Anthrax, Sharks & Probability
We’ve already covered the fact that there is no such thing as objective reporting. What’s worse is when the media perpetuate a self-serving agenda because reporters are ill-equipped to spot when it’s happening. This often occurs when estimates of probability are involved, as we discussed in Medical Risk.
Sometimes it’s funny. Sometimes it’s relatively harmless. Sometimes it scares the hell out of citizens, and sometimes it stops them from being scared when they should be.
Ordinary citizens can’t be expected to sort these things out. After all, most of them buy lottery tickets and believe in astrology. You’d think the news media would help out by being careful not to spread misinformation, but they don't, for two reasons:
1- Misinformation often makes better news than the real story.
2- They don’t know how.
This past August half a dozen people were bitten by sharks in Florida. Town fathers, in scenes humorously reminiscent of several in the movie “Jaws,” frantically sought out reporters so that they could reassure potential tourists that the danger wasn’t real.
As one beach community leader put it, smiling unctuously as he condescendingly delivered information he thought was so obvious should have been apparent to anybody with half a brain, “People need to remember that their odds of being bitten by a shark are about one in fifty million. One in fifty million! Do you realize how low that is? Why, you’ve got a better chance of being hit by lightning in your own backyard!”
To which the reporter nodded in knowing acknowledgment, and left it at that. (“Back to you in the studio, Tiffany.”)
One in fifty million, well; that is low indeed. So should we go swimming in east-facing beaches in Florida?
Not so fast.
The way that odds are calculated is basically quite simple. You divide the number of incidents by the total number of possibilities. What this town father did was divide the number of shark bite incidents (6) by the entire population of the United States (300 million), thusly:
300 million people
…which is how he got one out of fifty million. What could be simpler? What’s to argue?
In fact, I’m surprised that he didn’t divide 6 by the population of North America and come up with calculated odds of 1 out of 80 million, or use the population of the entire planet and get to one out of a billion. Sure would’ve strengthened his case.
Clearly, there’s a problem here. Actually, there are two.
The first is using the number 6 as the numerator. That means the time frame he picked was the month of August. This doesn’t include the number of people who were bitten last year in Florida. It also doesn’t include three surfers who were bitten in California three months before, or 200 crewman of the USS Iowa that went down in 1944 in shark-infested waters. So what he should have said was that your odds of being bitten by a shark during three weeks in August are one out of fifty million if you're not in the military or are at least stationed stateside in peacetime.
That's the problem with the numerator, but a bigger one deals with the denominator, i.e., the population being considered.
You see, probability is the science of what we don't know. The less we know, the more we rely on probability. But relying on probability that fails to take into account what we do know makes no sense whatsoever, unless you're a town father in south Florida trying to fool people into underestimating the danger of the beaches upon which your livelihood depends. Taking into account everything you already know makes your estimates of probability more precise.
Here are some things that we do know that the south Florida town elder conveniently ignored when he used the entire population of the United States as the denominator:
- The odds of being bitten by a shark if you live in Tulsa, Oklahoma, are zero.
- The odds of being bitten by a shark if you live in Wichita, Kansas, are zero.
- The odds of being bitten by a shark if you live in Houston, Texas, are zero.
- The odds of being bitten by a shark if you go flapping around in shallow water at dusk off an east-facing beach in southern Florida in late summer are definitely not zero.
In other words, the only people who should be included in the denominator of the simple division are those to whom the topic is relevant. Since every single person who was bitten by sharks had gone flapping around in shallow water at dusk off an east-facing beach in southern Florida in late summer, that’s the population that should comprise the numerator, because those are the only people for whom the statistic is meaningful. For everybody else, the odds of getting bitten are near zero.
And as for lightning, the odds of any random American getting hit (in a year) may be one out of 10 million, but for somebody who decides to put up a television aerial in Terre Haute, Indiana, during a thunderstorm in July, it’s more like one out of ten
Which brings us to anthrax. Some senator last week reminded us repeatedly that the odds of getting exposed to anthrax were still only 30 out of 300 million (30 people known to be exposed out of the entire US population). That’s true if you consider the entire population.
But once NBC and ABC got hit, the odds for people working at CBS were a little higher than 30 out of 300 million and, sure enough, hit they were. Some people were also smart enough to know that, once the Senate got dusted, the House might be not be too far off. So for the New York Post to call representatives “wimps” in 48-point type for shutting down the session was not only stupid philosophically (as if perhaps snorting anthrax was, like, a manly thing to do) but statistically; once the Senate was hit, the House became the most likely target in the country.
As Mark Twain put it, there are lies, damned lies, and statistics. Speaking of which, I don’t have much of a problem with our government leaders giving us facts and opinions; I have a much greater problem when they overtly try to manage our perceptions. If three thousand people are killed in a terrorist attack and three weeks later anthrax starts popping up in newsrooms and the capitol, we don’t need a senator telling us, “People shouldn’t be scared…just go about your normal business.” Who the hell is he to tell us that, unless he's dealing with a different set of facts than we are, in which case he's lying.
For some reason I've never understood, ever since FDR said we had nothing to fear but fear itself, we've somehow come to accept that as true. Now the thing that our leaders seem to be most afraid of is us being scared. (Which I suppose means they themselves are succumbing to fear. But let's not go there.)
So what's so wrong with fear? Fear keeps us alive. Fear keeps us from getting eaten by lions. Fear motivates us to do things that will keep us from getting killed by terrorists. One would also hope that fear would impel us to get a little smarter about what is worth being afraid of, rather than just watching CNN and believing what is said by people who are good-looking and can read a teleprompter but don't know the first thing about probability but instead believe the very people they should be questioning.
If you don’t buy into any of this, you probably also believe that, on the average, everyone in the world has one breast and one testicle.
Which is 100% correct and 100% useless. Like the shark bite statistics the media bought into without asking any questions.