Fun trivia on how many people it takes before chances are good that some or all share birthdays
Birthdays are in the news this month as the last of the Baby Boomers hit age 50—most notably Michelle Obama, but also my youngest sibling—brother Paul. A little game I’ve played with my larger statistics classes is to poll them for their birthday—month and day (one mustn’t dare to ask for the year). It turns out that with 23 people coming together at random the odds tilt in favor of at least two sharing this special date. Somehow that just does not seem likely but all one needs to do for working this out is calculate the probability of all having different birthdays, and then subtract the answer from 1.
By the way, it takes 88 people to achieve a good chance of 3 sharing a birthday.
This last statistic (88 for 3) comes from statistician Mario Cortina Borja in an article he wrote for the latest issue of Significance detailing “The strong birthday problem,” that is, not just one person but everybody in a group sharing a birthday with at least one other. By assuming that the birthdays follow a uniform distribution,* Borja worked out this complex problem. His results are somewhat counter-intuitive in the way probabilities decrease from 2 to 365 and rise thereafter—quickly gaining at 2000 and beyond. (Of course if only “me, myself and I” are gathered, that is, one person, the probability is technically 100 percent of a birthday match.) The answer to this strong birthday problem is 3064. At 4800 people there’s a 99% chance that everyone will share a birthday with another.
Borja suggests that it might be fun for a large celebration to award a prize to anyone with a lone birthday. If one won such a contest, it would really be a lonely experience.
*P.S. Borja provides the math for birthdays being distributed non-uniformly, but leaves it at that because the computational cost of solving it is “fiendish.” That’s OK because other statisticians who studied this problem found that the results change very little with deviations from the uniform distribution.
85 people have as much money as 3.5 billion
The 3.5 billion poorest people who account for half the world’s population can barely scrape up enough money to match the 85 wealthiest, according to the international relief organization Oxfam. I await verification on this statistic but, if true, it really boggles my mind.
Oxfam teed this attention-getting shot up in prep for the annual World Economic Forum in Davos, Switzerland this week. Let’s hope this convocation brings out the gnomes from Zurich who manage the gold from the hive of the weighty eighty-five. Perhaps a few coins might trickle out from the greedy to the needy.
Another round of three deaths now underway—triggered by the Professor
My favorite character in Gilligan’s Island–the Professor (aka Dr. Roy Hinkley)—passed away recently. 🙁 Who else will die, I wonder, because these always come in threes, or so it seems.
According to this newly-published study explaining “When Three Charms…, people gravitate to number 3. Being business school profs (Suzanne B. Shu of UCLA and Kurt A. Carlson of Georgetown U.), the authors focused on how to exploit this phenomenon for marketing purposes—their experiments pointing to the power of persuasion being optimized at three claims and no more—the fourth one pushes consumers over to being over-sold.
So be on guard from now on whenever someone tries to sell you on something by touting three reasons. 😉
Getting back to the morbid fascination with celebrity deaths, it may just be that this occurs from the natural tendency to conclude that three events in a row cannot happen just due to chance.
“You reach maximum streakiness at three events.”
– Kurt Carlson quoted by New York Times in 1/3/14 article about The Power of Three
Being somewhat savvy on statistics and generally a rational thinker, I know this is immensely overblown, but I cannot help but succumb to it, in particular when bad things come in bunches. My trick to put a halt to being unlucky is to resolve that whenever I’m hit by three unpleasant events then I watch for three good things to come. I suppose this is just the power of positive thinking overcoming the depressive impact of cursed karma, but this works for me—I encourage you to give it a try.
When the bunch of bad reaches three, that’s it for me–make that your mantra. 🙂
Must we randomize our experiment?
Posted by mark in design of experiments on December 31, 2013
In the early 1990s I spoke at an applied statistics conference attended by DOE gurus George Box and Stu Hunter. This was a time when Taguchi methods had taken hold, which engineers liked because the designs eschewed randomization in favor of ordering by convenience–with hardest-to-control factors changed only once during the experiment. I might have fallen for this as well, but in my early days in R&D I worked on a high-pressure hydrogenation unit that, due to risks of catastrophic explosion, had to be operated outdoors and well away from any other employees. (Being only a summer engineer it seemed that I was disposable.) Naturally the ambient conditions varied quite dramatically at times, particularly in the Fall season when I was under pressure (ha ha) to wrap up my project. Randomization of my experiment designs provided me insurance against the time-related lurking variables of temperate, humidity and wind.
I was trained to make runs at random and never questioned its importance. Thus I was really surprised when Taguchi disciples attending my talk picked on me for bothering to do so. But, thank goodness, Box had already addressed this in his 1989 report Must We Randomize Our Experiment. He advised that experimenters:
- Always randomize in those cases where it creates little inconvenience.
- When an experiment becomes impossible being subjected to randomization
- and you can safely assume your process is stable, that is, any chance-variations will be small compared to factor effects, then run it as you can in non-random order;
- but, if due to process variation, the results would be “useless and misleading” without randomization, abandon it and first work on stabilizing the process;
- or consider a split-plot design.
I am happy to say that Stat-Ease with the release of version 9 of its DOE programs now provides the tool for the compromise, as Box deems it, between randomizing or not, that is—split plots. For now it is geared to factorial designs, but that covers a lot of ground for dealing with hard-to-change factors such as oven temperature in a baking experiment.* Details on v9 Design-Expert® software can be found here http://www.statease.com/dx9.html along with a link to a 45-day free trial. Check it out!
*For a case study on a split-plot experiment that can be easily designed, assessed for power and readily analyzed with the newest version of Stat-Ease software, see this report by Bisgaard, et al (colleagues of Box).
Fake knee surgery shows it not really being needed
As reported here in today’s Wall Street Journal, Finnish surgeons split 146 patients with meniscus tears into two groups and ‘scoped them all, but only half had their cartilage removed. The remainder—the control group—underwent all the same post-operative processes and thus remained in the dark that they really did not get the full procedure. The end results showed that any advantages to this ‘partial meniscectomy,’ which purportedly accounts for $4 billion in annual medical costs on the USA alone, are relatively small and short-lived.
Naturally, an independent orthopedic surgeon asked by WSJ to assess these results did not agree that the arthroscopic procedure might be overdone, even though a previous study showed physical therapy to be just as effective for patients with somewhat similar knee problems.
Without strong affirmative evidence from double-blind studies such as this one, I myself am leery of just accepting any given surgeon’s advice to press ahead with a procedure. As Teppo L.N. Järvinen, co-author of the Finnish experiment, says:
Doctors have a bad tendency to confuse what they believe with what they know.
Cyclists wearing more visible clothes just make it easier for motorists to target them
Tuesday’s Health & Wellness section of Wall Street Journal passed along distressing news for folks like me who like to take a spin on their bicycle. New research by scholars at University of Bath and Brunel University* suggests that wearing noticeable clothes not only did nothing for getting motorists to back off, but when cyclists wore a “POLITE notice, Pass Slowly” vest, they were more likely to be harassed.
Perhaps wearing camouflage like this fellow shown here this fellow shown here might be the way to go.
*Detailed here by IrishCycle.com
White squirrel on fresh snow
On my triple-long commute into town this morning I enjoyed my scenic route along County Road B2 in Roseville. One may as well make a savory slurpee out of the snowstorm as sit in traffic stewing. This route paralleled the gob-stomped Highway 36 so moving along the stopped traffic made this bypass all the more satisfying. I happily paid heed to the calming advice of the mellifluous public radio announcer that “you will get to where you going in due time.”
While admiring the flakes falling on the white-bedecked urban forest I was startled by a clump of snow scurrying down a tree trunk and then disappearing when it hit the deck. It was an albino* squirrel who managed to survive standing out all summer amongst all the greenery. Cool!
You really can see a lot just by looking—to paraphrase Yogi Berra.
*Not being close enough to look it in the eye, I cannot be sure it wasn’t a plain old white squirrel (black eyed) but from the map posted at this website , my guess is it’s an albino. If so, that’s very rare—only 1 out of 100,000 squirrels exhibit this trait, according to my research.
Boo Yahoo for breaking bad on my MAD
Posted by mark in sports, Uncategorized on November 20, 2013
“Once is happenstance. Twice is coincidence. Three times is enemy action!”
— Ian Fleming
, Goldfinger
A simple, yet effective, measure of forecasting prowess is the mean absolute deviation (MAD). Yahoo’s computer projections for fantasy football do poorly on this measure. For example, one of my teams is thus far, through the first 11 weeks of this season, at 16 points MAD from an average projection of 70 per game. That’s an error exceeding 20%! But to make matters far worse, their forecast on this team is terribly biased. Given my indignation you can guess which way Yahoo has been erring (yes, I am a loser)—consistently over-estimating how points my players actually accumulate. Enough data has come in to make this statistically significant as indicated by the confidence interval on the margin of error (MOE) being below zero. Between my fantasy team and the Vikings it’s hard to say which is doing worse at underachieving. Thank goodness for the Minnesota Gopher gridioners exceeding all expectations. That is a ray of sunshine in a gloomy Fall for a football fanatic like me.
Statistics for good (per year-long celebration) or bad (as many still feel)
“As with a knife in a surgeon’s hands, it can save a life, but it could also kill someone, in the hands of a crook.”
— Sastry Pantula, Dean of the College of Science, Oregon State University
This quote caught my eye in yesterday’s Wall Street Journal article on “About 88% Through Year, 100% of Statisticians Find Field ‘Sexy’”—a recap of Statistics2013, which pays homage to the 300th anniversary of Jacob Bernoulli’s landmark book The Art of Conjecturing.*
My interest in statistics stems from a belief that one should live by what you see, not what supposedly should be. In other words, let the data speak. I have little patience for speculation based only on personal opinion, unless it comes from one who clearly possesses great subject matter knowledge—even then I would like to see peer-reviewed research supporting the contentions. The converse of this is being greatly off-put by people who obviously do not know what they are talking about using statistics as a weapon. This is crooked (as noted by Prof Pantula).
But never mind this dark side of statistics, it’s time to celebrate them as Gianluca Massimo and his Italian friends (including students in Statistical Sciences at the University of Padua) did in this ‘bromantical’ music video.
*For a scholarly review and historical context, see “The Significance of Jacob Bernoulli’s Ars Conjectandi for the Philosophy of Probability Today” by Glenn Shafer of Rutgers University.
Quants and nerds bring science and reason to the dark fortress of superstition
Posted by mark in sports, Uncategorized on November 2, 2013
Alison Gopnik, The Wall Street Journal’s “Mind & Matter” columnist, goes a bit over the top today while paying homage to baseball’s statisticians. But one must be mindful that she teaches at U Cal Berkeley—less than 15 miles from the home field of the Oakland Athletics and “Moneyball” wizard Billy Beane. At the other end of the country the Boston Red Sox rule supreme in Major League Baseball in large part to calculations by their adviser Bill James—inventor of sabermetrics: the empirical analysis of baseball, especially statistics that measure in-game activity.
However, BoSox hero (one of many!) Jonny Gomes, who got a lot of disrespect for his measures—yet came through in the clutch, came back with this shot in an on-field interview with FOX Sports’ Ken Rosenthal after the clincher at Fenway Park:
“There’s a lot of sabermetrics, there’s a lot of numbers and stuff. The whole WAR stat. But when you go to playoffs, you want me to go to war with.”
WAR stands for Wins Above Replacement. The Red Sox led MLB on this statistic as shown here. Gomes only rated a bit over 1 on WAR. A “solid starter” should achieve a WAR of 2 or more according to this white paper by Boston’s Yawkey Report.
It’s hard to argue with success, but take that Jonny!