Stats Made Easy

I am the oldest of seven siblings, so naturally I agree with new evidence reported by Benedict Carey of the New York Times that eldest children develop higher IQs. Aside from getting a big head over this news, what I find intriguing is the assertion by Robert Zajonc, a psychologist at Stanford University, that the main source for intellectual stimulation comes from tutoring — a natural role for the oldest.

“Explaining something … solidifies your knowledge and allows you to grow more extensively.” — Professor Robert Zajonc

That’s why when I teach workshops for Stat-Ease on-site I suggest that students work in teams of two, with the more advanced ones paired up with those that may be just beginning. Both partners learn more as a result of this tactic to encourage tutoring. Also, this purposeful pairing reduces the odds of two slow learners dragging back the class relative to a more dynamic duo. If students are allowed to select their own partners, it seems inevitable that the range between teams of two will be maximized, making it very difficult to achieve just the right pace for presentation.

An editorial cartoon by Steve Sack of the Minneapolis Star and Tribune (pointed out to me by Pat Whitcomb) provides an alternative explanation for why younger siblings end up a bit slower mentally: They get regularly rapped on the head by their elders! If you are the oldest, like me, you will get a kick out of emailing Sack’s cartoon to your family.

Baseball aficionados in Minnesota cringed last month when their home-state baseball star Joe Mauer laid down a bunt with runners at first and second and no outs. However, a self-styled ‘Twin’s Geek’ supported this decision with an interesting statistics grid called the “expected runs matrix” published by Pete Palmer and John Thorn in The Hidden Game of Baseball. I came across this today in the Gameday program for the contest between the Minnesota club and the Toronto Blue Jays (Twins win! :)). If you are a baseball nut like me and enjoy digging into all the stats, check out this case made for making the sacrifice. In a nutshell, statistics compiled over 75 years of major league baseball indicate that Mauer’s success in advancing two runners made the out moot – the expected runs did not change. The Twins’s Geek (TG) thinks that Mauer, the reigning American League batting champ, thought he might get a surprise bunt hit, which would have increased the expected runs by a big margin. However, TG notes that the sacrifice may have gone in vain by not advancing runners (force at third, for example) or created a disastrous double play (pop to the pitcher and double up at first). What made this really interesting for me was the juxtaposition of situational stats provided by Gameday in this same issue. It shows that Joe Mauer is the premier clutch hitter on the Minnesota Twins and possibly all of baseball. For example, he bats nearly .400 with runners in scoring position! Therefore I must say: Joe, give it a go – swing away and make our day!

Researchers from my alma mater, the Carlson School of Management at the University of Minnesota, have discovered that many people become confused when dealing with more than one percentage at a time. For example, when a store offered 25 percent off on top of a 20 percent discount, they enjoyed significantly more sales than the equivalent offer of a 40 percent reduction. Evidently most shoppers simply add the two discounts together — 25 plus 20 in this case.

I recall someone saying they saw an item that went on clearance for 50% off and after going unsold got marked down another 50%. They brought the item to the checkout only to be told by the clerk that this could not be right because then there would be no charge — 50 minus 50 is obviously zero! The shopper demanded that the store manager be called in to resolve the matter. However, after much deliberation, the superior declared that the clerk had it right and refused the sale because the store would go broke by giving away products for free.

Here’s a puzzler that will weed out those who do not deal well with percentages. Imagine you buy a stock for 100 and it shoots up 40 percent but then drops back by 30 percent. How much profit will you make by then selling this stock? See this report by UMNnews for the answer.

In today’s Ask Marilyn® column in Parade magazine, a reader questions whether a commuter might get to work earlier by leaving home later. Beam me to my cubicle Scotty!

I’ve never considered this idea as a possibility, but I have experimented on varying times of departing for my daily commute of 20 miles to the Stat-Ease office in Minneapolis. My goal is to precisely predict the rush periods and avoid them while working within our flex-time rules for full-time workers. The graph shown here illustrates my theory on traffic around the Twin Cities (I drive through Saint Paul from a suburb to the east – Stillwater, Minnesota).* My belief, based on decades of daily commuting and not refuted by these experimental results, is that cars congregate in waves due to differences in working hours – some drivers working the 7 AM factory shift and others expected to be at their desks by 8 AM, for example. For me the most desirable departure is at 6:34 AM,** which maximizes my sleep time and hits a trough in the waves of traffic – still 35 minutes on the road for my average commute. I call it the “hole” and when I hit it right, my car is like the container you put into the drive-through receptacles of the bank – it whooshes me into Minneapolis. My statistical colleagues question my theory due to the sparsity of recorded data, so if any of you can provide support, I’d appreciate it. It boils down to this: Obviously one can leave later and get to work faster, but the trick is not to be late.

*For all the details, see the One-Factor RSM [Response Surface Methods] Tutorial for Design-Expert® version 7 software.

** Refer to the One-Factor RSM Tutorial (Part 2 – Advanced topics) for details on how Design-Expert’s numerical optimizer found the most desirable combination for leaving at the latest, minimizing drive-time and making the results least susceptible to variations in departure via propagation of error – POE.

Professor Scott M. Stanley of the University of Denver in his keynote address to the 2002 Smart Marriages Conference,
What is it with Men and Commitment, Anyway?, cited a survey saying that 85% of divorced couples blamed their breakup on “lack of commitment.” Nadeem Irfan Bukhari, Lecturer on Pharmaceutical Technology for the School of Pharmacy at the International Medical University (IMU), Kuala Lumpur – Malaysia, offers this cartoon that speaks on this vital issue. Nadeem worked for about 10 years as a political cartoonist for the National daily press. I am very pleased that he has consented to contribute cartoons like this with a statistical bent. Thank you Nadeem — very enjoyable!

PS. Having been married now nearly a third of a century, I must counteract my training in statistics that one must never, ever say you are certain about anything. For the record, when my wife asks me this question, I always say “Yes — 100 percent!”