Hypothetical Bias

Math is hard

Virginia Postrel writes about decision research in today's NYT that includes a fun test (Would you take ...):

In decision research, individual differences "are regarded as a nuisance — as just another source of 'unexplained' variance," Shane Frederick, a management science professor at the Sloan School of Management at the Massachusetts Institute of Technology, wrote in "Cognitive Reflection and Decision Making." The article is published in the Fall 2005 issue of The Journal of Economic Perspectives, which includes a special section of articles devoted to "cognition, brain science and economics."

Professor Frederick discovered striking systematic patterns in how people answer questions about risk and patience, including those above. This short problem-solving test, he found, predicts a lot:

1) A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?

2) If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets?

3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half the lake?

The test measures not just the ability to solve math problems but the willingness to reflect on and check your answers. (Scores have a 0.44 correlation with math SAT scores, where 1.00 would be exact.) The questions all have intuitive answers — wrong ones.

Professor Frederick gave his "cognitive reflection test" to nearly 3,500 respondents, mostly students at universities including M.I.T., the University of Michigan and Bowling Green University. Participants also answered a survey about how they would choose between various financial payoffs, as well as time-oriented questions like how much they would pay to get a book delivered overnight.

Getting the math problems right predicts nothing about most tastes, including whether someone prefers apples or oranges, Coke or Pepsi, rap music or ballet. But high scorers — those who get all the questions right — do prefer taking risks.

"Even when it actually hurts you on average to take the gamble, the smart people, the high-scoring people, actually like it more," Professor Frederick said in an interview. Almost a third of high scorers preferred a 1 percent chance of $5,000 to a sure $60.

They are also more patient, particularly when the difference, and the implied interest rate, is large. Choosing $3,400 this month over $3,800 next month implies an annual discount rate of 280 percent. Yet only 35 percent of low scorers — those who missed every question — said they would wait, while 60 percent of high scorers preferred the later, bigger payoff.

Men and women also show different results. "Expressed loosely," he writes, "being smart makes women patient and makes men take more risks."

High-scoring women show slightly more willingness to wait than high-scoring men, while the differences in risk-taking are much larger. High-scoring women are about as willing to gamble as low-scoring men, while low-scoring women are even more risk-averse.

Not to boast, (as he boasts) but I got all answers correct. It took awhile before my first cup of coffee (click on the continuation section for the answers).

Timberlake gets to stomp on Laettner?

From SI's The Ten Spot:

Payback is a, well, you know: A bank in Lexington, Ky., is suing Christian Laettner over a $375,000 loan. Branch Banking and Trust says that Laettner defaulted on the loan that was made last November. The lawsuit, of course, comes 14 years after Laettner broke the hearts of many in Lexington by hitting the last-second shot in a 104-103 overtime victory in the NCAA East Regional. It would be even more interesting if the bank sent out Aminu Timberlake to make the collection.

Will we ever forget Christian stomping on Aminu?

Update: Here is the game story from ESPN.

ratemyprofessor, cont.

John, as usual, was ahead of the curve in a post discussing his rating on  ratemyprofessor.com.
A story in the Raleigh News and Observer focuses on the flip side.  One professor's response to his rating was starting a blog that rates students.

Incidentally, students didn't need to attend my class, I am apparently quite sarcastic, a "tool", and -- most importantly -- not at all a "cutie" like John.  (in truth, all four observations are entirely accurate.) I was also introduced to a new slam on the state's flagship university -- "Carowina".  So my vocabulary is embiggened, and that's a good feat for a Monday morning.

No liberal bias in Krugmans' textbook

From BusinessWeek "up front" (by Peter Coy, $$$):

Making Nice To Make Sales

In his column in The New York Times , Paul Krugman is one of President George W. Bush's most outspoken foes. "Heck of a Job, Bushie," the Princeton University economist taunted on Dec. 30, accusing the President of breaking the law and misleading the public. But Krugman is far more generous to the President in his introductory textbook, Economics (Worth Publishers), which came out on Dec. 22. There he praises Bush's advisers for supporting "aggressive" measures to fight the 2001 recession. Photos contrast a confident Bush with a squinting Herbert Hoover, whose policies worsened the Depression. Far from picking fights with Republican academics, Krugman writes that "media coverage tends to exaggerate the real differences in views among economists."

The homogenization of Paul Krugman may illustrate a basic principle of economics: The customer is always right. Textbooks are chosen by professors of all political stripes. Krugman says in an interview that he and his wife and co-author, Robin Wells, were "extremely careful" to be evenhanded.

So far, Krugman says, there's no evidence that buyers have been turned off by his column. Good thing. His competition includes two of Bush's former chief economic advisers: R. Glenn Hubbard of Columbia University, who has a new textbook, and best-selling N. Gregory Mankiw of Harvard University, whose fourth edition arrives in March.

A numbers quiz from the WSJ's Numbers Guy

The WSJ's Numbers Guy column looks at math mistakes in the news (Monitoring the Numbers in the News). He lays down a challenge to his readers to find some mistakes. Below in italics is my feeble attempt at the answers. The quiz makes me feel like an idiot. A complete idiot.

Each example has a numerical problem. Some are flat-out wrong; others are simply unclear or missing key bits of information. I invite you to put yourself in the role of the copy editor assigned to the article, and write in to suggest how you would change these passages, or which questions you would ask the reporter in order to change them. Send your responses to [email protected], subject line "quiz." In the next column I'll go over the responses.

1. Boosting the state's economy was a central tenet of Governor Smith's campaign as a challenger in the 2002 election. His supporters note that statewide economic growth of 3.5% in 2004 was a new record under Gov. Smith.

Hmmm. Boosting the economy above an all-time high growth rate might be tough? Or, could it be that the economy is boosted even if the growth rate falls, as long as the growth rate is positive?

2. A crowd of 93,356 saw the U.S. women's soccer team beat China, 1-0, to clinch the World Cup. That was the largest crowd to witness a women's athletic event since the 1996 soccer final at the Atlanta Olympic Games, which drew a record 84,975 fans.

I'm stumped, does that make me a dolt? Ok, maybe this is one of those missing information, like the year in which 93,356 same the 1-0 rout?

3. Visa announced that its new credit card will carry an adjustable rate set monthly at four percent above the prime rate, in line with other variable-rate cards.

Hmmmm. I'm stumped again. Or is that that "adjustable rate" and "variable-rate" are not synonymous?

4. The glaciers that span much of Greenland are melting quickly; one of them has more than doubled in speed, moving at a rate of 5.2 miles an hour, compared with 2.3 miles an hour a year earlier.

2.3 x 2 = 4.6 < 5.2 so the "more than doubled part is OK. I think this one has something to do with the time period. Maybe "rate of" should be before 2.3? I'll stop. I'm just guessing.

5. College grades carry the most weight, making up 56% of the final score. Fourteen percent is composed of test scores, recommendations and activities. The final 29% comes from 10 other criteria.

A gimme: 56% + 14% + 29% = 99% < 100% (please tell me that I'm right)

6. Since the displaced soil had a volume of more than 450,000 square yards, construction required many cranes.

Only one crane was required. You can move the same volume with one crane but it will take a longer time period. Many cranes weren't required except to move the volume in a given time period.

7. The charity said it would keep 30% of the funds it raises, with the remaining 70% divided as follows: grants to professors, 35%; grants to students, 20%, and grants to universities, 15%.

The divided amounts should be scaled by 1/.70 so that the remaining 70% sums to 100%: .35/.7 = .50, .2/.7 =. 29, and .15/.7 = .21.

8. Battling Hunger, a food pantry, said it delivered 110,000 tons of food to Detroit last Thanksgiving. The food was delivered to help residents there overcome the effects of a severe economic slump, particularly in the automobile industry.

Imagine John sitting slack-jawed staring at the screen.

9. The football program has a 100% graduation rate, near the top of Division 1 colleges. The national average is below 50%.

A 100% graduate rate would put the football program at the top!

10. Chipper Jones is batting just .176 in 85 at-bats with the Braves. But he has had more success as a pinch hitter, with five hits in 30 at-bats, including one that clinched a playoff spot.

Five hits in 30 at-bats is a BA of .167.

Help!