An Encyclopedia of Probability

A dollar donated by a foundation had about a 1 in 19 chance of being received by an environmental or animal organization in 2004. That’s roughly the same probability that a female age 50 to 59 in the late 1980s drank a fruit drink or ade at least once a day. Such a quirky convergence of two unrelated events is made possible by a new Web site, the Book of Odds, that has compiled thousands of probabilities and grouped them by topic but also by the magnitude of the probability. The idea, according to founder and president Amram Shapiro, is to create “a 19th-century style reference work that met the standards of scholarship” for such works, but which also taps into all the possibilities of an interactive medium. Users, according to Shapiro, will help conquer the fear of uncertainty, which he said “leads to a great deal of mischief.”

Why It’s Hard To Measure Spanking’s Effects

My print column this week examines three recent studies tying spanking of children to their impaired cognitive development. One study, co-authored by Lisa J. Berlin, a developmental psychologist at Duke University, found that spanking at age one is linked to lower scores on a cognitive test at age three. Another study, co-authored by Murray Straus, also ties spanking at one age to lower cognitive scores at a later age. And a third study by Straus, presented at a recent conference, ties nations’ high rates of spanking to lower average IQs.

Skeptics of such studies note that they often fail to demonstrate that spanking caused the measured effects; perhaps cognitive problems are tied to behavioral problems, which themselves cause spanking. Berlin’s study addressed this by examining whether cognitive development at age two was tied to spanking at age three; it wasn’t.

Study: At New York Chain Restaurants, Low-Income Diners Don’t Count Calories

Carl Bialik for The Wall Street Journal

Joey Chestnut may not have noticed, but Nathan’s Famous at Coney Island now reports calorie counts.

I wrote last summer about menu labeling of calorie counts, and questioned whether they would influence diners to make healthier choices. This week, a widely reported study of a New York City law mandating menu labeling in chain restaurants revealed that low-income diners didn’t order lower-calorie meals when confronted by the calorie counts, when compared with New York diners before the law was passed and with diners in Newark, which doesn’t have mandatory labeling. The study undercuts a major notion behind menu labeling: that, when confronted with mammoth calorie counts, diners will choose healthier options.

Pierre Chandon, a marketing professor at Insead, the international business school in France and Singapore, said that the study adds to prior results that are discouraging for menu-labeling advocates. “Although its results are disappointing to those (including me) who are in favor of calorie information in restaurants, they are not that surprising,” Chandon said. “We know that informing people about nutrition value and changing their food preferences are two very different things. In fact, some studies have even shown that calorie disclosure can backfire and increase unhealthy choices among people who, for example, think that unhealthy (high-calorie, high-fat) food is tastier.”

Polling Controversy Raises Questions of Disclosure

My print column this week examines a polling controversy. The American Association for Public Opinion Research publicly criticized Strategic Vision LLC for failing to disclose details about its methods. Blogger Nate Silver analyzed the firm’s numbers and found statistical irregularities. And the firm, though it didn’t respond to Wall Street Journal requests for comment, has defended its work in comments to other publications.

Mathematicians said the Silver analysis was troubling but want to see more evidence. Jordan Ellenberg, a University of Wisconsin, Madison, mathematician, blogged that the case isn’t as persuasive as investigations into possible fraud in the Iranian election. “It’s not so substantial that I would have gone public with it, if it were me,” Ellenberg said, but he does think it merits further investigation.

Lottery Math 101

My print column this week examines the math of the lottery. A government-run gambling game may indeed be a tax on people who are bad at math, as mathematicians, T-shirts and bumper stickers suggest, but it’s also a useful means for exploring concepts in math, particularly probability.

The latest teachable moment came when the same set of six numbers turned up as winners in two consecutive drawings of a Bulgaria lottery. Because each number could range from 1 to 42, and could only be chosen once, there were 42-choose-6 possible sets of winning numbers, or more than 5.2 million. Each one had an equal probability of turning up. Yet what did turn up on Sept. 10 was the same group of six numbers as were chosen just four days earlier. This led to a government probe that cleared the lottery of any trickery. “it just happened,” a spokeswoman for the Bulgarian embassy in Washington, D.C., said.

Counting the Tea Party Protesters

Without an official head count for the inauguration crowd on the National Mall in Washington, D.C., news organizations reported a wide range of estimates. Even before the Tea Party protest against federal government spending in the same place on Sept. 12, supporters and opponents were predicting widely varying figures.