This article first appeared in the St. Louis Beacon, Jan. 22, 2009 - A friend of mine came to me recently with a riddle he'd heard on a TV quiz show. It had him stumped and he wanted to see if I could help him solve it. Here's how it went:
Three people go out to dinner. At the meal's end, the waitress presents them with their bill in the amount of $25. Each diner contributes a $10 bill for a total of $30. The waitress brings them five one's for their change. They split the change by taking one dollar apiece, leaving the remaining $2 for the waitress.
Since each person gave a ten dollar bill and got a one in return, they ultimately paid $9 apiece. $9 x 3 = $27. The waitress' tip brings the total to $29. What happened to the missing dollar?
My initial reaction was to explain that the entire incident was improbable because people this cheap would have eaten at home. What kind of dining experience can a party of three expect for 25 bucks? And don't even try to get the waitress' phone number after leaving her an 8 percent tip.
That said, the solution to the riddle is fairly simple: The dollar isn't missing because it doesn't exist - it's an accounting figment created by an inaccurate conceptualization of the problem. The $27 the three skinflints paid included the meager tip for the miffed waitress. By improperly adding that amount to the total paid, you count the tip twice and thus create the illusion of a missing dollar. The only reason that the dollar is "missing" is because the riddle tricks you into thinking it existed in the first place.
I mention all this to point out how important the formulation of a problem is to its ultimate solution. If an engineer were to make a mistake like the one cited above, his bridge would collapse into a ravine and his error would be readily apparent. In matters of public policy, however, where the desired outcome can be both vague and remote (e.g. "better public health"), we can spend billions of dollars and years of effort chasing phantoms.
Secondhand Smoke
Nowhere is this tendency better illustrated than in a study recently released by the Centers for Disease Control. Breathlessly reported by an uncritical press, the study purports to demonstrate that eliminating secondhand smoke in public places results in dramatic reductions in the rate of heart attacks.
The city of Pueblo, Colo., enacted a smoking ban in 2003. Researchers compared the 2002 heart attack rate of 257 per 100,000 people to the 2005 rate of 152 per 100,000 and concluded that the smoking ban had caused the heart attack rate to drop by 41 percent. This is a bit like reasoning that because my dog barks when the mailman comes, if the dog is barking, the mail must be here. Question: Is there anything else that might prompt the dog to bark?
The pre-ban rate translates to .26 percent of the population being afflicted with heart attack in a given year. The post-ban rate reduces that number to .15 percent. The variation thus affects just over one-tenth of 1 percent of the total population. While every life is precious, this difference can be explained as easily by random chance as it can by improvements in public policy.
Reports cite previous research in Helena, Mont., that also found a significant drop in heart attacks following the enactment of a smoking ban. But as Jacob Sullum argues in Reason magazine, if smoking bans were causing this phenomenon, we should see similar declines wherever they're put into place. Yet, there's no evidence that the populations of New York, Chicago or Los Angeles are enjoying better heart health as a result of their respective smoking bans.
Remarkably, the researchers in the Pueblo study neglected to discriminate between smokers and non-smokers among their heart attack victims. By failing to isolate the independent variable (secondhand smoke inhalation), they render measurements of the dependent variable (heart attack rates) meaningless because they can never demonstrate that the former caused the latter to occur. This is the kind of fundamental methodological flaw that will get you thrown out of the 6th grade science fair.
Indeed, Dr. Michael Siegel of the Boston University School of Public Health reports that smokers comprised about 26 percent of the population in Pueblo County in 2002 and less than 21 percent in 2005. That's 5,000 fewer smokers per 100,000 people. As it's widely understood that smoking is horrible for the health of the smoker, couldn't the decline in active smoking just as easily explain the decline in disease?
A Real Study
Rather than argue over the fate of the missing dollar, maybe it's time we determined whether the damned thing even exists. In the spirit of empirical research, I offer the following challenge to both anti-smoking zealots and tobacco industry flaks:
Form a bi-partisan research team jointly funded by smoking ban proponents and their adversaries. That should off-set research bias as each side can keep an eye on the other.
Sample the air in both the smoking and non-smoking sections of bars and restaurants where indoor smoking is allowed. Purchase 300 white mice: the stalwart victims of medical research. Divide the mice into three equal groups.
Expose Group #1 to eight hours a day of smoking section air, thus simulating the experience of a non-smoking employee working in a smoking environment. Subject Group #2 to eight hours per day to the atmosphere of the non-smoking section, representing non-smoking employees' working nearby a smoking environment. Group #3 remains smoke-free.
If secondhand smoke is truly lethal, Group #1 should have the highest mortality rate, Group #2 the second-highest, while Group #3 should be the longest-lived. A reliable finding to that effect indicates a causal relationship.
As of this writing, the only thing we can say for sure about secondhand smoke is that it stinks. And so do the research methodologies of its critics.
M.W. Guzy is a retired St. Louis cop who currently works for the city Sheriff's Department. His column appears weekly in the Beacon.