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Last week's column by The Wall Street Journal's "Numbers Guy" Carl Bialik discusses the important distinction between absolute and relative risk. Here's how Bialik explains the latter:

Relative risk tells us how many times more prevalent an outcome or characteristic…is among one group compared with another.

For instance, suppose that a certain behavior, B, increases your risk of getting disease, D. B's relative risk is determined by dividing the risk of getting D if you do B by the risk of D if you don't B. In other words, the relative risk is the ratio between the risk of D when doing B and that when not doing B.

An absolute risk, of course, is a risk that is not relative to anything. So, the absolute risk of getting disease D if you do B is simply the probability of D if B, that is, the conditional probability of D given B (see the entry for Probabilistic Fallacy for more on conditional probabilities).

The problem with relative risks comes about when dealing with rare conditions. For example, if D is a rare disease, then the relative risk of B may be high while its absolute risk is low. Suppose that only 1 in 100,000 people who don't do B get D, whereas 2 in 100,000 Bers come down with D. Then the relative risk of Bing is 2, which may also be expressed as 200%, since twice as many people who B get D than those who don't. This sounds like a lot. However, the absolute risk of Bing is only 1 in 50,000, which sounds like a little. So, doing B makes an extremely rare disease only slightly less rare.

As a consequence, when people want to emphasize the riskiness of something, they may cite only its relative risk rather than its absolute risk. Journalists, in particular, are fond of reporting relative risks because they sound riskier and increase the drama of a story. Whenever a news report talks about something increasing or decreasing risk, it's probably talking about a relative risk.

Sources:

In the Mail: God and the Folly of Faith

Victor Stenger, physicist and author of The Fallacy of Fine-Tuning, has a new book out: God and the Folly of Faith: The Incompatibility of Science and Religion.

Resource: New Books: The Fallacy of Fine-Tuning & Believing B.S., 6/17/2011

Poll finds Obama's approval rating remains steady

It would be bad enough if these three headlines reported three conflicting polls, but the third headline actually reports the same Reuters/Ipsos poll as the first! So, what's going on? Here's the beginning of the article under the first headline:

For the first time since early July, more Americans approve of the job President Barack Obama is doing than disapprove, according to a new Reuters/Ipsos poll that shows his approval rating now at 50 percent. The poll, taken March 8-11…indicates that Obama's rating has risen by 2 percentage points during the past month. The percentage of Americans who disapprove of the Democratic president was 48 percent, down from 49 percent in February.

Both the 2 percentage point rise in the approval rating and one percentage point drop in the disapproval rating are within the 3 percentage point margin of error (MoE) of the poll, so that the third headline is the more accurate report. But what about the other poll reported in the second headline?

You might guess that this divergence is due to the polls being conducted at different times, but the CBS News/New York Times poll reported in the article under the second headline was conducted on the 7th to 11th of this month, thus overlapping almost exactly in time with the Reuters/Ipsos poll. Obama's approval rating was down nine percentage points in the CBS/Times poll, which is well beyond the three percentage point MoE. However, the fact that two polls taken at the same time differ in their results so much is reason for caution. They can't both be right―though they could both be wrong―but, assuming that one is right and one is wrong, we won't know which is which until future polls either confirm or disconfirm the large drop in the approval rating.

To continue the theme begun in the previous entry of praising the news media when they do a good job, The Los Angeles Times has an excellent article on recent conflicting poll results (see the Resource, below), including the ones discussed above. Check it out.

Resource: David Lauter, "Obama is up in the polls―or maybe down", The Los Angeles Times, 3/14/2012

Good News

I tend to be quite negative about news coverage of health and science issues―but what do you expect from a site called The Fallacy Files? However, health news often deserves harsh criticism. For that very reason, though, I think it's a good idea to point out when health journalists do a good job.

CBS News has a well-done report on a study showing a higher risk of heart attacks in men who drink sweetened beverages, such as sodas. The report mentions twice that the study only shows an association, not causation, and that there may be some other reason for the heightened risk of heart attack than the sweet drinks. My only qualm is that the report's first half is a typical health scare story, so that it has a "bad news first, good news second" structure. It would be better if it were made clear at the start that the fact that the soda drinkers had a higher risk of heart attack than the non-soda drinkers does not mean that soda drinking causes heart attacks. However, the typical report of this story would never get to the good news at all, or bury it in the last sentence.

So, well done, CBS!

Update (12/14/2016): The bad news is that this video report appears to be no longer available.

Doublespeak Watch

John Stossel on a recent example of the old political doublespeak of calling an increase a "decrease" simply because it's a smaller increase than originally requested or projected:

President Obama said in his State of the Union speech last month, “We’ve already agreed to more than \$2 trillion in cuts and savings.” That was reassuring. The new budget he released this week promises \$4 trillion in “deficit reduction”―about half in tax increases and half in spending cuts. But like most politicians, Obama misleads. … “We have a budget of, what, almost \$4 trillion? So if we’re doing \$2 trillion of cuts,” [Cato Institute economist Dan] Mitchell said, “we’re cutting government in half. That sounds wonderful.” But what the president was talking about is not even a cut. The politicians just agreed that over the next 10 years, instead of increasing spending by \$9.48 trillion, they’d increase it by “just” \$7.3 trillion. Calling that a “cut” is nonsense. Mitchell gave an analogy: “What if I came to you and said, ‘I’ve been on a diet for the last month, and I’ve gained 10 pounds. Isn't that great?’ You would say: ‘Wait, what are you talking about? That’s insane.’ And I said: ‘I was going to gain 15 pounds. I’ve only gained 10 pounds, therefore my diet is successful.’" Democrats use this deceit when they want more social spending. Republicans use it for military spending. And the press buys it. The Washington Post has been writing about “draconian cuts.” “The politicians know this game,” Mitchell said. “The special interests know this game. Everyone gets a bigger budget every year.” … Bottom line: Don’t trust the politicians’ numbers.

Source: John Stossel, "We are on the road to bankruptcy", Fox News, 2/15/2012

Resources:

Where's the harm?

Here:

The crowds and teams may have long departed Indiana after Super Bowl XLVI, but something else has lingered: an outbreak of measles. Two days before the big game, two people infected with the virus visited the Super Bowl Village together and made stops at a coffee shop, a restaurant and the Indianapolis Colts' merchandise store in Lucas Oil Stadium. State health officials confirmed 13 confirmed cases of measles within two neighboring counties in central Indiana last week. … A 14th case was diagnosed Friday in one of the same counties as the previous cases. … But Larkin said even if the numbers stay where they are, there's a wider lesson to all of this. "This is just so highly infectious and so significantly preventable," he said.

When administered, the measles, mumps and rubella vaccine can be 95 percent effective. In part due to high vaccinations rates in the United States, ongoing transmission of the endemic measles virus was declared eliminated in the country in 2000. But it can still easily spread in pockets of unvaccinated people. Most measles cases in the U.S. can be traced to unvaccinated travelers who vacation abroad, become infected and carry the disease home. According to Larkin, the first 13 individuals infected had all chosen not to be vaccinated.

Although some 90 percent of Americans are immunized, last year more than 200 cases―the highest number since 1996―of the measles were reported in the U.S. … "At a sporting event like the Super Bowl, you are going to have a whole mix of different people gathering," said Dr. William Moss of the Johns Hopkins Bloomberg School of Public Health. … This outbreak isn't the first time measles has spread after a big sporting event. Foreign visitors were blamed for a large measles outbreak following the 2010 Winter Olympics in Vancouver, Canada. A smaller outbreak that occurred after the 2007 Little League World Series in Pennsylvania was traced to a Japanese player.

As global sporting events like the 2012 Summer Olympics in London and the 2014 World Cup in Brazil approach, infectious disease experts say there's little that can be done to prevent a reprise. "It's very difficult, if not impossible for public health officials to regulate that type of thing," Moss said. "It comes back to the question of how do people protect themselves. It's relatively simple: They need to be vaccinated with the measles vaccine."

Source: Allie Morris, "Ind. Measles Outbreak, Linked to Super Bowl, Raises Vaccination Concerns", PBS NewsHour, 2/20/2012

Previous "Where's the harm?" Entries: