward.
Being one of just 10 schools across the country to be named national finalists, they earn $50,000 in Samsung technology and supplies for their classroom. To top it off, Archer and his classmates won an additional $10,000 by winning the Community Choice award based on a popular vote.
I expect Archer and all will go far by their STEM power. Hopefully, the birds will also continue to go far by being better protected from light pollution along their way.
A “divine and cosmic” geometric shape—practical and pleasing
Posted by mark in architecture, geometry on April 15, 2024
The Venice Beach Pavilion—just a short walk away from my winter home in Florida—features a distinctive hyperbolic paraboloid roof dating back 50 years. I love its elegant wavy shape that sails into the sky. Therefore, I am rooting that the City succeeds in getting this iconic structure—characteristic of the Sarasota School of Architecture—registered as an historic landmark, thus enabling funding for badly needed repairs.
Check out an overhead view of the Pavilion here. It is far more impressive when seen from below. There’s no better place to enjoy a fried shrimp basket at a shady mid-century modern, round-concrete table being cooled by the ocean breeze and soothed by the sounds of crashing waves.
The best way to describe the hyperbolic paraboloid is it being the shape of a Pringles potato chip. It’s easy to create in Stat-Ease software by setting up a full three-level response surface design on two factors and then entering a quadratic equation via its simulation tools. The 3D view below stems from a model that includes only a two-factor interaction term, which creates the simple, but pleasing, twisty surface similar to the Venice Pavilion. However, the colors may be a bit much. ; )
“The hyperbolic paraboloid has been seen as a representation of the divine and the cosmic. Its symmetry (one axis but no center of symmetry) and balance have been seen as a reflection of the inherent order and beauty of the universe.”
Nick Stafford, Pringles, A Reflection of the Order and Beauty of the Universe
Weather Tiger predicts a “hyperactive” hurricane season
Posted by mark in Uncategorized on April 3, 2024
Owning a second home In Venice, Florida just a few blocks from the Gulf is great for me and my wife Karen to dodge winter (she really, really hates the cold!). However, there’s always a catch to the good things in life: From June 1 through Nov. 30 our snow haven stands in harm’s way of hurricanes.
Hurricane Ian created quite a scare in September of 2022 before veering south just before landfall. Whew! Last year our closest call came from Idalia in late August—it hitting hard at Category 3 in the Big Bend region of Florida.
This year could be a doozy according to the Weather Tiger, who provides “expert analysis of Florida hurricane threats, with a twist of dad humor” (my kind of guy!). He predicts a “75% chance of hyperactive hurricane season with likely US landfalls.”
“Our model boldly suggests a 10% to 15% chance that 2024 bests 1933’s record for the most intense season, though laying firm probabilities on outliers is a statistical mug’s game.”
– WeatherTiger President and Chief Meteorologist Ryan Truchelut, 3/28 Sarasota Herald
Accuweather’s forecast for the 2024 hurricane season is even more hyperbolic—describing it as “explosive” and “super-charged” and warning that “forecasters may even run out of names for storms amid a frenzy of tropical systems.” Oh, my!
Good thing I just did an extensive remodel to bolster our 1960 cinder block home with a new roof, high impact windows, flood vents, etc. Bring it on!
On second thought…do not.
Scroll sawers put blades to the statistical test by cutting out ducks
Posted by mark in Uncategorized on March 3, 2024
Years ago I helped Quality Assurance Manager John Engler solve a tricky issue at Robinson Rubber via design of experiments (DOE). He contacted me last fall to help him apply DOE to a nagging question about scroll sawing: Does it pay to buy pricier blades?
We worked together to design a simple-comparative randomized-block experiment on 10 competitive blades. John enlisted 20 fellow hobbyists in his NorthStar Scrollers club to cut out a duck from pine (see pattern below) using the selected blades (such as the one taped on the board) in a random order.
They then rated the results on a 1 to 9 scale—higher the better—for speed of cut, blade jumpiness, fuzzies (undesirable!), edge smoothness, burns and line following.
The blades differed significantly by all attributes at p < 0.0001 other than the line following (p = 0.3419). For the most critical measure—speed of cut, blades 3, 8 and 9 stood above all others on average.
The power of doing 21 replicates—widely spread as indicated by the red dots—and, furthermore, blocking out the scroller-to-scroller differences, is seen by the narrowness of the least significant differences (based on a p of 0.05).
Accounting for all the attributes via Stat-Ease software’s multiple response optimization these three blades held up overall with number 3 being the winner by costing less than the other two.
After I reported my findings to the group, John laid out a number of mitigating factors:
- Experience of the scroll sawers
- Type of wood, e.g., something a lot harder
- The life of the blades (important to consider for the cost)
But all-in-all, this planned experiment proved to be a big hit with the NorthStar Scroller hobbyists. What impressed me was their depth of knowledge on scroll-saw blades and why we observed such significant differences due to the patterns and orientation of their teeth, etc. I was also struck by how some individuals could tell right away which blades worked best—even before seeing the entire set of data. This reinforces my feeling that laying out and analyzing experiments works best by combining the know-how of a DOE expert (like me) with subject matter experts (not me in this case—far from it!).
“This went much better for me than I thought it might and I learned some things about blades along the way. This was fun!”
–Helen (a NorthStar Scroller blade-tester)
Classic case of sensory testing snubbing off a beer snob
Posted by mark in food science on February 26, 2024
The feature story on sensory evaluation in the new issue of ASTM Standardization News brings back a fond memory of a rare victory over an overly smug colleague.
I developed a taste for sensory science as a young chemical engineer determined to prove that mass produced American lagers differed only imperceptibly—consumers being brain washed by deceptive advertisers. This hypothesis drew strong condemnation from one of my colleagues—a chemist named Harold who dissed lesser brews such as Old Milwaukee, which he deemed “Old Swillwaukee”.
To put this beer snob to the test, I organized a tasting at a Super Bowl party attended by a dozen or so fellow researchers. Beforehand, I engaged a sensory professional that our employer hired to guard against “off odors” from our manufacturing plants. She advised that we limit drinking of each beer to a small sip, then eat saltless crackers and wash them down with water before going to next brew. Also, both the presenter of the beer and the taster should be blind to the brand, thus avoiding bias.
However, given my mission to snub a beer snob, we first rated a selection of undisguised beers—including Miller, Budweiser, Old Milwaukee and others (in those days there were no ‘craft’ brews*). Harold rated “Old Swillwaukee” dead last. That was my plan! Then we repeated the tasting with the order re-randomized, but this time not revealing the names. Harold rated Old Milwaukee at the top of his list, thus providing a Super Bowl victory for me (badly needed being a Vikings fan).
My conclusion from this experience, and my work over the years helping food scientists improve the taste and other attributes of their products, is that it would be best to adhere by ASTM’s upcoming revision to Guidelines for the Selection and Training of Sensory Panel Members. For beer and the like, then bear down on the Standard Guide for Sensory Evaluation of Beverages Containing Alcohol (E1879).
We make panelists learn chemical names. For example, isoamyl acetate is a specific compound that smells like candy banana…I make panelists drink heavy cream for mouthfeel attributes. They’re unfazed by whatever we give them anymore because it’s always weird.
– Ali Schultz, sensory manager, New Belgium Brewing Company and leader of the current revision to E1879 (“Accounting for Taste”, ASTM Standardization News, January/February 2024)
However, if you are having a party, it’s more fun to be unprofessional and ignore the mandates to sip and spit, etc. ; )
*PS: The specialty beer brewers are getting a bit out of control nowadays, IMO. For example, I just got an alert from my Stillwater, Minnesota neighborhood microbrewer Lift Bridge to their release this weekend of Taking Care of Breakfast—a “barrel aged imperial breakfast stout aged in 10-year Willet and 6-year Wild Turkey bourbon barrels, infused with peanut butter and banana chips.” This new brew comes in at 12% ABV. Perhaps it may be best to go with orange juice first thing in the morning.
To bean or not to bean, that is the question for coffee
Posted by mark in food science on February 13, 2024
In my most recent blog post on coffee I reported that a finer grind may not always be better. Now another piece of the puzzle for producing java that jives falls into place: Spritz your beans with water.
Evidently this is not a new discovery—those who really know their coffee-making craft routinely moisturize their grind to reduce clumping. A new study reported here by New Scientist reveals the problem: static electricity. Following up on the link to the original publication, I see that the research team, led by a volcanologist (sensible considering the lightning generated by particle-laden eruptions), deployed this $3000 German-made, handcrafted machine to produce extremely uniform grinds. I will definitely buy one soon (after winning the lottery).
Another approach to better coffee takes a completely different route—create it from cells grown in bioreactors. Environmentalists like this because the demand for sun-grown beans leads to destruction of rain forests. Per this Phys.Org heads-up, a Finnish team just released a recipe to accelerate the creation of a new “coffee ecosystem.” This seems promising. But there is a problem: Though the current lab-grown concoctions contain twice as much caffeine as ever before, it remains much lower than those in farmed beans.
Another approach to avoid the problems keeping up traditional methods for making coffee is to go to a beanless brew, such as the imitation now being rolled out by Seattle-based Atomo Coffee. Based on this January 24th report by CBS Saturday Morning show, I would be willing to give it a try, especially given they load up their brew with caffeine at the upper end of the normal range of real coffee. Full steam ahead!
One last idea (my caffeine levels now running low) for improving the taste of coffee is being selective about the shape and material of your cup. For example, see what the Perfect Daily Grind says about pouring your brew into a wine glass or other specialty containers.
“A drinking vessel has a significant impact on perception of flavour and aroma because it changes the way the coffee smells and tastes, as well as how you drink coffee. What’s more, our senses, feelings, and emotions also impact how we experience coffee.”
Marek Krupa, co-founder and CFO of Kruve
Being ‘bird-brained’ merits reconsideration
First off, writing this blog from my winter home in Florida, I appreciate the sensibility of snowbirds who abandon their northern climes every fall. Smart! Furthermore, studies show that avian brains, specifically crows and ravens (collectively known as “corvids”), can accommodate statistical thinking—a skill that many humans lack based on my experience as an educator. Researchers from the University of Tübingen worked this out via a clever experiment that required crows to assess the probability of getting a treat based on prior experience pecking at differing images.
“True statistical inference requires subjects use relative rather than absolute frequency of previously experienced events. Here, we show that crows can relate memorized reward probabilities to infer reward-maximizing decisions.”
Johnston, et al, Crows flexibly apply statistical inferences based on previous experience, Current Biology, Volume 33, Issue 15, 7 August 2023, Pages 3238-3243
This gives new meaning to the saying that “if the p-value is high, the null must fly.”
Chance discovery on random walk in Utrecht
Posted by mark in science, Uncategorized on December 11, 2023
Last week I taught a class on design of experiments to a biotech company in Leiden, Netherlands. Afterwards I spent a few days in Utrecht with some friends from Germany. Imagine my excitement (nerd alert!) when on my first walk from our hotel to the city center just a few hundred feet down the sidewalk I encountered this mural featuring a differential equation.
Not being a physicist, I did not immediately grasp the formula’s importance, nor the clue provided by the fellow high-stepping down a street. It turns out this fellow is a drunk whose walk has become random. The mural, as explained by Utrecht University, pays homage to their famous professor Leonard Ornstein who, in the early 1900s along with another physicist—George Uhlenbeck—developed an important variant of the “random walk”—a term introduced by pioneering statistician Karl Pearson. The Ornstein-Uhlenbeck process is used to derive models from “big” financial data, including inflation rates, commodity prices and stock values.
I did not expect to gain an education on a vacation expedition.
Very cool!
PS: I thought about asking my colleague Martin Bezener, a PhD statistician, for his opinion on the chances of coming across something so relevant to our mission at Stat-Ease while on a random walk. But I will not bother, because I already know what he would say: “One-hundred percent: It already happened”.
British system of messed up measures hilariously skewered
Upon graduation as a chemical engineer in 1975 I took a job as a process developer at a California oil company. There I learned that a barrel amounted to 42 gallons—not the 55 in the drums at my previous employer—a specialty chemical company. In the wacky British system of volumes, the number of gallons in a barrel depends on the material—31 for beer, 53 for rum (yo ho ho!), 60 for wine, etc. Their weights and distances are just as unfathomable (pun intended).
That same year of 1975 that I first became employed as a degreed engineer, President Gerald Ford signed the Metric Conversion Act, which went nowhere before being abolished in 1982 by President Reagan. Having endured all this measurement mess throughout my career, I thoroughly enjoyed this October 28 Saturday Night Live skit:
I raise my US pint (16 fluid ounces) of beer to SNL’s clever comedy writers, though a British pint (20 fluid ounces) would be more filling and a liter even sweeter. Let’s not get into US versus Imperial ounces (or gallons)—that would get us over our head by at least a fathom (equivalent to 4 cubits, by the way).
PS. This rant about measures brings me full circle to an outburst at the outset of this year involving a whimsical unit of distance called the ‘smoot’.