10 Times Correlation Was Not Causation

Katie Carey
Katie Carey

It’s a scientist’s mantra: Correlation does not imply causation. But sometimes wrong feels so right.


If you want to boost blood flow to your brain and (potentially) slow cognitive decay, consume flavanols. The plant compounds, found in green tea and cocoa, are great for getting blood into your noggin. That made New York doctor Franz Messerli wonder: Would a nation of bonbon–eaters be more intellectually accomplished than a country that didn’t consume as much cocoa? In a tongue-in-cheek 2012 paper published in The New England Journal of Medicine, he found that countries that ate a lot of chocolate also won the most Nobel Prizes. Messerli published the study with a wink, but some media outlets took the news seriously, failing to see that a confounding variable was at play—wealth. A richer country (like Switzerland, which has 26 Nobel winners) will have more quality scientific research—and well-stocked shelves of chocolate, too.


Nearsightedness has been increasing worldwide for decades. In some Asian countries, up to 90 percent of adults can’t see distant objects clearly, and in 1999, researchers at the Children’s Hospital of Philadelphia thought they’d found the cause: night-lights. The evidence suggested that kids who slept with a light developed myopia later in life. But two groups of researchers argued that the study failed to see the evidence in front of its nose—myopic parents have myopic kids. And myopic parents, who can’t see well in the dark, are more likely to install night-lights in their children’s rooms.


Are black cats bad luck for your sinuses? In a January 2000 paper for the Journal of Allergy and Clinical Immunology, researchers found that people with dark-colored cats suffered more allergic reactions than owners of light-colored cats (or no kitty at all). But the correlation appears to have just been a coincidence. Cat allergies are actually caused by a protein called Fel d 1, which is produced in salivary and sebaceous glands. A research team in New Zealand found that cat allergies simply aren’t related to cat color or hair length.


For centuries, natives of the New Hebrides islands considered a head full of lice a sign of good health. “Observation over the centuries had taught them that people in good health usually had lice and sick people very often did not. The observation itself was accurate and sound,” writes Darrell Huff in How to Lie with Statistics. But the correlation didn’t mean lice are the key to good health—it’s the other way around. Healthy people had lice because their body was just the right temperature, a perfect home for bugs. But when people ran a high fever, their flesh became hot, sending the lice scattering. Lice didn’t cause good health—they preyed on it.


We’ve all heard that kids who eat breakfast do better in school. It makes sense; it’s hard to focus on an empty stomach. But despite their best attempts, researchers haven’t been able to pinpoint why breakfast aids learning—if that’s even the case. A 1996 study of Jamaican students found that, in some schools, kids behaved better after they ate breakfast; in other schools, they acted worse. The gap probably had more to do with each school’s resources than with a student’s daily ration of Cocoa Puffs. Students at well-equipped schools behave better regardless of their diet.


Storks do not deliver babies. That bit of German folklore likely originated because the white stork’s migration rituals last nine months. (Plus, Hans Christian Andersen helped popularize the myth in his short story “The Storks.”) But that hasn’t stopped scientists from acknowledging a striking correlation: Between 1970 and 1985, the number of breeding pairs of white storks in Lower Saxony dropped. Over the same period, the birth rate there also fell. Meanwhile, stork numbers increased in Berlin’s suburbs, where doctors delivered more babies. As Robert Matthews writes in Teaching Statistics, “While storks may not deliver babies, unthinking interpretation of correlation ... can certainly deliver unreliable conclusions.”


Hours after the Seattle Seahawks lost the Super Bowl in 2015, fan Michael Sven Vedvik died. In his obituary, his family blamed the team’s “lousy play call for Mike’s untimely demise.” The joke echoed 2011 research in Clinical Cardiology linking Super Bowl losses to a 15 to 27 percent increase in cardiac deaths in the loser’s hometown. (The Grim Reaper has tried wearing cleats at least once: When the Steelers’ Jerome Bettis fumbled in a 2006 playoff game, a fan watching from a bar became so upset that he had a heart attack. Fortunately, he survived.) Problem is, the studies don’t take non-football variables into account. And the data in one study investigated deaths that occurred two weeks after the game. “I don’t think that everyone who dies within 14 days of the Super Bowl died because of the Super Bowl,” David Prince of Albert Einstein College of Medicine told Live Science.


In 1958, economist William Phillips published a paper claiming that when unemployment increased, inflation decreased (and vice versa). “That led nations to start thinking of these two variables as trade-offs,” says Rebecca Goldin, professor of math at George Mason University and director of the website Sense About Statistics. “Some would focus on unemployment while others focused on controlling inflation, but they all saw this as a causal trade-off.” Then came the 1970s, when many countries saw both high inflation and high unemployment. Turns out Phillips’s “rule” was just a short-term coincidence. While inflation can affect unemployment for short periods, it can’t fix joblessness over the long run.


In Scandinavia, people fight the cold of winter with cozy candlelit social gatherings. Called hygge in Denmark and koselig in Norway, the tradition suggests there’s a connection between physical temperature and the “social warmth” of friends. In 2011, Yale researchers suggested that people may instinctively reach for that connection in the shower. In a study, they found that lonely people were more likely to take long, warm showers and baths. Was it because higher temperatures make them feel less isolated? Well, the methodology left critics cold. The study used a small sample (only 51 undergrads); of those, 90 percent reported bathing or showering less than once a week. Not exactly a trusty sample. In 2014, a different team tried to replicate the results using a larger (and presumably better-smelling) group, and failed.


According to the 2008 study “Rugby (the Religion of Wales) and its Influence on the Catholic Church,” the Pope is more likely to die when the Welsh rugby team wins the sport’s Grand Slam. The paper—which appeared in the British Medical Journal’s humorous annual Christmas issue—found no connection between the pontiff’s mortality and teams from other countries. Just Wales. We expect a Dan Brown book about this any time now.

8 Ways Science Can Boost Your Halloween Fun


Halloween is all about embracing the supernatural, but science shouldn't entirely fall by the wayside during the spookiest of holidays. Here are a few ways it can actually improve your holiday, from making trick-or-treating easier to fooling your brain into thinking you're eating tasty treats even though you're nibbling on candy cast-offs.

1. Slow the decomposition of your Halloween jack-o'-lantern.

A Halloween display of five jack-o-lanterns

You don't have to be an expert gardener to keep your jack-o'-lantern looking fresh all Halloween season long. While scouting out pumpkins, pick hard, unblemished ones and steer clear of those with watery dark spots. These splotches indicate frost damage.

Hold off on carving until right before Halloween so your gourds won't rot—but if you can't resist, try squirting their exteriors with lemon juice after you're done slicing and dicing. The acid inhibits pumpkin enzymes, which react with oxygen and cause browning. A light misting of bleach solution will help keep fungus at bay. Some apply vegetable oil or Vaseline to prevent shriveling and drying. We experimented with various techniques in this video.

For extra TLC, you might even want to bring your jack-o'-lanterns in at night if temperatures dip; if you live in a hot and humid area, extend its life by placing it in the fridge overnight. Try using glow sticks or LED lights instead of flesh-singeing candles.

2. Use apps to plan a treat-or-treating route.

Three children in Halloween costumes trick-or-treating

Thanks to technology, trick-or-treaters (and their hungry adult companions) can now scout out which neighbors are doling out the best candy and which are sticking with Tootsie Rolls, apples, and toothbrushes. Simply download the app for Nextdoor, the neighborhood-based social network, to check out an interactive "treat map" that lets users tag whether their home is handing out treats, and what that treat is.

Since safety is far more important than sugar, guardians should also consider adding a tracking app to their arsenal come Halloween, especially if their kid's venturing out alone. The Find My Family, Friends, Phone app gives the real-time locations of trick-or-treaters, provides alerts for when they turn home, and also comes with a "panic" button that provides emergency contact details when pressed.

3. Optimize your candy's flavor (even if it's SweeTarts).

Hard candies and gummies strewn across a table

Not crazy about this year's Halloween loot? Fool yourself into thinking those black licorice pieces and peanut chews taste better than they actually do by eating them after you scarf down the chocolate and Sour Patch Kids. According to a 2012 study published in Psychological Science, being aware that these items of candy are your very last candies actually tricks the brain into appreciating them more (and thus thinking they're tastier than they really are).

Meanwhile, a 2013 study from the same journal found that creating a candy-eating ritual enhances flavor and overall satisfaction. Nibble the ridged edges off a Reese's peanut butter cup before tackling the creamy center, sort the M&Ms by color, and take your time unwrapping a chocolate bar.

4. Create a DIY fog machine with carbon.

Dry ice in a glass bowl

Save money at Party City by creating your own fog machine at home. When dropped in water, dry ice—or frozen carbon dioxide—creates a gas that's a combination of carbon dioxide and water vapor, but looks like the fog you'd see rolling through a haunted graveyard [PDF].

5. Eat sort-of-heart-healthy Halloween candy.

A stack of dark chocolate chunks on a dark stone background

Halloween candy isn't always bad for you. While shopping for this year's trick-or-treat bounty, steer clear of sugary confections and milk chocolate mini-bars. Opt for dark chocolate treats instead. Research suggests that our gut microbes ferment the antioxidants and fiber in cocoa, creating heart-healthy anti-inflammatory compounds. Plus, dark chocolate or cocoa also appears to help lower blood pressure for people with hypertension, decrease bad cholesterol, and stave off cardiovascular disease and diabetes, among other benefits.

6. Analyze data on Halloween candy trends and give the people what they want.

5second/iStock via Getty Images

Thanks to data science, you can make sure you're giving out the best treats on the block. Bulk candy retailer CandyStore.com combed through 10 years of data (2007 to 2016, with a particular focus on the months leading up to Halloween) to gauge America's top-selling sweets. They created an interactive map to display their results, which includes the top three most popular Halloween handouts in each state and Washington, D.C. Be prepared for plenty of stoop-side visitors and adorable photo ops.

7. Bake better Halloween treats with chemistry.

Frosted Halloween cookies shaped like ghosts and pumpkins

Cooking is essentially chemistry—and depending on your technique, you can whip up chewy, fluffy, or decadent Halloween treats according to taste.

Folding chunks of chilled butter into your dough will give you thick, cake-like cookies, as will swapping baking soda for baking powder. When butter melts, its water converts into gas, which leaves lots of tiny holes. If the butter flecks in question are colder and larger, they'll leave bigger air pockets. As for the baking powder, it produces carbon dioxide gas both when it's mixed into the dough and when it's heated. For an extra boost in texture, you can also try adding more flour.

Prefer chewier cookies? Start out with melted butter in the dough, and stick with plain old baking soda.

And for extra-fragrant and flavorful baked goods, opt to use dark sugars—like molasses, honey, and brown sugar—because they're filled with glucose and fructose instead of plain old sucrose. As cookies bake, they undergo two processes: caramelization, in which the sugar crystals liquefy into a brown soup; and the Maillard reaction, a chemical reaction between the dough's proteins and amino acids (flour, egg, etc.) and the reducing sugars that causes tasty browning.

8. Take deep breaths to stay calm in haunted houses.

A brown-haired woman in a red polka dot blouse standing with a frightened expression next to a spider web.

Halloween can be tough for people with anxiety or low thresholds for fear. While visiting a haunted house or watching a scary movie, remember to take deep breaths, which fends off the body's flight-or-fight response, and reframe your anxiety in your mind as "excitement." It's also a good idea to schedule spine-chilling activities after an activity that triggers feel-good endorphins—say, after a walk to check out your neighbors' awesome Halloween displays.

Some Mathematicians Think the Equal Sign is On Its Way Out

Paperkites/iStock via Getty Images
Paperkites/iStock via Getty Images

A growing number of mathematicians are skeptical that the equal sign, traditionally used to show exact relationships between sets of objects, holds up to new mathematical models, WIRED reports.

To understand their arguments, it’s important to understand set theory—a theory of mathematics that’s been around since at least the 1870s [PDF]. Take the classic formula 1+1=2. Say you have four pieces of fruit—an apple, an orange, and two bananas—and you put the apple and the orange on one side of a table and the two bananas on the other. In set theory, that’s an equation: One piece of fruit plus one piece of fruit on the left side of the table equals two pieces of fruit on the right side of the table. The two sets, or collections of objects, are the same size, so they’re equal.

But here’s where it gets complicated. What if you put an apple and a banana on the left side of the table and an orange and a banana on the other side? That’s clearly different from the first scenario, but set theory writes it as the same thing: 1+1=2. What if you switched the order of the first set of objects, so instead of having an apple and an orange, you had an orange and an apple? What if you had only bananas? There are potentially infinite scenarios, but set theory is limited to expressing them all in only one way.

“The problem is, there are many ways to pair up,” Joseph Campbell, a mathematics professor at Duke University, told Quanta Magazine. “We’ve forgotten them when we say ‘equals.’”

A better alternative is the idea of equivalence, some mathematicians say [PDF]. Equality is a strict relationship, but equivalence comes in different forms. The two-bananas-on-each-side-of-the-table scenario is considered strong equivalence—all of the elements in both sets are the same. The scenario where you have an apple and an orange on one side and two bananas on the other? That’s a slightly weaker form of equivalence.

A new wave of mathematicians is turning to the idea of category theory [PDF], which is based in understanding the relationships between different objects. Category theory is better than set theory at dealing with equivalence, and it’s also more universally applicable to different branches of mathematics.

But a switch to category theory won’t come overnight, according to Quanta. Interpreting equations using equivalence rather than equality is much more complicated, and it requires relearning and rewriting everything about mathematics—even down to algebra and arithmetic.

“This complicates matters enormously, in a way that makes it seem impossible to work with this new version of mathematics we’re imagining,” mathematician David Ayala told Quanta.

Several mathematicians are at the forefront of category theory research, but the field is still relatively young. So while the equal sign isn’t passé just yet, it’s likely that an oncoming mathematical revolution will change its meaning.

[h/t Wired]