Commuting by car or bike: Studies by UK statisticians
This month’s issue (June 2011, volume 8, issue 2) of the Royal Statistical Society magazine Significance [motto “statistics making sense” 🙂 ] features two intriguing articles on commuting.
The first one details Martin Griffiths, a math lecturer at U Manchester, “trying to pull out of the drive” (pp 89-91). This poor fellow must wait upwards of 2 minutes just to get on the road from his property. Imagine the frustration of a somewhat random stream of cars blocking your way out. Then, just as you see a gap, another car comes along to fill it. Griffiths provides a very impressive formula for average wait time based on a Poisson distribution. He factors in the average number of cars passing by as well as the time taken to pull out into the flow. The bottom line: It does not pay to be timid. You’d best mind the gap (inside joke for anyone who’s traveled London’s subways) and make a move!
The second study* comes from a biker, Dr. Jeremy Groves, who spends up to 2 hours or more commuting to his work at Chesterfield Royal Hospital. Thankfully his ride gets considerably shorter in summer when he needn’t wear baggy outerwear, which creates a real drag (Groves estimates 30% more wind resistance). This cycling enthusiast bought a new bicycle recently – one that featured a carbon frame, as opposed to the steel one he’d bought second-hand. Being a fan of randomized (“randomised” in UK spelling) trials, Groves completed a series of runs with one or the other of his bikes – measuring the times taken for the ride from his home in Sheffield to his work at hospital. Seeing his run chart starting off very raggedly at the high end in January, I transcribed only the latter 28 runs (14 of each) for the chart shown. 
Obviously from the overlap in the least-signficant-difference (LSD) bars the results remain inconclusive. (If you have trouble seeing this, click the graph for a larger view of it.) The difference is less than 1 minute in favor of the very costly carbon-framed bicycle. Given a 3.5 minute standard deviation under summer conditions, it would take 400 total runs (200 each) to resolve whether this is a true advantage, according to a power calculation I did with the aid of Design-Expert® software. Dr. Groves has moved on to another experiment for this summer – he plans to randomly load a 4 kg weight on his bicycle (the carbon one, I presume). Aside from being a glutton for punishment, I suppose this fellow wonders how much it slows him down when he must carry in his laptop.
* “Bicycle weight and commuting time: A randomised trial,” pp95-96.
Fun summer-time experiment: Super-cool beer so it instantly freezes solid
It turns out that if a bottle of beer is put in the freezer for long enough, and then removed while it is still liquid and, lastly, given a sudden shock, the beer will instantly freeze solid. I saw this confirmed by the pop-science TV show Mythbusters in their episode 153, originally aired on 11/10/10. Based on trial-and-error experimentation their Build Team found that 3 hours of cooling time sufficed to create the delightful phenomenon. See the instant beer-freeze demonstrated by EasyBarTricks.com here. For detailed instructions on how to try this at home or in a classroom, plus a nerdy explanation (think PVNERT) by physics and math teacher Daryl Taylor, check out this website.
Of course I had to try this for myself. However, not being one who ever leaves well-enough alone, I tried light beer (Miller, bottled in clear glass) side by side with the recommended Corona – two of each. Could this be a factor (light versus regular brew)? After being careful to wait at least 3 hours for the quartet of brews to super-cool, I brought them out for a family party. Two of the beers crystallized when smacked on our kitchen cutting board, but the other two did not. Here’s a twist, though: None of the bottles were uncapped first, so how does that gibe with the PV-nerd’s explanation?
Alas, one of the light beers crystallized and the other did not – ditto for the Corona, so my results, albeit semi-successful, were indeterminate on the issue of light vs regular brews. The good news is that we salvaged two bottles of beer (the frozen ones become undrinkable).
Feel free to weigh in with your theories and experimental results from this beer trick. One thing I learned from my first try – a lot more beer would be good, along with a walk-in freezer (or the backyard in mid-winter).
Strategy of experimentation: Break it into a series of smaller stages
Posted by mark in design of experiments on June 20, 2011
Tia Ghose of The Scientist provides a thought-provoking “Q&A” with biostatistician Peter Bacchetti on “Why small is beautiful” in her June 15th column seen here. Peter’s message is that you can learn from a small study even though it may not provide the holy grail of at least 80 percent power.* The rule-of-thumb I worked from as a process development engineer is not to put more than 25% of your budget into the first experiment, thus allowing the chance to adapt as you work through the project (or abandon it altogether). Furthermore, a good strategy of experimentation is to proceed in three stages:
- Screening the vital few factors (typically 20%) from the trivial many (80%)
- Characterizing main effects and interactions
- Optimizing (typically via response surface methods).
For a great overview of this “SCO” path for successful design of experiments (DOE) see this detailing on “Implementing Quality by Design” by Ronald D. Snee in Pharm Pro Magazine, March 23, 2010.
Of course, at the very end, one must not overlook one last step: confirmation and/or verification.
* I am loathe to abandon the 80% power “rule”** but, rather, increase the size of effect that you screen for in the first stage, that is, do not use too fine a mesh.
** For a primer on power in the context of industrial experimentation via two-level factorial design, see these webinar slides posted by Stat-Ease.
Why coaches regress to be mean
Posted by mark in Consumer behavior on June 13, 2011
In a column for Newsweek magazine, science writer Sharon Begley* discusses how ignorance about the statistical principle of regression to the mean** causes all sorts of crazy behavior. For example, sufferers of colds try a new remedy that seems to make them better, but in reality, they were already recovering. This behavior leads to over-use of antibiotics, which breeds drug-resistant bacteria. Ultimately, according to this quote passed along by Begley:
“People die at a biblical scale because of such stupidity.”
– Ben Goldacre, author of Bad, Science: Quacks, Hacks and Big Pharma Flacks.
On a lighter (?) note, this tendency by people to attribute cause-and-effect relationships to random ups-and-downs explains why some teachers, coaches and instructors hold back praise and only berate their pupils. A case in point is the flight instructor who lavishes praise on a training-pilot who makes a lucky landing. Naturally the next result is not so good. Later the pilot bounces in very badly — again purely by chance (a gust of wind). The instructor roars disapproval. That seems to do the trick — the next landing is much smoother. So now you know why coaches yell so much: It’s their regression to the mean.
* “Wanted: BS Detectors” – 11/8/10.
**First brought forward by France Galton in 1886 via this essay on “Regression towards Mediocrity in Hereditary Stature”
How hot? 103 under our shade tree!
According to my morning newspaper (St. Paul Pioneer Press), yesterday’s record temperature made it hotter hereabouts than a billy goat in a pepper patch, or the devil’s underwear (I hope he is not a tweeter like that New York Congressman), or two bears fighting in a forest fire (down in Arizona, I suppose). Even so, a vestige of the once 60-foot high pile of snow dump in downtown St. Paul remained intact. Perhaps it will disappear today. I hope so, because it will be back in the 60’s by Friday – colder than a basement toilet seat as Minnesotans like to say.
Video of paper-helicopter fly-offs at South Dakota School of Mines & Technology
Posted by mark in design of experiments on May 10, 2011
Stat-Ease Consultant Brooks Henderson produced this video — it’s quite impressive!
For background on the paper helicopter experiment, see this previous StatsMadeEasy post.
Simple and cheap safety precautions against the small risk of drowning in an automobile
I always thought that if I was in a car that went into water, I’d be cool enough to roll down the windows, or wait until it submerges before opening the door (otherwise the pressure differential makes it impossible). Based on actual experimentation, the hosts of the television show Mythbusters felt the same way, that is, until viewers pointed out that many cars turn turtle as they sink. So in a show I watched last month they [Jamie Hyneman and Adam Savage] tried this. It was a disaster! The Mythbuster driver [Adam] survived only by breathing from an emergency air source, and the safety diver had to cut his way out of a seat belt that wouldn’t release! See this recap to learn what went wrong. What they don’t show is how at first the car just floated, so it seemed like no big deal; but then when it sank, the automobile went down incredibly fast. En route to the bottom of the lake the car spun around so much that the occupants would’ve drowned for sure. Scary!
After this epiphany, I ordered several of these inexpensive (<$5) safety hammers (see one pictured) for cars owned by me and my offspring.
Check out this post by First Aid Monster for another video showing how fast you can go underwater when a car runs into a canal, river, pond, lake or ocean. They suggest buying a safety hammer and provide a link to one similar to what I bought.
When I advised family and co-workers to be prepared for being trapped in a car that goes underwater, it was met by a few with great skepticism.
One individual wondered how many people die this way, figuring it being so unlikely as to not be worth any worries. From internet research, the best I can figure is that about 10% of all drowning occur in submerged cars. Then using statistics from this graphic by the National Safety Council putting the odds of death by drowning at 1 in 1000, I figure that dying this way in a car occurs at about a 1 in 10,000 rate – somewhat less likely than dying in a plane crash. I’ve flown hundreds of times and never yet come across anyone refusing to buckle up as required when taking off and landing. Why not?
Another person expressed strong doubts as to whether the hammers could break an automobile window. I cannot yet say from first-hand experimentation, but this video provides convincing evidence, I feel.
Anyways, I’m putting the little <$5 safety hammers in all my cars. Why not? It could come in handy some day, if not for me to escape a submerged car, then maybe for some other event that requires breaking glass – someone trapped in a car crash on land, for example.
Bear in mind that I am a Minnesotan — a state that boasts of having 10,000 lakes and where a bridge fell down into the Mississippi not that long ago. Furthermore, I live in a town (Stillwater) with a rotten old lift bridge that may be the next to fail according to this recent report by The History Channel.
Eggs-plosion in the aftermath of Easter
Posted by mark in science, Uncategorized on April 30, 2011
I’ve become accustomed to hard-boiling an egg for my breakfast so I was pleased to see a surplus of Easter eggs after celebrating this holiday last Sunday. My dexterity for shelling eggs is not a-pealing (ha ha) so I decided to try an eggs-periment: Microwave an Easter egg just long enough to heat it up and loosen it up for eggs-traction. If I’d have quit after my first try of 15 seconds, I may’ve succeeded. But the egg just didn’t feel hot enough so I added more time. Kapow! The eggs-plosion left nothing more than a millimeter of shell intact. The uniformity of organic matter throughout the inner surface of the microwave oven was very interesting, I think – quite impressive.
Although I consider this to be a very successful experiment, it’s one that I don’t feel needs to be replicated. My colleagues at Stat-Ease have provided a number of suggestions for another eggs-periment such as boiling the Easter eggs in vinegar or baking them. This creates a looser shell, they say.
Feel free to provide other ideas, but keep in mind that disaster seems to lurk behind me whenever I try an experiment. My failures tend to be quite spectacular. But, on the other hand, that’s what makes experimentation so eggs-citing!
An Easter experiment for those who still believe a bunny bears eggs* *(Beware of the green ones!)
Today’s Saint Paul Pioneer Press “Bulletin Board” provides an idea on how to provide some added delight for any children who still believe in the Easter Bunny: Have them plant one of their jelly beans, then watch for it to grow into a lollipop. Doesn’t that sound like a fun experiment!
By the way, be careful with the green jelly beans – they cause acne (p<0.05) according to this exhaustive statistical-study of every available color.
Winter not loosening its icy grip on Spring
I woke up to snow yesterday morning. It couldn’t quite cover the greening grass underneath, nor did it seem to discourage the budding bushes. Today the snow has disappeared and the near 40 degree F temperature seems mild with the power of April’s sun and the abatement of fierce northern winds. However, our Canadian neighbors are not faring quite as well, as evidenced by this very cool (literally and figuratively) photo from my sister – a resident of Calgary. Notice how the snow fingers feature icy nails — chilling!
When will Winter finally loosen up and let Spring spring free, eh? Maybe May…