Correlation and Causation

Read this example-rich tutorial, which explains the difference between the two relationships of correlation and causation. Scientists looking for cause-and-effect relationships in the natural world need to be careful not to misconstrue causality with mere correlation.

We experience the world in a time-oriented manner through cause and effect. First Lucy ate that white berry, then she became sick. First I hit Bob's foot with a hammer, then his foot swelled with a purple bruise. I conclude that eating the white berry is what actually made Lucy sick later. I conclude that being hit with a hammer is what later caused Bob's foot to swell. It is logical enough on the surface. Often, it seems clear--absolutely clear--that a specific action caused a second event to happen. This is what is known as causation. Many events appear to be the results brought about by identifiable causes, and the human mind is geared to look for these cause/effect relationships.

We get into trouble when the mind seeks or creates an artificial cause/effect relationship that doesn't actually exist. After something especially beneficial or harmful occurs, we want to know what caused it. We tend to focus on the first action we noticed before the effect, then assume that it must have been the catalyst triggering the later event. Nine times out of ten, we're right. It was the white berry that made Lucy sick. It was true that hitting a foot with a hammer makes that foot swell and bruise. That makes us lazy intellectually; we forget that, one time out of ten, we pick the wrong cause. In Latin, this type of logical mistake is called the post hoc ergo propter hoc fallacy, which means "After this, therefore because of this." It's the idea that any event which happened first must be the particular event that caused a good or bad event later, and once we find a possible answer we tend to snatch hold of it and then stop thinking about other possibilities. 

For example, suppose the fall term of classes ends in December. The manager of a toy store in the local mall hires one new worker. This worker is a college student named Stacy. She wants to do some work before spring term classes start. After Stacy is hired, the store's sales shoot up by 300%. "Wow!" the manager says to herself, "That Stacy is a fantastic sales worker! I haven't hired anyone else but Stacy. Still, since we hired her, our sales have tripled! I'd better give her a raise!" Is the manager's conclusion logical? Is it true that Stacy must be fantastic at her job?

Odds are, nine out of ten readers at this point are nodding, thinking to themselves, "Yeah, it makes sense to me. You hire a new girl, and the sales go up. No other girls were hired. It must be the new girl's work."

On the other hand,the tenth reader stopped and thought, "Wait a minute.... Didn't you say Stacy was hired in December? That's right around Christmas time. Maybe the reason the sales went up wasn't because of Stacy, but because of the time of year." The manager's conclusion now vanishes in a puff of logic.

Which one were you? If you spotted the logical fallacy, puff out your chest and strut around in pride as an intellectual champion. You were clear-headed and avoided the post hoc error. If you didn't spot the problem, and made the same assumptions the manager did, don't feel too ashamed. Often causation is trickier than it looks.

The problem is that correlation is different from causationCorrelation is when two or more things or events tend to occur at about the same time and might be associated with each other, but aren't necessarily connected by a cause/effect relationship. For instance, in sick people, a runny nose and a sore throat correlate to each other--they tend to show up in the same patients. That doesn't mean runny noses cause sore throats, or that sore throats cause runny noses, however. Forgetting that leads to sloppy thinking. 

Proud journalists point out that, in the last hundred years, no peaceful nation with a free press has ever experienced severe famine. They argue that freedom of the press prevents blunders in governmental policy and it allows more efficient advertising and dispersal of commodities like food. But is that true? On the other hand, no country with a tradition of honest, publicly monitored elections has ever experienced massive famine in the last hundred years either--at least not in times of peace. Which factor "caused" the surplus agriculture and trade to prevent the fearsome famine? Was it free speech or free elections? 

Arguably, neither caused it. Perhaps it's all accidental. Free speech or elections might have no effect on agricultural output. Or have we got our cause and effect backward? Did having sufficient food ensure a stable society so that free speech and democracy could blossom in the first place? Perhaps in famished lands, free speech and free elections fall by the wayside during and after the famine, and thus these hungry countries tend to slide into repressive dictatorships. If that's true, then repressive dictatorships might not actually bring famines upon themselves through clumsy management or a lack of advertising, as earlier suggested. 

This is not just a moot intellectual point. Public policy often hinges on spending money to bring about a specific effect. For instance, consider New York City in the 1980s. The city at that time was a dangerous place. Crime was at an all-time high then. Murders, prostitution, and drug-dealing had reached epic levels. New York had tried stiffer penalties, longer jail terms, mandatory counseling, methadone treatments, and a variety of other approaches without denting the ugly problem. Mayor Guiliani hired researchers to come in. What was one of the early findings? Analysts spotted a correlation between graffiti in an inner-city neighborhood and the relative crime-rate in that area. The more graffiti, the higher the crime rate. Treating this as a cause/effect relationship, New York's mayor Guiliani decided to alter the funding for the police department, cutting back money for some types of law-enforcement, pouring money into an city-wide anti-graffiti campaign, and arguing that a cleaner city would diminish the visual "mindset" of crime in the area. He enacted a zero-tolerance policy by prosecuting taggers who painted on public property, and he cleaned up Times Square and the trashiest parts of the city. As overall crime rates dropped in the 1990s, the mayor touted his program as a success. 

Impressed and surprised, other cities tried to duplicate New York's approach. They enacted similar financial policies and created similar laws. They hauled in hoodlums and cleaned up graffiti . . . and they all failed miserably. Crime in these cities either remained the same or in one or two cases, worsened slightly, even though the changes they made were nearly identical to that of New York. 

What happened? Why couldn't they duplicate New York's success? The problem may be one of false causation. That correlation between the amount of graffiti and the overall crime rate doesn't necessarily mean that graffiti causes crime to happen--no more than the correlation between black eyes and broken noses in people who lose fist fights means that black eyes "cause" broken noses. The crime-rate in an area also correlates to the rate of unemployment, for example, and New York's unemployment was dropping steadily through the 1990s. Perhaps rising employment caused crime to drop at just about the same time the mayor started his anti-graffiti campaign. The rate of drug abuse in a given area also correlates to the number of crimes in that area. The city had started constructing larger drug treatment clinics in the late 1980s after the decade's peak of cocaine addiction. Although the construction funding had been spent in the late 1980s without visible effect, many of these clinics actually started operation only two or three years before the fall in crime in the early 1990s. Perhaps after two or three years of treatment, a significant fraction of cured addicts no longer needed to engage in crime sprees to support an expensive and illicit habit. It's not at all clear if there was just one cause--maybe the combination of rising employment, drug clinics, and the mayor's anti-graffiti campaign together had a synergistic effect that was missing in other cities where the anti-graffiti program didn't work. One recent book on applied economic theory, entitled Freakonomics, has gone so far as to suggest plausibly the source of the crime-drop nationwide in the late 1990s and the early 2000s has been an unintentional result or by-product of abortion policies thirty years earlier!

To give a more recent example, on June 28, 2003 Reuters News Agency reported on a Hungarian medical study of 221 men who carried cell phones. The study found that men who carry cell phones in the front pockets of their pants rather than in a jacket or briefcase had a 30% lower sperm count than the average male population as previously measured in 1970. Immediately an outcry appeared to start lawsuits against cell phone companies for causing sterility in men, and some consumer watchdogs called for warning labels on cell phones. 

The problem is that the study only found correlations--it did not determine clear causation. As Dr. Hans Evers pointed out, many individuals who carry their cell phones in their pants pockets rather than their jacket pockets do so because they are smokers. They carry their cigarette pack in their jacket pockets instead of a pants pockets--to avoid crushing their cigarettes--and thus must carry the cellphone in their pants instead. It has long been known that smokers have a reduced sperm count. Perhaps smoking caused the lower sperm count rather than position of the cell phone per se. Also, the study did not take into account other factors like stress levels (stress can also cause a drop in sperm count); perhaps the men carried cell phones constantly because of a stressful job in which they needed to stay in contact with a company twenty-four hours a day. Finally, the overall sperm count of men may have dropped locally or globally as a whole since the earlier 1970 findings used as a control--possibly due to the increasing levels of chemical pollution worldwide. (Male alligators in parts of Florida, for example, also have 30% lower sperm counts than they did in the 1970s, but nobody thinks that's a result of their cell phone use!)

The point to all this is that, if you are writing an argument, and you claim a cause-effect relationship exists, you should double-check and triple-check that it is causation and not mere correlation. It's hard to nail down causation conclusively, as evidenced by tobacco company lawyers who argued for forty years that smoking merely "correlated" to lung cancer rather than actually caused it. However, the least you can do is pause and ask yourself what other possible causes exist in addition to the one you point to in a paper. If they do exist, you need to think through the evidence and determine why these other causes are less likely than the one you propose.

Source: L. Kip Wheeler,
Copyright Dr. L. Kip Wheeler. Permission granted for non-profit, educational, and student reproduction. 

Last modified: Wednesday, September 11, 2019, 4:17 PM