Posts Tagged statistics
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.
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.
Poll says no MOE to the current Congress—83 percent disapprove
I just saw this NBC/WSJ poll graphically displayed on the nightly news. In the small print I saw “MOE +/- 3%” which threw me for a moment wondering if this data was being disrupted by the leader of the Three Stooges. But then I realized this was the margin of error. For a helpful detailing of MOE that breaks things down to simpler terms—a giant jar of a 200 million jelly beans—check out this white paper by Roper Center. Despite the inherent uncertainty of polls (estimated by MOE), the politicians in Washington cannot discount this clarion call (a record percent!) for change.
“naked statistics” not very revealing
Posted by mark in Basic stats & math, pop on July 18, 2013
One of my daughters gave me a very readable book by economist Charles Wheelan titled “naked statistics, Stripping the Dread from the Data”. She knew this would be too simple for me, but figured I might pick up some ways to explain statistics better, which I really appreciate. However, although I very much liked the way Wheelan keeps things simple and makes it fun, his book never did deliver any nuggets that could be mined for my teachings. Nevertheless, I do recommend “naked statistics” for anyone who is challenged by this subject. It helps that author is not a statistician. ; )
By the way, there is very little said in this book about experiment design. Wheelan mentions in his chapter on “Program Evaluation” the idea of a ‘natural experiment’, that is, a situation where “random circumstances somehow create something approximating a randomized, controlled experiment.” So far as I am concerned “natural” data (happenstance) and results from an experiment cannot be mixed, thus natural experiment is an oxymoron, but I get the point of exploiting an unusually clean contrast ripe for the picking. I only advise continued skepticism on any results that come from uncontrolled variables.*
*Wheelan cites this study in which the author, economist Adriana Lleras-Muney, made use of a ‘quasi-natural experiment’ (her term) to conclude that “life expectancy of those adults who reached age thirty-five was extended by an extra one and a half years just by their attending one additional year of school” (quote from Whelan). Really!?
Issues on inflation, such as 79.6 billion percent in one month
May’s National Geographic pictured a very impressive One Hundred Trillion Dollar bill from the Reserve Bank of Zimbabwe, which in November of 2008 hit the 79.6 billion percent level for inflation before stabilizing their currency. Check out the 100T note here. You can buy one of your own for less than ten bucks USD!
Meanwhile back home in here in the USA everyone is up in arms over a measly 0.1 percent difference in inflation caused by “chaining” our CPI. The gist of this is explained in this recent Time-magazine personal-finance column. It seems like much ado about very little. However, those who get cost-of-living adjustments (COLA) fight like crazy over anything that reduces their income. Here’s a spin on statistics: A 0.1 percent reduction from 1.5 percent is actually a 7 percent loss in COLA. No wonder seniors want to throw off those chains!
The fiddling with money supply and shenanigans on inflation computations reached a new low not long ago in Argentina when the government forced out statistician Graciela Bevacqua for rounding rather than dropping decimal points, which made the government look better with their official rate. It’s all reported here by The Economist. Now working in private industry Bevacqua continued to present a truer calculation on inflation and got fined $100,000 for her honesty. After an uproar from far and wide, including the American Statistical Association (ASA), the courts in Argentina overruled the government and spared this outspoken statistician, according to this news from Buenos Aires Herald. Someone ought to give her a medal for speaking the truth. But as the great statistician George E. P. Box said:
“Whenever we see virtue rewarded, we are completely surprised.”
Educational fun with Galton’s Bean Machine
Posted by mark in Basic stats & math on June 3, 2013
This blog on Central limit theorem animation by Nathan Yau brought back fond memories of a quincunx (better known as a bean machine) that I built to show operators how results can vary simply by chance. It was comprised of push-pins laid out in the form of Pascal’s triangle on to a board overlaid with clear acrylic. I’d pour in several hundred copper-coated BB’s through a funnel and they would fall into the bins at the bottom in the form of a nearly normal curve.
Follow the link above to a virtual quincunx that you can experiment on by changing the number of bins. To see how varying ball diameters affect the results, check out this surprising video posted by David Bulger, Senior Lecturer, Department of Statistics, Macquarie University, Sydney, Australia.
Mind over matter—scale malfunction leads to temporary euphoria
Posted by mark in Consumer behavior on May 26, 2013
I’ve diligently recorded my weight every several days for some years now. The short-term variation always astounds me—going up and down by a number of pounds from one week to the next. However, on average month-by-month my weight remains surprisingly stable. Unfortunately the trend over years is very slightly, but significantly, upwards. Thus my battle against the bulge continues.
A few weeks ago I stepped up for a weighing and received a pleasant surprise: It seemed that I’d dropped 10 pounds during a five-day business trip. Although deep down I knew this could not be, I indulged myself for the day with the thought that something magical had whisked away this weight. Then after getting home from work I got back down to earth by discovering that the base of the scale had got off kilter. I mentioned this to my wife and daughter. It was funny seeing them being so crestfallen—they also were hanging on to the belief in a mysterious, but real reduction.
I suppose all this supports the use of control charting* for filtering out common-cause variability (not worth reacting to) from statistically-significant process upsets (special causes that merit attention). At least that’s what my logical side says. On the other hand, it was fun to believe for some hours in supernatural forces. Ignorance can be bliss!
*(See this detailing posted by the George Mason University College of Health and Human Services.)
Brain scientists flunk statistical standards for power
Last week The Scientist reported that “Bad Stats Plague Neuroscience”. According to researchers who dissected 730 studies published in 2011, neuroscientists pressed ahead with findings on the basis of only 8 percent median statistical power. This falls woefully short of the 80 percent power that statistician advise for experimental work. It seems that the pressure to publish overwhelms the need to run enough tests for detecting important effects.
“In many cases, we’re more incentivized to be productive than to be right.”
– Marcus Munafo, University of Bristol, UK
Statistics provide a decisive advantage to taking one route to work versus another
Posted by mark in pop, Uncategorized on April 7, 2013
See the results graphed on an experiment I just completed to decide whether to commute straight in to Minneapolis on Minnesota Highway 36 or take US Interstate 694 –a speedier, but longer, freeway bypass. Notice that the least significant difference bars do not overlap, thus providing more than 95 percent confidence that the scales tilt to one way (36) being faster–to put it simply.
For each run into work I randomly chose one route or the other based on a recipe sheet produced by Design-Expert software and timed it with a stopwatch app on my smart phone. Then I entered the results in the software and it gave me the answer I wanted.
It appears that I can save the better part of a minute by not shooting around on 694. That is good to know!
Speak softly but carry a big statistic
I heard on CBS Radio radio today this play on Teddy Roosevelt’s famous words. It was quoted by U.S. Senator Amy Klobuchar as her secret weapon (statistics, that is) for women politicians. Searching internet I think it originated from Anne E. Kornblut in her book Notes from the Cracked Ceiling in a section dedicated to Klobuchar. She (the Senator) figures on making an impact on the impasse over the coming “fiscal cliff”. I have no doubt that Senator Klobuchar and scores of other politicians, male and female, will be slinging a lot of statistics during this debate on how to avert financial disaster for us taxpayers. It will take some work to ferret out what’s really true out all the partisan hyperbole.