Mark Twain once said, “There are three kinds of lies: lies, damned lies and statistics.” Confusion between correlation and causation has been the source of statistical lies for years. Technology such as radio, TV, and now the internet (especially spam email), have been ripe breeding ground for this sort of misinformation, which is almost always used to reinforce one’s bias.
As polarizing as our news sources can be, I’m not nearly so concerned with bias, which I have come to expect, as with unfounded causal claims – often statistical – that support those biases. With all the bias out there, however, it’s important not to become so skeptical of numbers that we refuse to form opinions about important issues. This apathetic approach is a real temptation for me because there’s just so much data out there. The small portion that is accessible has been neatly packaged into far-left- or far-right-wing ideologies with political strings attached. I mean, really, who has the time to sift through all this stuff?
On the other side of the opinion-forming spectrum, there is a very natural tendency to dive headlong into arguments when we hear statistics that justify our biases, especially from individuals who share our religious or political background. While cultural wisdom should not by any means be thrown by the wayside, when we lazily refuse to combine our analytical thinking powers and overly-rely on others who seem to know what they’re talking about, we risk being deceived and deceiving ourselves. This type of thinking leads to empty rhetoric, populism, and, frankly, an uninteresting existence. Hans Christen Anderson’s famous The Emperor Has No Clothes illustrates this idea well.
Learning to separate correlation and causation is a valuable tool. It often makes it easier to identify bias and discredits the arguments of the overly-biased.
Separating Correlation & Causation
Statistics can show many correlations, meaningful or otherwise. Take, for instance, water consumption and murder rates. While these two behaviors have increased concurrently over time – one could plot their correlative relationship very nicely on a graph – their correlation is not causal, they just happen to be related. Drinking bottled water does not turn people into killers, nor do killers disproportionately demand bottled water, i.e., one behavior does not cause the other.
Consider another demonstrable correlation – shoe size and reading skills. This would be a great science fair project for a third or fourth grader. Your young budding scientist could go around measuring his schoolmates’ shoes and administering reading comprehension tests, generating enough correlative data to make the case for some startling conclusions. After exercising some healthy skepticism and venturing into the world of correlation and causation, he would hopefully conclude that age and, by deduction, exposure to new words, not shoe size, is the probable cause of better reading skills. Ugh, how uninteresting! And he could have attracted so many more visitors to his booth with a flashy title like, “Want Small Feet? Read Fewer Books!”
Generally, correlation is much easier to identify than causation, perhaps because it is so much more prevalent. All causal relationships are correlated, but not all correlations are causal. When we are indifferent to the outcome of the correlation, it is easy to dismiss a cause, but when dealing with a charged issue, say gun rights (no pun intended), something weird happens, especially when we are surrounded by like-minded people. We tend to become blinded to truth, jump prematurely to conclusions, and swallow statistics hook, line, and sinker.
Take the following example of confusion between correlation and causation. It comes from a popular spam email that I’ve also seen surface on Facebook:
Doctors vs. Guns
(A) The number of physicians in the U.S. is 700,000.
(B) Accidental deaths caused by Physicians per year are 120,000.
(C) Accidental deaths per physician are 0.171.
(Statistics courtesy of U.S. Dept of Health and Human Services.)
Now think about this:
(A) The number of gun owners in the U.S. is 80,000,000.
(Yes, that’s 80 million)
(B) The number of accidental gun deaths per year, all age groups, is 1,500.
(C) The number of accidental deaths per gun owner is 0.0000188.
(Statistics courtesy of FBI)
So, statistically, doctors are approximately 9,000 times more dangerous than gun owners.
Remember, ‘Guns don’t kill people, doctors do.’
FACT: NOT EVERYONE HAS A GUN, BUT almost everyone has at least one doctor.
This means you are over 9,000 times more likely to be killed by a doctor as by a gun owner!!!
You be the judge: lie, damned lie, or statistic? . . . While I feel that supporters of gun rights shoot themselves in the foot when they forward this stuff on, I am neither excusing medical malpractice nor making a statement against second amendment rights. I simply use it as an example of the type of misinformation that should be insulting to our intelligence. Falsehoods in general, and correlation/causation falsehoods in particular, often follow a duck-duck-goose pattern, i.e., truth, truth, BIG FAT LIE. And it’s no wonder – throughout history, this type of lie has always been most effective.
All these statistics show is that there is a greater correlation between accidental deaths and people who see doctors than between accidental deaths and people who come into contact with gun owners. You could walk past a non-gun-carrying gun owner on the street or at church, and statistically, this would help lower the latter correlation. So, while relative levels of correlation have been established with fancy statistics, the comparison between the two correlations is pretty meaningless. Here’s why.
In order to prove a causal relationship, in this case that seeing a doctor causes you to die 9,000 times more readily than from accidental gunshot (although the conclusion of the spam mail leaves the accidental part out at the end), one would need to perform a controlled study in which two groups share all meaningful characteristics. People who are seen by doctors typically have health conditions vastly different than your Average Joe walking down the street. Emergency rooms are filled with people having a much higher probability of being accidentally diagnosed and dying as a result than I have of being killed by a gun owner while I sit and type this article.
When we come into contact with a poor line of logic that is being used to persuade us to believe a certain way or do something, we should naturally feel uneasy. Skepticism and doubt are healthy senses that should always be addressed and never ignored. Dealing with these feelings appropriately will weed out mistruths and give us greater clarity and confidence in those assertions that survive the weeding out process. When confronted with biased statistical misinformation, that correlation does not always imply causation is often at the core of our unease.
So, why, I have wondered, does this type of misinformation spread so quickly? To paraphrase someone (and it has never been more true than it is now), “Rumors and lies can make their way around the world before the truth can get out of bed and put its boots on.” One universal human shortcoming is that we are much more entertained by a good story – forget about whether it’s true or not – than the poor old, humble, boring truth. Stretched stories and half truths are strewn throughout the canon of our national literature and songwriting. Hyperbole, machisimo, smoking guns, bravado – this is the American part of us, most expressed in the American South (and to a lesser extent in the West) that is exciting and invigorating. Too much New England sensibility and life becomes uninteresting, even if rational.
Another aspect of our national character that may ripen the breeding ground for poor statistical reasoning is over-confidence in our moral superiority. Most of us see ourselves as moderate with all the coo-coos on either side of us. I know that’s how I see myself as a driver – everyone else drives either too fast or too slow. When we are convinced that our way is the right way, statistics that confirm our previously-held conclusions simply don’t undergo the same amount of scrutiny as those that question our conclusions.
Both of these tendencies – flare for the dramatic and certitude of one’s rightness – can be used to either further human progress or dull its mental capacity. They led Jefferson to write the Declaration of Independence but they also led a misguided spammer to claim that doctors kill 9,000 times more people than gun owners.
One of my big concerns and, I suppose, a source of sadness, is that as we become more and more informed in this information age, we are not becoming, as one might expect, more unified. On the contrary, we are becoming more opinionated and polarized. Information, much of which is statistical, has become a weapon for putting down others. What we are doing with information is destroying our civility. Social networking is pushing us further into circles of shared belief and the people with whom we share information are becoming more homogeneous. At some point, when we come to believe there can’t possibly be anything new that we haven’t already considered, when our world becomes so narrow that we despise surprise, we enter a thick-walled box of self-deception that is at the root of conflicts small and large.
So what? I guess my conclusion is that we should avoid judging too quickly without a fair level of sophistication on one hand, and we should avoid not judging at all due to apathy on the other hand. And whatever we conclude, we should leave some room for surprises.