Microwave popcorn still expanding nicely but in shrinking amounts
When I first ran a multifactor design of experiment (DOE) on microwave popcorn in 1993,* the bags contained 3.5 ounces of product. Since then, this product and many other foodstuffs suffered from shrinkflation—a way for their manufactures to fool us into paying the same for less. For example, Pop Secret—one of the snacks tested in my 1993 DOE, now comes in 3.2-ounce bags—a shrinkage of 8.6 percent over the years. Tricky!
I asked Google’s experimental Generative AI for stats on shrinkflation. GAI (my new go-to guy!) tells me that:
- The most common products to experience shrinkflation are savory snacks, chocolate, and sweets. (Popcorn fits the bill.)
- In the US, 71% of people have noticed shrinkflation, with 57% reporting multiple incidents in the past year. Baby boomers are more likely to notice shrinkflation than millennials and Gen Zers. (I am a baby boomer and I am well aware of this trend.)
- Shrinkflation can be harder to notice than price increases because the price of the item stays the same, making it harder to budget. (That’s the idea!)
- According to the US Bureau of Labor Statistics (BLS), shrinkflation has little impact on overall inflation rates. A BLS report from March said that the price of snacks inflated by 26% from January 2019 to October 2023. However, shrinkflation accounted for only 2.5 percentage points of the increase. (OK, so maybe we are making too big of a deal about this, but nobody likes to be tricked.)
The increasing cost of food products is currently creating a great deal of consternation, despite it seemingly abating. But so long as there’s plenty of delicious popcorn to share, even at a higher price for less of it, I don’t mind much.
However, when it comes to the recent trend for popcorn manufacturers selling “mini bags” with 1.5 ounces of product, I draw the line!
Hoping to cell-abrate meat substitutes before I die
Posted by mark in food science, Uncategorized on October 14, 2024
As a consultant on statistical design and analysis of experiments, I’ve been working with many leading-edge developers of cell-based meats (and fish). I am a carnivore—me loving a juicy burger, tender pulled pork, medium-rare steak or barbecued chicken. However, I’d happily switch to lab-grown protein once it passes a properly designed double-blind taste test. This will be a huge breakthrough by not killing animals and greatly reducing greenhouse gases—including “enteric fermentation” (nice way of referring to cow farts, ha ha).
Some experts do not foresee this happening in our lifetime according to this report last February by CBC. But after reading this cover story posted yesterday by Chemical & Engineering News on recent developments on lab-grown meats, I am more optimistic.
There is a fly in the food, so to speak, though: I cannot eat lab-grown meat while wintering in my Florida home—it’s been banned per this May 1 press release from Governor DeSantis. No fair!
“Today, Florida is fighting back against the global elite’s plan to force the world to eat meat grown in a petri dish or bugs to achieve their authoritarian goals.”
– Governor Ron DeSantis
By the way, I do agree with the Governor on one thing by not being a big fan of eating bugs. On the other hand, I applaud a Stat-Ease client from Bulgaria—Nasekomo (meaning ‘‘insect’’)—for developing a high-protein chicken feed made from soldier flies. I helped one of their researchers on her experimentation after first being assured that the EU approves the use of their product only for animals, not humans. She told me that chickens who eat the fly-based food tend to be less aggressive and healthier. Sounds good to me: Cock-a-doodle-do!
Analytics explain why the NFL stiffs running backs
My Minnesota Vikings are on a roll this year due to unexpectedly stellar play from their quarterback Sam Darnold. After being drafted very highly, Darnold turned out to be a dud. But suddenly he blossomed—no doubt helped greatly by our superstar wide receiver Justin Jefferson. This Sunday the Vikings play in London against the New York Jets and their future hall-of-fame QB Aaron Rodgers.
There’s no doubt that quarterbacks are the most important factors for success in the NFL, so it’s no surprise that there’s a positive correlation of 0.7 between annual passing yards and annual revenue according to Harvard economist Roland Fryer.* But it’s quite shocking that he finds a negative correlation of 0.01 for the value of running backs. I agree with Fryer that its delightful to “see analytics put to good use but sad to see football’s best position taking a back seat.”
Go Darnold, go Vikes!
P.S. As reported earlier this year by SI, The NFL Treats Elite Wide Receivers Very Differently From Top Running Backs. As a case in point, they highlight the huge contract just signed by Jefferson. “Show me the money”—the demand given by the wide receiver to his agent Jerry McGuire played by Tom Cruise—isn’t working for running backs, though they do make a lot more money than kickers or punters as seen in this ESPN ranking of pay by position.
*Comments on “The Economics of Running Backs,” Wall Street Journal, September 4.
Australia overcomes USA for Olympian heights: Seriously?
Now that Tom Cruise swooped in on the Stade de France outside of Paris and carried off the Olympic flag to Los Angeles, the final reckoning can be made on which country ‘won’ the 2024 Summer Games. I figured that by tying for tops in gold medals and winning the most silver and bronze, the USA was the clear winner.
However, to be fair, one must take population by country into account (within reason by excluding very small countries such as Grenada, who only need to win a few medals top the Olympic chart on a per capita basis). Earlier this year Robert Duncan and Andrew Parece proposed a population-adjusted probability-based index “U”.*
See how your country ranks in by this measure in this final ranking for the Paris Olympics. Aussies rule—gold medals to all! The Peoples Republic of China, who outnumber Australians by 53 to 1, fall to 89th on the list—second to last. Ouch! Kudos to France for coming in second (silver) and Great Britain third (bronze). The USA ranks fifth—not too bad.
Congratulations to all the Olympians and the organizers of this summer’s games for a very entertaining spectacle. Let’s not bogged down by the medal counts—all who participated get full credit for their all-out efforts.
*Per equation 9 in their Journal of Sports Analytics vol. 10, no. 1, pp. 87-104, 2024, research paper on Population-adjusted national rankings in the Olympics
The secret sauce in Guinness beer?
Posted by mark in design of experiments on August 9, 2024
I highly recommend Scientific American’s May 25 Opinion by Jack Murtagh explaining How the Guinness Brewery Invented the Most Important Statistical Method in Science. It nicely illustrates the t test—a landmark statistical method developed by William Sealy Gosset to assess a key ingredient in Guiness beer for ideal bitterness and preservation—soft resin content in hop flowers. Gosset calculated that a 1% difference in the amount of soft resins in the hops, the best and cheapest being purchased from Oregon,* increased their value to the brewery by almost 11%.
“Near the start of the 20th century, Guinness had been in operation for almost 150 years and towered over its competitors as the world’s largest brewery. Until then, quality control on its products had consisted of rough eyeballing and smell tests. But the demands of global expansion motivated Guinness leaders to revamp their approach to target consistency and industrial-grade rigor. The company hired a team of brainiacs and gave them latitude to pursue research questions in service of the perfect brew.”
– Jack Murtagh
Back in 2017 on National Beer Day, celebrated yearly on April 7 to commemorate the end of USA’s prohibition of its sale, I saluted Gosset and his very useful t-test of the significance of one treatment versus another, that is, a simple comparative experiment.**
“They began to accumulate data and, at once, they ran into difficulties because their measurements varied. The effects they were looking for were not usually clearcut or consistent, as they had expected, and they had no way of judging whether the differences they found were effects of treatment or accident. Two difficulties were confounded: the variation was high and the observations were few.”
– Joan Fisher Box,*** “Guinness, Gosset, Fisher, and Small Samples,” Statistical Science, Vol. 2, No. 1 (Feb., 1987), pp. 45-52
To see how the t-test works, check out this awesome graphical app developed Even Miller. Using Stat-Ease software, I cross-checked it against a case study (Example 3.3) from the second edition of Box, Hunter and Hunters’ textbook Statistics for Experimenters. It lays out a simple comparative experiment by a tomato gardener who randomly splits 11 plants for treatment either with her standard fertilizer (A) or a far more expensive one (B) that supposedly produces far better yields. Here are the yield results in pounds, which you can assess using the t test:
- 29.9, 11.4, 25.3, 16.5, 21.1
- 26.6, 23.7, 28.5, 14.2, 17.9, 24.3
On average the new fertilizer increases the yield by nearly 2 pounds, but is the difference statistically significant? That would be good to know! I have the answer, but it would be no fun to tell you, being so easy to find out for yourself.
PS: Due to the large variation between plants (a greater than 6-pound standard deviation!), this tomato study is badly underpowered. If you do an experiment like this, do anything possible to get more consistent results. Then assess power for whatever the difference is that makes changing fertilizers worthwhile. For example, let’s say that with better plant management you got the standard deviation reduced to 3 pounds and a difference of 4 pounds is needed at a minimum to make the switch in fertilizer cost-effective. Then, using Stat-Ease software’s power calculator, I figure you would need to test 3-dozen plants each in your randomized experiment to achieve an 80% probability of detecting a difference of 4 pounds given a 3-pound standard deviation. I hope you like tomatoes!
*As reported by Eat This Podcast in their 4/10/18 post on Guinness and the value of statistics
***I was very fortunate to meet Joan Fisher Box in 2019 as related in this StatsMadeEasy blog/
What not to wear to a dinner hosted by mosquitos
Posted by mark in Nature, Uncategorized on August 2, 2024
Yesterday I stopped by Minnesota’s Metropolitan Mosquito Control District (MMCD) booth at our local county fair. They display live mosquito larvae swimming in a shallow pan of water. Visitors can pipette them on to a slide and view them with a microscope. Fascinating!
Thanks to the mosquito control services by MMCD (and/or developments reducing habitat) I’ve seen a dramatic decrease in these pests since moving into my home in Stillwater almost 30 years ago. However, there were plenty of ‘skeeters at the Anderson family get-together up north at Pine Terrace Resort last month. While packing for our getaway, my wife advised that to be less attractive to these flying insects I bring white or lightly colored clothes and none with any reds. Being a professional skeptic of such assertions, I immediately looked for any science to support her advice. As usual, she was right, as you can see in this 2022 publication by Nature on The olfactory gating of visual preferences to human skin and visible spectra in mosquitoes.
If you are put off by too much information, watch this LIVENOW interview of co-author Jeffrey A. Riffell—a biology professor at the University of Washington, Seattle. I like his heads-up that mosquitos learn not to bite people swatting them away and go for easier prey. In other words, if you are going for a hike in the woods, bring along someone who would rather get bitten up than look like a city slicker. Then diligently swat all mosquitos over to your trail-mate—better to look like a fool than be bitten-upped cool.
PS: I am a big fan of DEET repellants for deterring mosquitos and, equally important, ticks. I also wear a cap treated with permethrin, which is a real game changer as advised by Hiking Thru Life. Of course, in areas where mosquitos gather in visible clouds, covering up completely, starting with a head net, is the only way to go. Given the huge increase in mosquito-borne and tick-borne diseases in the United States and elsewhere, it’s best to “fight the bite”.
Design of experiments (DOE): Secret weapon for model rocketry
Posted by mark in science, Uncategorized on June 27, 2024
Attracted by its focus on model rockets, I took a summer class on physics at Macalester College in my early teens. What a blast—literally! I really enjoyed learning about force, mass, acceleration and all the other aspects underlying aerospace. (Keep in mind this being the height of the 1960s race to the Moon.) But the best part was building a scale model of the Saturn V featuring multiple solid propellant motors and a parachute recovery system. For the grand finale of our class, we successfully launched our rocket. The parachute did deploy. However, our ship drifted over Saint Paul’s magnificent urban forest (soon to be decimated by Dutch elm disease) and got hopelessly hung up 100 feet overhead.
These great memories from my youth came back to me earlier this year when asked for advice on validating the OpenRocket simulator. The question came in from a mentor using Stat-Ease® 360 software on a low-cost educator license to support a high-school rocket club achieve the American Rocketry Challenge goals for altitude and flight duration. I happily deferred this request for stat help to my colleague Joe—a physics PhD who plays a dual role providing statistical advice and programming. Without getting into the details (after all, this is rocket science!), suffice it to say that, yes, our DOE software does provide “the right stuff.”
By the way, just last week a NASA sounding rocket carrying student experiments reached an altitude of 70 miles. See the video for the launch. (I advanced it to the countdown. After the blast off, move on. That is the only exciting bit.)
What I find most amazing is that the nose cone on this rocket can carry up to 80 plastic cubes as payload. These accommodate experiments by 11-18 year old students. Check out this Cubes in Space STEM program. Page down to the BREAKING NEWS about an important discovery made by a group of elementary students from Ottawa. I recommend you watch the CTV video—very impressive to hear from such science-savvy grade-schoolers. They will go far!
Coin-flip hack: How to call it—heads or tails—to improve your odds
Posted by mark in Basic stats & math on June 12, 2024
As I reported in this 2009 StatsMadeEasy blog, math and stats experts Persi Diaconis, Susan Holmes and Richard Montgomery long ago worked out that “vigorously flipped coins tend to come up the same way they started.”* Based on principles of physics, the “DHM” model predicts about a 0.51 chance that a coin will come up as started. That is not a big difference over 0.50 but worth knowing by its cumulative impact over time providing an appreciable winning edge.
Now in a publication revised on June 2nd the DHM model gains support by evidence from 350,757 flips that fair coins tend to land on the same side they started. All but three of the 50 (!) co-authors—researchers at the University of Amsterdam—flipped coins in 46 different currencies and finally settled on 0.508 as the “same-side bias,” thus providing compelling statistical confirmation for the DHM physics model of coin tossing.
This finding creates many potential repercussions, for example on NFL football games going into overtime, particularly under the old rules when a team that won the coin toss could immediately win with a touchdown. The current rules provide one chance for the opposing team to tie under these circumstances. Nevertheless, it seems to me that referees should randomly pull their coin out without knowing which side came up, keep it covered up from sight of the caller and then flip it.
Let’s keep things totally fair at 50/50. (But do sneak a peek at the coin if you can!)
*Dynamical Bias in the Coin Toss, SIAM (Society for Industrial and Applied Mathematics) Review, Vol. 49, No. 2, pp. 211–235, 2007.
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.