Going nerdle on Wordle
I am habituated to my daily Wordle, the addictive online word-puzzle. It hinges on the 5 letters you lay out at the start. It’s too boring to enter the same vowel-heavy word, such as “adieu” or “orate”, every time, so I go with a different one every day of the month, referring to my top-secret list garnered from Wordle experts. Every day I compete (not especially well) against 4 or my adult children—us all posting our play to the family WhatsApp.
Here’s my stats thus far (nicely maintained and bar-graphed by Wordle): 152 games with 0 in 1 word, 5 in 2, 51 in 3, 45 in 4, 40 in 5, 7 in 6. The other 4 times I failed to get the word worked out in the 6 tries allotted, thus ruining those 4 days for me. However, my success rate of 97.4% is not too shabby, I think. (Because it is so easy and tempting to cheat with online Wordle solvers, getting valid stats on players’ performance is problematic.)
The current issue (June) of the Royal Statistical Society’s Significance magazine features a breakdown of the “War of Wordlers” by Mary J. Kwasny—a Northwestern University professor. She collected results from 20 Facebook friends (including herself) to compare with the performance of computer-based Wordle solvers. After a plethora of nerdy statistics, step plots and simulation graphs, Kwasny concludes that the computer will probably win out over an expert player. But that will be no fun at all.
If you have more of an appetite for Wordle as well as statistics (I’ve had enough!), check out this blog by data scientist Esteban Moro on Playing (and winning) Wordle with R.
Finis! (By the way, this is a valid Wordle word according to this list.)
PS Two of our family—my wife Karen and a son-in-law Ryan—quit playing after they made Wordle’s in one. Ryan got his ace on his first try at Wordle. With roughly 13,000 words in the hopper, that was extremely ‘skillful’.
LEGO bricks used to build regression model
LEGOs are very popular around here in the Twin Cities of Minnesota. They keep our kids, such as my grandson Archer, occupied during the long winter when our cold weather limits outdoor activity. See his creative solar-powered banana-research station pictured. No wonder the local Mall of America features a LEGO Imagination Center!
Thus, naturally, this recent Journal of Statistics and Data Science Education publication on “Building a Multiple Linear Regression Model with LEGO Brick Data” caught my eye. The article lays out a fun class-project by two Iowa State University Statistics Department Associate Professors—Anna Peterson and Laura Ziegler. They developed an “innovative activity that uses data about LEGO sets to help students self-discover multiple linear regressions” that “explore the relationship between the Amazon price and the number of pieces per set for two sizes of bricks, small and large.” The students start with graphical displays, then progress to simple linear regression, and, finally, develop models that uncover interactions of factors.
Using the spreadsheets provided by Profs Peterson and Ziegler, I used the Import tools in Design-Expert® software (DX) to reproduce their results.
First off, Graph Columns revealed a strong correlation (r=0.986) between the total number of pieces and the number of unique pieces per LEGO set—this being a measure of the potential cost for individual molds. Seeing this I decided not to include both factors in my modeling—going forward only with the total number of pieces, as did Peterson and Ziegler.
Next, I did a Design Evaluation of a polynomial model with the main effects of size (A), theme (B) and number of pieces (C), plus their three two-factor interactions (AB, AC and BC), and the quadratic term for the number of pieces (C2). The results revealed an aliasing between size and theme—only the Duplo came in the large size. Thus, theme dropped out of my focus.
I then deployed DX to do a regression on the model A, C, AC and C2. Residual diagnostics revealed via the Box-Cox plot that a log transformation would do significantly better. The only catch in this metric is a high Cook’s Distance for the large-pieced Duplo Modular Playhouse set—not a problem, per se, but curiously influential.
In the end I reproduced the interaction shown in Figure 4 of the publication, but with a bit of flair for some curviness and the addition of confidence bands as seen below.
You can see that the effect on price by the number of LEGO pieces depends greatly on size of the bricks. My conclusion is that going for the small sized LEGOs is by far the most cost-effective way to keep kids busy, provided them being old enough to do so safely and with the exceptional focus needed to make something out of them.
PS While researching this blog, I noticed that in just the few years from when the costs got gathered by Peterson and Ziegler, LEGO prices went way up on Amazon. Given the recent performance of stocks and bonds, you might do well by investing in these toys per January’s Research in International Business and Finance. See the highlights (average long-term return of 11%–better than gold!) at LEGO: THE TOY OF SMART INVESTORS.
Will our boreal forests become a carbon bomb?
Leading up to Earth Day on Friday, last week’s CBS Mornings show featured several reports on environmental issues. One that caught my eye provided a birds-eye view of 10 giant octagonal glass chambers in northern Minnesota’s Marcell Experimental Forest operated by the U.S. Forest Service. They look very much like an alien colony!
It turns out, though, that this out-of-this-world complex is the home of the “SPRUCE” experiment, providing data on Spruce and Peatland Responses Under Changing Environments. From what I saw on CBS, things do not look good for boreal trees subjected to the most extreme conditions of temperature and carbon dioxide. However, it will be best not to make any conclusions until this “largest climate change experiment on the planet” ends it’s 10-year run some years from now.
“Will deep belowground warming in future release 10,000 years of accumulated carbon from peatlands that store one-third of earth’s terrestrial carbon?”
– The ‘bombshell’ question that the SPRUCE experiment hopes to answer
Major League Baseball goes all in for humidors to dampen homeruns
As I reported back in 2018 in my blog on Boffins baffled by baseballs being bashed beyond ballpark borders, MLB experimentally imposed humidors in select stadiums with high rates of home runs, such as Coors Field in Denver and Chase Field in Phoenix. The moistening evidently worked well enough* to make humidors mandatory for all teams, including my home-town squad—the Minnesota Twins, this season.
Perhaps the humidors will dampen down the homers a bit, at least in the drier climates of Denver, Phoenix and the like. But, despite dealing with the reduced coefficient of restitution (?), our “Bombas” blasted 6 round-trippers on Sunday at Target Field in Minneapolis. So, I am skeptical (though happy for my Twins).
This will not be a big deal in most parks but the most humid parks (San Francisco, San Diego, Miami, Tampa Bay) may get an offensive boost as the humidors will dry the balls out a little.
Eno Saris, baseball analytics writer for The Athletic, Mar 25, 2022 tweet
I suggest that MLB try deadening bats to further reduce home runs. This worked well for the Little League—reducing homers by 70%.** The trick will be working out a way to do it with wood. Going to plastic and/or metal would be ruinous for the Grand Old Game.
In any case, it would be great to see MLB get back to fast moving shorter games. Though home runs are exciting, they do not balance off the boring plethora of strikeouts and the inaction of the 7 position players.
*For the statistics, see this Hardball Times April 26, 2019 blog by David Kagan on The Physics of Humidors: A Second Case Study at Chase Field.
** “Little League Slows the Home Run Revolution”, Wall Street Journal, Amanda Christovich, 4/19/19.
The Feynman Technique for mastering concepts
After I watched a statistics webinar on the Stat-Ease channel, YouTube laid out a series of further videos that ‘they’ (the artificial intelligence) thought I might like to see next. They did well by suggesting this simple explanation of “How to Learn Faster with the Feynman Technique”. Being an admirer of this famous physicist and his incredible ability to explain complex concepts, I am happy to now know that his secret is simple: Once you understand something, spell it out as simply as possible to an imaginary listener. In other words, teach what you’ve learned to someone else.
Though, thanks to the AI wizard at YouTube, I only just came across the Feynman Technique, it turns out that I inadvertently applied this approach in my first try at teaching statistical design of experiments (DOE). I understood DOE very well, or so I thought until I had to lay it out the first time for a group of industrial researchers. As soon as the questions started, I realized that I should have rehearsed a lot more with a dummy audience, such as a goldfish.
“The questions of the students are often the source of new research. They often ask profound questions that I’ve thought about at times and then given up on, so to speak, for a while. It wouldn’t do me any harm to think about them again and see if I can go any further now. The students may not be able to see the thing I want to answer, or the subtleties I want to think about, but they remind me of a problem by asking questions in the neighborhood of that problem. It’s not so easy to remind yourself of these things.”
Richard Feynman, Surely You’re Joking, Mr. Feynman!‘
To make matters worse, the class was held at a restaurant on stilts just off the shore of San Francisco Bay. During the first few hours of my class an earthquake hit. The whole building wobbled back and forth for a minute or so. That night another earthquake shook me out of bed.
Somehow, I made through the week-long class relatively intact, but with a vow to never again come in so unprepared for a presentation.
Lesson learned!
Daylight elimination time
With virtually no opposition, the US Senate passed the Sunshine Protection Act, which, if approved by the House and signed by President Biden, will make daylight savings time (DST) permanent beginning next March.
I was hoping for an end to the very annoying biannual change in time, but figured it would revert to standard, not daylight time. It will be very unsettling for those living in the far north to delay sunrise from 8:30 to 9:30 on the mornings around the winter solstice when days are shortest. However, I suppose that with the creep of DST over the years from 6 months in 1966 to only 4 months now, standard time stood no chance. Evidently the majority prefers not being woken up too early by the bright sun, and they like lighting up evening activities, for example, trick or treating on Halloween.*
An extra yawn one morning in the springtime, an extra snooze one night in the autumn is all that we ask in return for dazzling gifts. We borrow an hour one night in April; we pay it back with golden interest five months later.
Winston Churchill
Going to fixed time nationwide, even if it must be DST, will be very welcome. The clock fiddling got completely out of control in my Twin Cities years ago when the whole region split on going to DST. It came to a head with Minneapolis and Saint Paul being one hour apart for two weeks in 1965.**
It’s about time to settle on one time per zone and allow for the natural variation in daylight caused by our planet being so ‘tilty’. If you do not like it, move to the equator.
*See How Retailers Got American Kids an Extra Hour To Trick-Or-Treat On Halloween
**See Two Cities, Two Times
Statbot AI a bust…sad…now in need of Woebot consoling
Sir David Cox, a giant in the field of statistics, passed away early this year at age 97. Boffins like him cannot be easily replaced—hence the interest in creating artificial intelligence (AI). Therefore, I was excited to see this announcement of NelsonBot5000 (NB5k)—an automated “statistical concierge”. Alas, after submitting several questions such as “what is a p value”, I discovered that NB5k referred all questions to Google. Lame (but a clever gimmick to create engagement!).
“When I was a young cyborg, knee-high to a dial-up modem, PapaBot_x86 used to tell me tales of what the future would hold. However, I never dreamt that we’d ever see the day where free statistical expertise would be available to everyone, instantly.”
– NelsonBot5000
This got me got me going on the state of AI in general. The first thing I found via Google was a New York Times report on an “automated conversational agent” called Woebot that, according to this randomized controlled trial (unblinded), significantly reduces depression. I wanted to share my disappointment about NB5k but Woebot would not talk to me—it requiring a referral from a mental-health provider. My colleague Pat Whitcomb, founder of Stat-Ease, had a good response when I shared similarly trivial woes with him: “GOI!” (get over it).
On the bright side, my work as a consultant, trainer and educator on statistical design of experiments (DOE) remains secure from smart bots. All I ask is that before you ask me for stat help, please consult with Google or the like. Or, better yet, read the trilogy of “Simplified” books on DOE, lead-authored by me based on brainpower from Pat and statistician Martin Bezener.
*“Something Bothering You? Tell It to Woebot. When your therapist is a bot, you can reach it at 2 a.m. But will it really understand your problems?”, Karen Brown, 6/1/21.
Industrial statisticians keeping calm and carrying on with p-values
Posted by mark in Basic stats & math on February 11, 2022
Last week I attended a special webinar on “Statistical Significance and p-values” presented by the European Network of Business and Industrial Statistics (ENBIS). To my relief, none of the speakers called for abandoning the use of p values. Though I feel that p’s should not be a statistic to solely rely on for deeming results significant or not, when used properly they certainly reduce the risk of pressing ahead with spurious outcomes. It was great to get varying perspectives on this issue.
Here are a couple of fun quotes on that I gleaned from this ENBIS event:
- “Surely, God loves the .06 nearly as much as the .05. Can there be any doubt that God views the strength of evidence for or against the null as a fairly continuous function of the magnitude of p?” – Rosnow, R.L. & Rosenthal, R. “Statistical procedures and the justification of knowledge in psychological science”, American Psychologist, 44 (1989), 1276-1284.
- “My definition of a statistician is ‘one who prefers true doubts to false certainty’.” – Stephen Senn (Statistical Consultant, Edinburgh, Scotland, UK)
If you have a strong stomach for stats, see this Royal Society review article: The reign of the p-value is over: what alternative analyses could we employ to fill the power vacuum? It includes discussion of an alternative to p values called the “Akaike information criterion” (AIC). This interested me, because, as a measure for goodness of model-fit, Stat-Ease software provides AICc—a version of this statistic that corrects (hence the appendage “c”) for the small sample sizes of industrial experiments (relative to large retrospective scientific studies).
A very scents-able invention for detecting odors
Posted by mark in science, Uncategorized on January 23, 2022
I was impressed to see this recent New York Times ‘heads-up’ featuring a fellow chemical engineer from University of Minnesota, Chuck McGinley, who operates a lab just a few miles down the road from my home in Stillwater, MN. They got a great shot of Chuck using his Nasal Ranger to sniff around in South St. Paul, last summer. That area of the Twin Cities has emitted unpleasant odors throughout my lifetime—it being founded as a regional stockyard and still the home of a stinky rendering plant.*
“Some of the most recognizable and potent odors, like hydrogen sulfide (think rotten egg) can be sensed at even the tiniest concentrations, like 1 part per billion. ‘If you were to map out the distance from New York to Los Angeles, 1 part per billion would account for only a few inches along that route’.”
– New York Times quoting Professor Jacek Koziel, Iowa State
It turns out that there’s a surprising amount of science behind detecting and characterizing odors as detailed in this blog by St. Croix Sensory, where Chuck works as Technical Director. Unfortunately, the main focus of these experts on smelling must, by necessity, be on detection of ‘off-odors’, such as that emanating from kitty litter (yuk!). If I had a Nasal Ranger, it would be aimed at a rose garden or at a barbecue grill, that is, “on” odors.
PS: Sadly, the current coronaviruses not only cause the loss of smell but also a perverse reversal of olfactory senses called “parosmia.” This can make savory foods smell like rotting sewage as noted in a 1/18/22 report by CNBC on how Covid can turn kids into ‘fussy eaters’ if it changes their sense of smell.
*As reported in 11/22/21, Des Moines Register, ‘You can’t escape it’: Stench spoils downtown experience for some in Des Moines , the residents of South St. Paul won a settlement in 2020 for $750,000 for putting up with the off-putting odors.
Megastudy uncovers secret to motivation for exercise
Posted by mark in Consumer behavior, Wellness on January 10, 2022
Over half of all Americans making resolutions for 2021 made exercise their top priority according to this report from Statista. Unfortunately, most people who decide to work out more often after being ‘flabbergasted’* by the year-end holidays will fall off by the 17th of January—cruelly declared as “Quitter’s Day” by fitness tracker Strava.
However, the results of a new ‘megastudy’ reported by this report last month in Nature provides some hope for certain interventions getting folks back on their treadmills or the like. A team of scientists in collaboration with 24 Hour Fitness created a “Step Up” program that, with a small incentive ($1 in Amazon points), drew in 61,000 members. They then divided up the group into groups to test over 50 four-week programs aimed at increasing weekly gym visits.
Only 8% of the interventions led to participants making a significant change in their behavior. The most successful approach, increasing attendance by 27% versus the control group, came by giving people about 10 cents in reward points for returning to the gym after missing a workout. Surprisingly, a larger monetary reward (~$1.75) produced slightly less improvement.
“Try not to miss more than one workout.”
Advice from lead-author Katy Milkman, a behavioral scientist and professor at the Wharton School of the University of Pennsylvania
I like the New York Times December 8th “Phys Ed” take-home on this megastudy. “Find small ways to reward ourselves when we exercise as planned. Drop a dollar into a bowl for every workout, for instance, and let the proceeds mount.” Better yet, make an appreciable monetary bet with a friend that you will keep up your workouts. Along those lines, why not make it mutual? Fun!
Since this study only involved people motivated enough to join a gym, it would be a stretch (fitness pun?) to expect similar results for those remaining anchored to their couch. Perhaps attaching a dollar bill to a reeling fishing line might lure these slackers into moving about a bit. Worth a try!
*A neologism (newly coined word) becoming popular in these pandemic times of chronic overeating meaning “appalled over how much weight you have gained.”