Caffeine helpful for brain health…or not—a mindbender
The other day I watched CBS News medical contributor Dr. Celine Gounder report new findings that drinking caffeinated coffee reduces the likelihood of dementia. She warned that this may be due to correlation, not causation—creating puzzled looks from the hosts. Then Dr. Gounder explained that individuals in poor physical and mental health will often be put on a diet that restricts caffeine. Aha!
It never ceases to amaze me how often people fall for correlation being causation. Here are some of my favorite examples:
- As I reported in a blog a few days before Christmas of 2012,* partygoers took advantage of a buy-one-get-one-free (BOGO) sale on a fine wine—paying $17 for one bottle and a nickel ($0.05) for the other. They drank the first bottle and thus worried greatly if it would be OK to bring the cheap wine to the party.
- Per Google’s AI, the most popular example of correlation versus causation is that ice cream sales and shark attacks both increase during the summer months. While they correlate, eating ice cream does not cause shark attacks; rather, a third variable—hotter weather—causes both, leading people to eat more ice cream and swim. Banning ice cream (addressing the correlation) would not reduce shark attacks (the causation), highlighting the mistake of assuming one directly causes the other.
- Most popular with statistics teachers—Umbrellas and wet streets both increase on rainy days, but umbrellas do not cause the streets to get wet.
- Being called in to troubleshoot processes at our manufacturing sites the operators explained to me that performance varied due to the phase of the moon.
“Cars with flames painted on the hood might get more speeding tickets. Are the flames making the car go fast? No. Certain things just go together. And when they do, they are correlated. It is the darling of all human errors to assume, without proper testing, that one is the cause of the other.”
― Barbara Kingsolver, Flight Behavior
But don’t become too skeptical about seemingly spurious connections between cause and effect, such as me questioning my daughter’s assertion that the color of otherwise identical flying disks affect their performance.
*Correlation of price of wine with the fineness of its taste–an absurd example
Downhill racing, like statistics, means never having to say you are certain
Immediately after starting my first process development as a chemical engineer in the summer of 1974 between my junior and senior years at University of Minnesota, I learned that the real world does not operate exactly as one would expect from the first principles of science learned in school. All my results varied, making it difficult to know what was real and what occurred due to chance. That led me to embrace statistics as preached by my supervisors at General Mills Chemical. (Thank goodness for the company’s agricultural heritage and thus an appreciation for the knowledge imparted by pioneering statistician Ronald Fisher to crop developers.) Thus, I can appreciate the randomness of Olympic results, particularly for downhill ski racers.
As explained by two-time gold medalist Ted Ligety in the New York Times, The Best Ski Racers Often Do Not Win Gold. Two days later Breezy Johnson won gold in downhill by only 0.04 seconds. (Sadly, this was the race where Minnesotan Lindsey Vonn crashed.) To provide some context, blink your eyes—this typically taking more than twice as long as the margin of Johnson’s victory.*
Ligety explains that the greatest women’s skier of all time, Mikaela Shiffrin, has won only 20% of her Olympic races, whereas Michael Phelps, the best swimmer ever, won over 75% of his Olympic races. He says this far greater uncertainty stems from variables such as wind, snow, light and ruts. By watching the audiovisual breakdown by Ligety et al (see for yourself by clicking the link above in you did not do so already), I gained a great appreciation of these and other factors affecting the outcome of any given race.
“If … a cloud comes and there’s super flat light … and … the girls in front of you had sun … that is going to make a huge difference. When you are in the start gate you have to go no matter what.”
– Trica Mangan, two-time U.S. Olympian
P.S. Along these lines of the razor’s edge separating skiers at Olympian levels, I highly recommend the classic 1969 movie “Downhill Racer” starring Robert Redford. After he died in September, I watched this for the first time. I highly recommend it. Gripping!
*Check out the amazing graphics theTimes provided after the race to See How Breezy Johnson Won
Bulky-bonneted NFL players—not a Super look
Posted by mark in sports, Uncategorized, Wellness on February 6, 2026
On Sunday the Seahawks play the Patriots in the Super Bowl. I will be on the lookout for any with oversize “bobbleheads”—a derisive term by J.J. Watt of the Cardinals for fellow players who wear Guardian Caps to protect themselves against concussions. The manufacturer of these soft-shell, foam-padded, helmet claims a 40% reduction in HARM—head acceleration response metric,* That is a very clever acronym, but does it really lessen brain trauma? The NFL thinks so, citing nearly 50% reduction in concussions for players wearing them. Many position players, for example, running backs and linebackers, must wear Guardian Caps during all practices involving contact—use in games remaining optional.
However, as recently reported by the New York Times,** “independent neurologists are generally skeptical, if not outright dismissive, of the benefits of any product claiming to reduce concussions because few rigorous studies have been done to demonstrate their effectiveness.” The rate of concussions in NFL preseason practices from 2018 to 2023—after the advent of Guardian Caps—declined between 54 and 62 percent. However, the statisticians who gathered the data admitted that the use of the protective covering did not significantly reduce concussions from helmet hits.
“There’s no question that every injury or injury reduction strategy is multifactorial.”
– Jeff Miller, NFL’s chief spokesman
I’ve suffered several concussions—the first one in 3rd or 4th grade (I forget) gym class diving at a dodge ball and smacking into the wall.
After that I joined a football team at a small playground that in my 8th grade made it to the Saint Paul City ‘superbowl’ the year of Superbowl I. However, every full contact practice and game caused me such headaches that I shifted over to playing ‘pickup’ touch football. This saved me (I hope) from persistent post-concussion syndrome turning into chronic traumatic encephalopathy (CTE).
Many years later playing with me buddies from General Mills Chemical R&D I knocked myself out diving for a softball hitting my noggin on a sprinkler head. (I am a bit too competitive at sports!)
My third concussion, the cause of which I’d rather not discuss, sent me to ER for dozens of stitches and a night in intensive care at Hennepin County Medical Center.
So, I can feel the pain and very much hope that further developments in head protection will protect contact-sports players of all ages from concussion and CTE.
*See their video on The Science Behind Guardian Caps
**“The Questionable Science Behind the Odd-Looking Football Helmets,” Ken Belson, Feb. 3, 2026.
Stats add teeth to gripping news about Tyrannosaurus rex
In a page ripped out of Michael Crichton’s book Jurassic Park, featuring brilliant mathematician and “chaotician” (chaos theory specialist) Ian Malcom, three scientists applied a new statistical approach to combine analyses from 17 different T. rex specimens, thus revealing that these tyrant lizard kings did not reach maturity until age 40.* Enjoy some fearsome pictures of T. rex’s big and small in this press release from Oklahoma State University citing lead author Dr. Holly Woodward, professor of anatomy and paleontology.
Dr. Woodward says that previous studies estimated that T. rex growth stopped around age 25. The longer development time expands the role of knife-teethed, fleet-footed juvenile T. rex’s to dominate the mid-carnivore niche.
A four-decade growth phase may have allowed younger tyrannosaurs to fill a variety of ecological roles within their environments. That could be one factor that allowed them to dominate the end of the Cretaceous Period as apex carnivores.
– Coauthor Jack Horner, technical advisor for the Jurassic Park films (inspiring the Alan Grant character)
Sensational!
For a healthy 2026, resolve to lengthen your walks
I love to walk, cross-country ski or bike. It invigorates me physically and mentally. Thus, I found it interesting that, according to this October 2025 study published in the Annals of Internal Medicine, longer walks might provide more benefits than shorter ones at the same step counts.
But be careful drawing this conclusion because the results show correlation, not causation. Furthermore, the study focused on suboptimally active adults with step counts at 8000 or less per day. I am satisfied only by achieving at least 10,000 steps in a day.
I think a good new year’s resolution is to increase your step count per day by taking longer walks. However, on days when you cannot spare much time, try taking a number of short walks and do so a bit faster.
If you also like to walk and/or are resolved to do so this new year of 2026, see today’s post by RTÉ—the website of Raidió Teilifís Éireann, Ireland’s National Public Service Media—on 5 ways to make your daily walk more beneficial in 2026.
Get a move on!
Shocking outcome from purple potato
Along the lines of the video below, my oldest grandson Archer came up with some very interesting results from his 8th grade science project: Magic Molly purple potatoes produce more electricity gram-for-gram than Yukon Gold or Red Norland; 10.6 vs 7.9 vs 7.6 millivolts; respectively. All the potatoes came fresh from his family’s garden. He chained 3 potatoes together for each voltage measurement, thus dampening out potato-to-potato variation.
Archer also tested a sweet ‘potato’, which did very poorly on his voltage measurement (5.9 mV)—perhaps not surprisingly, it not actually being a potato.*
Archer had hypothesized that “all of the potatoes will create the same amount of volts because the phosphoric acid in the potatoes that gives them power has no color, and color is the difference between most potatoes; therefore, there shouldn’t be a difference in voltage output.” However, given his sample size being only one per variety of potato, further testing would be needed to disprove his hypothesis with adequate statistical power (e.g., p<0.05).
I advise starting with at least 4 of each potato variety and doing the testing via a randomized plan, that is a proper design of experiment. It would also be interesting to do add other factors, such as boiled versus raw and extend the test out for some days to see if the voltage drops.**
Who knew such an unglamorous vegetable (“starchy tubers”, ha ha) could be so much fun?
* See Carnegie Museum of Natural History’s explanation: Potatoes, Sweet Potatoes, and Yams: What’s the Difference?
** For clues on this, see The Not So Humble Boiled Potato! by Samantha Parker, Museum Educator, National Electronics Museum, 2020.
Response surface methods hit the spot for optimizing projectile hurling siege engines
Posted by mark in design of experiments, physics on November 12, 2025
A few weeks ago, Professor Ernst Ferg, Associate Professor – Physical Chemistry at South Africa’s Nelson Mandela University bounced (pun intended) some questions off me about deploying response surface methods (methods) on a catapult operated for education purposes by three of his students. I built up power and developed insights on relative performance of the artillerists by rebuilding his results into a fully replicated blocked design.
Now, aided by Stat-Ease software for DOE, you can see surprisingly close agreement on the central composite design’s center-point set-up (red dots) for the catapult (the reason for this soon to be revealed).
Pooling all the results into one model produced a very impressive 3D graph of distance as a function of the two biggest factors—release angle (A) and cup elevation (B).
Being impressed by Ernst’s initiative to teach his students RSM, I asked him to send me pictures of them operating the catapult. Ernst replied, “LoL, I am approaching this very much in the digital way of things: I made them use Virtual Catapult© from SigmaZone.”
It turns out that Ernst learned about the Virtual Catapult (free!) from Tom Keenan—one of four DOE educators who shared their experiences Teaching Design of Experiments in Higher Education. Tom said that “I love the way that it shoots the ball but doesn’t give you the measurement. It comes to rest next to a tape measure that the students have to read.”
Tom also likes the way that the Sigma Zone simulation incorporates some variability, thus every student gets slightly differing results. He collects the results in blocks and does an analysis similar to what I did for Ernst—being watchful of students who deviate from the others.
Fun!
PS: After gaining possession of a South Dakota Mines trebuchet from Professor Dave Dixon (one of the four panelists), I enlisted my son Hank to run an RSM optimization on this more efficient counterweight-driven cousin of the catapult (powered by torsion). We ran a Box-Behnken design, which simplified the operation to only 3 levels of each factor (versus 5 levels required for a central composite design). Ultimately, we worked out a set up that would shoot a salt-weighted raquetball over our backyard bush into a bucket on the upper level of our play fort. Empowering! For all the details on our trebuchet experiment (and pictures), see Messing With Medieval Missile Machines (Part 2).
Fresh-made mac and cheese—the ultimate comfort food
Posted by mark in food science, Uncategorized on November 5, 2025
The New York Times Wirecutter team came out with a report in early September that rated Kraft Mac & Cheese Original their favorite out of the 19 boxed options tested, saying that its “buttery and silky-smooth sauce clings to each soft noodle.” If that doesn’t make your mouth water for a fresh hot bowl of gooey orange pasta, nothing will. But as writer Ciara Murray Jordan reveals in her video recap of the Wirecutter test, even a comfort food like mac and cheese becomes nauseating when binged.
Two decades ago, I ran statistically design of experiment (DOE) on Kraft Mac & Cheese Original versus their recently released Easy Mac—a more convenient, single-serve microwavable variation on their traditional stovetop, boxed brand. My goal was to see how two experimental recipes for canned mac and cheese from a Stat-Ease client (confidential) performed against King Kraft.
My wife Karen cooked up the four competing foods and presented them in random order for blind taste testing by me, my three daughters—Emily (age 21 at the time), Carrie (16), Katie (14) and three of her friends—seven in all. We rated the mac and cheese on a scale of 1 to 5—higher the better.
As you can see from the one-factor plot produced by Stat-Ease software, my client made great improvements via application of DOE on the recipe and processing of their canned product. (The numbers by some points indicate multiple results at that rating.)
Unfortunately, as you can see by the least-significant-difference bars (essentially a 95% confidence interval), this project failed to meet its goal—a canned mac and cheese just cannot best a fresh made one. As seen in the scatter plot by taster, Kraft (in one form or the other–the red and blue points) consistently came out on top.
So it goes for researchers and process developers—you win some and lose some (more of the latter). However, I did feel good seeing the original recipe (green points) rated so low by all the tasters and their far greater liking for the DOE-enhanced product.
By the way, I am now quite hungry for mac and cheese.
You too?
Today’s Major League Baseball batters all hit below average
Posted by mark in sports, Uncategorized on October 24, 2025
This headline gets your attention if you like statistics. It makes no sense without the context: See Baseball Reference’s report on batting average (BA) by year. In 2000 MLB batters averaged .270 (expressed as “two seventy”), but after years of decline they bottomed out at .245 (two forty-five) or so. This reflects a more analytical approach to hitting that disrespects batting average as a metric, it being likened to counting the number of bills in your wallet but not amount of money.
Nowadays MLB teams value players who excel at on-base-plus-slugging (OPS). This mashup of stats creates percentages over well over 100 (“one thousand” in baseball terms) for the utmost elite players—in 2025 only Aaron Judge of the New York Yankees and Shohei Ohtani of the Los Angeles Dodgers. MLB adopted OPS in 1984 after Pete Palmer introduced it in the pioneering book (co-authored by John Thorn) The Hidden Game of Baseball, A Revolutionary Approach to Baseball and Statistics.
OPS combines simplicity with reasonable accuracy and I think that is why it is popular.
– Jim Thorn, Why OPS Works, Fall 2019 Baseball Research Journal, Society for American Baseball Research (SABR)
I’ve been a fan of baseball since 1961 when the Washington Senators moved to the Twin Cities to become the Minnesota Twins. I was 8 years old then. My grandpa had been following the Minneapolis Millers since the late 19th century as a young boy. He turned 8 in 1896 when his home team won their first Western League pennant.
Grandpa was an accountant, so, naturally he collected statistics on every Twins game—carefully ruling out rows and columns for the 9 batters and 9 innings and noting each players batting average. Because of that I am a holdout for appreciating players with high batting averages. I would rather see more hits and the strikeouts that come along with trying to hit a home run at every at bat.
On the other hand, I do not doubt that a lot of people will tune in tonight for Game 1 of the World Series to see if Shohei Ohtani lives up to his “Shotime” nickname by blasting at least one home run, if not several as he did in Game 4 of the National League Championship Series. American League fans like me will be rooting for George Springer (3rd in MLB for 2025 OPS at .959) of the Toronto Blue Jays to hit another dramatic home run like he did for in Game 7 of the AL Championship Series.
Baseball is the greatest game!
Experiment creates a reversal in time
When your boss applies maximum time-pressure by saying “I want your results yesterday,” consider lining up a couple of lasers to get the job done. Next, as demonstrated by scientists at the University of Toronto, gather up rubidium atoms and chill them to near absolute zero. Then take some shots with your lasers and take your time from the subsequent reversal. It’s all laid out by experimental evidence that a photon can spend a negative amount of time in an atom cloud.
“It took a positive amount of time, but our experiment observing that photons can make atoms seem to spend a *negative* amount of time in the excited state is up!”
– Aephraim Steinberg, a physicist at the University of Toronto
For an easier 5-minute readout from Scientific American, see this 9/30/24 post: Evidence of ‘Negative Time’ Found in Quantum Physics Experiment.
Next on the agenda for making your work easier is to capture some negative energy. Soon, thanks to advancements in physics, you will be getting jobs done yesterday with no effort whatsoever!