5 Ways Statistics Are Used to Lie to You Every Day

5 What We Call "Average" Actually Isn't

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Here's a shocking statistic: The average income in the United States is around $70,000. If your income is below that level, reading that is quite a kick. You thought you were actually doing pretty well for yourself, but now you're tempted to get a second job just to bump your net worth up to what the asshole next door is probably making. What's their secret, damn it? Are they all cooking meth?

The Problem Is ...

The popular use of the term "average" is way different from the mathematical term, but they get used interchangeably. That's why we're so often shocked at how the "average" person is richer/fatter/taller than us. In everyday language, we use the word "average" to mean "most people," or the most representative person (as in, "The average person doesn't read classic literature" or "The average Joe can't afford to dress like Prince"). But then when they start using the word "average" to talk about statistics, you get weird results, like the fact that 67 percent of people in the USA make less than the "average" income. So how the fuck can "average" mean "most people" when most people aren't average?

Well, we all learned in school how to calculate an average: You take all the values you're averaging, add them up, and divide them by the number of values. This is fine if what you're trying to average is pretty uniform -- the average of 1, 2, 3, 4, and 5 is 3, right there in the middle. The problem is that averages are absolutely useless if a minority of numbers are unusually high -- the average of 1, 2, 3, 4, and 40 is 10, which doesn't help anybody know shit about anything.

And that's the problem with the "average income" statistic -- a few rich people are skewing the shit out of the number. If you're earning less than the average income, it's not because your job is screwing you, it's because you live in the same country as Bill Gates, Mark Zuckerberg, and whoever owns Coke. Mr. Coke or whoever.

Why Does It Matter?

This is so stupidly obvious when explained, but it creates more myths by the day. For instance, you can see one study showing that for every 100 Americans, there are 88 guns, which could lead someone to reasonably assume that it's hard to find an American who isn't packing heat. Then you see another study from the same year showing that only 43 percent of households have guns in them. It's the same deal -- the people who have tons of guns skew the average upward ... and in the process make it hard as hell to get an idea of the overall picture. More often than not, telling us the average just muddles the issue.

That's why most reputable sources who try to figure out wealth distribution use the median income, not the average. The median is the actual middle point: You get there by crossing out values on either end until you get to the center, which gives you a more relatable sum of around $50,000. There, we've just made 17 percent of you feel a little better about yourselves.

4 A Claim of "99 Percent Accurate" Can Be Both True and Meaningless

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You're sitting on the bed in the doctor's office, and he's got bad news. You've tested positive for some kind of cancer. You say, "Are you sure, doc?" and he goes on to inform you that the particular test they used is 99 percent accurate at detecting cancer when it's there, and it produces a false positive only 1 percent of the time in healthy people.

Holy shit, you're 99 percent doomed! Strap on your parachute and buy a monkey, it's time to start on that bucket list!

The Problem Is ...

Actually, even though everything the doctor said was true, there's still only a 1 in 80 chance that you have cancer.

Wait, what? How is that possible? Because what you have come down with is instead an acute case of base-rate fallacy.

Yes, it's true that if you have cancer, the test is 99 percent accurate in telling you -- meaning out of 100 people with the disease, it only misses once. The problem is that other number; the fact that when the cancer isn't there, it still comes back positive 1 percent of the time. So in the course of trying to find the cancer, it's telling so many other people that they have it that a positive result almost becomes meaningless. How can that be true when it only gives a false positive 1 percent of the time? Because that's still a huge number.

For instance, the number of people with, say, pancreatic cancer is actually only about 1 in 8,000. But if this test gives a "you have cancer" result in 1 percent of the cases, the doctor would tell 80 of those 8,000 people they're sick -- even though statistically, only one of them actually is. So for any one person, a "you have cancer" result only has a 1 in 80 chance of being true. It's still good reason to take more tests, but probably not enough to tell your boss off and start cooking meth.

Why Does It Matter?

A lot of technology makes promises like this that sound impressive, but only if you ignore the base rates. For example, in the U.S., the Transportation Security Administration a few years ago started talking up their new terrorist screening technology. They claimed it could catch over 99 percent of terrorists that pass through, while only identifying 0.01 percent of innocent people as al-Qaida operatives.

Those numbers sound fantastic, but as with our cancer example, this means that a gigantic number of innocent people are getting treated as terrorists. So for instance, in 2010, about 700 million times, somebody boarded a plane that flew in the USA. If their terrorist detector "only" throws out positives 0.01 percent of the time, that means 70,000 fucking people are getting pulled out of line, accused, and searched. And in most years, statistically 0 percent of those people are terrorists. So that 0.01 percent sounds great, until you're the one they accuse of having a tiny bomb wedged in your rectum.

3 Claiming to Be the "Fastest Growing" Group/Company/Etc. Might Not Be All That Impressive

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We recently mentioned a viral video that went around talking about how everyone should be afraid of the looming Muslim threat. Islam is, after all, "the fastest-growing religion in the world." Run!

Some respected and reputable sources have carried this headline, and conservative commentators cite it as evidence that Western nations are soon going to have to cloak our women and bow down to Mecca unless we wise up and start simultaneously banging Christian women and being mean to Muslims.

The Problem Is ...

Most sources who bring out the "fastest-growing religion" statistic are using percentages to get there -- has the religion doubled in size? Increased by half? By that measure, Islam figures pretty highly, increasing by 2.13 percent per year. But there are at least two religions higher on the list. Can you guess which? Hinduism? Buddhism? Try Zoroastrianism and Baha'i, weighing in at 2.65 percent and 2.28 percent, respectively. Forget hijabs and turbans -- you better get used to following a 19-month calendar and praying to the great Ahura Mazda.

Which is to say, going by the rate of change isn't that helpful. If the bacon-based cult that your crazy uncle and his four friends invented gains two members at the local country club, then the Church of Baconism just grew by 40 percent.

So if you turn things around and measure a religion's growth by sheer number of new adherents per year, then the religion that had the most people join, convert, or get born into it gets the "fastest-growing" title -- in that case, it's probably Pentecostal Christianity.

Going by the other measure gives us the rate of change fallacy, which only becomes meaningful if you can somehow predict the future. If Baconism continues to grow at 40 percent per day, then after two months they'll have 5.7 billion followers! Or, it could stay right at seven until they all have heart attacks at age 43.

Why Does It Matter?

"But Cracked," someone is already saying, "the fact that they're the fastest growing still means that if current trends continue, they'll eventually be number one!"

Right, if current trends continue. But current trends don't always continue, otherwise the alarmists would have no reason to be alarmed -- their whole reason for freaking out is that some prior trends didn't continue. The point is, any time you hear a company boasting of being the "fastest growing," you should take a moment to find out if they mean they just increased their workforce from three to six people before you invest.

And if someone is using "fastest growing" as a way to make you scared of another group, you might want to stop and consider if they're full of shit for other reasons.

2 What They're Calling an "Epidemic" May Actually Be Random Chance

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Studies show that people who live near power lines have a higher rate of cancer and other diseases! That means electricity is quietly killing you from within! It's a good thing that right this minute, your face isn't near any glowing devices that run on electricity ...

The Problem Is ...

The "power lines cause cancer" thing was a real study that caused real panic not too many years ago. They looked at a map, drew a circle around people who lived near power lines, and looked up what diseases those people had. Sure enough, it wasn't hard to find neighborhoods just chock full of tumors.

But in doing so, they fell victim to what is called the Texas sharpshooter fallacy, or the clustering illusion -- that's when you see false patterns in random data. The name alludes to a theoretical cowboy who shoots randomly at the side of a barn, then paints a target wherever the most shots are clustered together and tells people he's a sharpshooter.

The truth is that in a large enough population, you're going to get random patterns -- especially if you give yourself infinite room to find similarities. For instance, the above study may also have found that kids living near power lines are 5 percent more likely to be named "Steve," or that they are 3 percent more likely to prefer red bicycles. When you're talking about tiny differences, you can find all sorts of weird-ass connections. So, they found that in some areas, kids were up to four times as likely to have leukemia (holy shit! Power lines are murdering our children!), but they ignored the fact that in other areas, the kids were actually less likely to have it (holy shit! Power lines have magical healing abilities!). In reality, it was all averaging out.

And if you just found yourself saying, "Yeah, but with those kids who were four times as likely to get sick, there has to be something to it," you've already forgotten at least two of the points in this article (hint: leukemia is rare and it doesn't take many cases to get a fourfold increase).

Why Does It Matter?

Remember that crazy story about the guy in Miami who went insane and ate another dude's face off? Then every day after that, there was another story of a biting attack? Even the skeptics were all "Wow, another crazy person bit somebody on the subway! There has to be something to this."

And there was: When humans get into fights, we tend to bite each other, but only in the wake of the Miami thing was there any reason for such incidents to become news -- the only thing that changed was that suddenly every bite became a headline. We started looking for a pattern, and there it was. Then we quickly got bored with it, even though right now somebody, somewhere, is biting someone else.

Over the centuries, this fallacy has caused us to invent entire epidemics out of whole cloth. Hell, this is even thought to be one of the reasons for the "witch hunts" that took place throughout history (or, you know, today) -- everyone in the neighborhood suddenly got sick, there's a weird woman living in the neighborhood, therefore said woman must have caused the sickness using her devil magic.

Now, sometimes the trend is in fact real, but caused by something totally unrelated. That brings us to the biggest fallacy of them all ...

1 Correlation Does Not Equal Causation

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The media love to report on the latest scientific study that tells us what's going to kill us today. According to this report on a study about the effects of television on health, scientists are stunned to discover that watching TV is as bad for you as smoking cigarettes after finding that every half hour of TV you watch after the age of 25 shaves a whopping 11 minutes off your life. But how can we possibly cut down when there are six whole shows about baking cakes?

Or, you may have run across someone who still believes that vaccines cause autism in children -- they may even have incredibly convincing line graphs showing that, yes, as the rate of vaccination has gone up, so has the rate of autism diagnosis. How can you argue against graphs?

The Problem Is ...

If you know anything about how a television works that doesn't involve the word "sorcery," then you'll notice that it's just a box of lights and wires. It's difficult to understand how a benign pile of electronics can suck your life force out of your body from the other side of the room. And that's the problem -- the article is reporting on a causation, when all it really has is a correlation.

The difference is that until you know how television is murdering you, all you know is that television and death are related in some way. There's no way to tell whether watching a lot of television and dying a little earlier are both symptoms of something else.

And that, by the way, seems to be exactly what's going on here -- it turns out that people who don't like exercise tend to reach for hobbies that don't involve moving (like television), and not getting enough exercise is what's killing us. Which is to say, reading a book is much more deadly than watching TV on a stationary bike.

Another well-known example is the myth that kids who eat breakfast perform better at school. It's true that the statistics do show a correlation between eating breakfast and higher academic achievement, and this in turn led to parents cramming cereal down their children's throats in the hopes of force-feeding them into college. But when the phenomenon was finally investigated, researchers found that the act of eating breakfast really didn't affect the kids' intelligence at all. It's just that the type of kids who have things going on in their lives that keep them from eating breakfast are also the type to have trouble at school.

Why Does It Matter?

It wouldn't, if the only result was increased waffle sales during school months. But shit gets serious when we start misidentifying the cause of society's problems. Like if, say, we decide that life-saving vaccines are causing autism when in reality the number of kids being diagnosed with autism rose not with the rate of vaccinations, but with our ability to detect autism. To demonstrate this, opponents to the vaccine hysteria whipped up another graph:

Nathaniel lives on a boat, where the only statistic he has to deal with is the frequency of pirate attacks. James has a degree in physics and chemistry, and you can follow him on Tumblr, where he talks about neither.

For more "facts" you should be weary of, check out The 6 Most Frequently Quoted Bullsh*t Statistics and The 6 Most Statistically Full of Shit Professions.

If you're pressed for time and just looking for a quick fix, then check out The 4 Worst Things People Are Making with 3D Printers.

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