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June 11th, 2017 (Permalink)

Cuckoo for Cocoa Puffery

There are three sets of words to be on the lookout for in media reports of statistical studies of medicine or nutrition:

  1. "Could", "may", "possible", "suggest", and other words indicating that the results of a study are weak.
  2. "Link", "association", "connection", "relationship", and other words that mean that two variables are related statistically, but not necessarily causally.
  3. Other words, such as "help", that indicate that any possible effect is probably small.

With that in mind, I have highlighted every occurrence of these words in the following excerpt from a recent news story1. They first make an appearance in the headline:

Eating chocolate may help prevent a fairly common heart problem

Eating chocolate has been linked with a reduced risk of heart disease and stroke. Now a study from Denmark suggests that regular consumption of the treat may help to prevent the development of atrial fibrillation, a type of irregular heartbeat.

In the study…researchers found that people who ate chocolate at least once a month had rates of atrial fibrillation that were 10 to 20 percent lower than those who ate chocolate less often. …

When researchers took into consideration other factors that might influence development of atrial fibrillation, such as alcohol intake, smoking, obesity, high blood pressure and cholesterol levels, the study showed an association between people with a moderate intake of chocolate and a lower risk of developing atrial fibrillation.

The study does not prove a cause-and-effect relationship. And although the exact mechanism of how chocolate may prevent atrial fibrillation is not known, itís possible that compounds in chocolate called flavonoids may play a role, the researchers said.

Flavonoids have antioxidant and anti-inflammatory properties…. They may limit the inflammatory process in the body, reducing the stickiness of the blood and leading to less scarring of connective tissue. All of these factors may help prevent the electrical remodeling of the heart that leads to atrial fibrillation….

The findings showed that for women, the strongest association was seen in those who ate a one-ounce serving of chocolate once a week: This level of consumption was linked to a 21 percent lower risk of atrial fibrillation compared with those who ate less chocolate. For men, the strongest association was seen in those who ate two to six one-ounce servings of chocolate weekly. These men had a 23 percent lower risk of atrial fibrillation. …

All in all, the findings suggest that compared with some other snack choices, a moderate intake of chocolate may be a heart-healthy snack….

If only The Washington Post and other news media would publish health articles with these three types of word highlighted, as above, then it would be obvious how weak the studies often are. I don't pick on the above story on the grounds that it is especially bad; rather, it's a typical example of this type of reporting.

It's also typical in its first-the-good-news-then-the-bad-news structure: in the first half, we're given the good news: chocolate is good for you! In the second half, we're told the bad news: never mind! This is why, as I've noted before2, you should read these articles all the way to the end. Unless, of course, all you want to read is the fake news.


  1. Cari Nierenberg, "Eating chocolate may help prevent a fairly common heart problem", The Washington Post, 5/27/2017
  2. Caveat Lector, 9/3/2011

June 9th, 2017 (Permalink)

Puzzle: Your Mileage May Differ

A family owns two cars: a sport utility vehicle that gets 20 miles per gallon and a compact car that gets 40 MPG. Both vehicles are getting old and the family has decided to trade one in on a replacement that gets better mileage on a tank of gasoline. The possibilities are switching the SUV for one that gets 25 MPG or replacing the compact with one that gets 50 MPG. They drive each car about the same amount. Assuming that the only relevant consideration is how much they can save on gas, which vehicle should they trade in?


June 8th, 2017 (Permalink)

Amphibolous Headline

Teen accused of killing Uber driver with machete in one hand, knife in the other1

My first thought when I saw this headline was: if an Uber driver came at me with a machete in one hand and a knife in the other, I guess I'd kill him, too. However, if you read the story beneath the headline, it was the teen who is accused of using a machete and knife to kill the driver.

This headline isn't funny and neither is the story beneath it. However, it is ripe for misinterpretation since the headline is ambiguous; more specifically, it is amphibolous2 because of a misplaced modifier3. Grammatically, the modifying phrase "with machete in one hand, knife in the other" should modify "Uber driver", which it immediately follows, and not "teen" or "killing". Using brackets to indicate the scope of the modifying phrase, three distinct meanings of the headline can be disambiguated:

  1. Teen accused of killing [Uber driver with machete in one hand, knife in the other]

    The phrase acts as an adjective, modifying "Uber driver", which means that the driver had the weapons.

  2. [Teen with machete in one hand, knife in the other] accused of killing Uber driver

    Again, the phrase acts as an adjective, but now modifies "teen". The teen had the weapons, but when accused, not necessarily while killing.

  3. Teen accused of [killing, with machete in one hand, knife in the other] Uber driver

    The phrase now acts as an adverb, modifying the verb "killing" rather than a noun. This version accurately represents what the news story reported the teen was accused of doing.

I can sympathise with the editor who wrote the headline, since it's difficult to pack so much information into a brief headline unambiguously. However, here's a suggested revision:

Teen accused of using a machete in one hand and a knife in the other to kill Uber driver

This is four words longer but three times clearer.


  1. Samantha Schmidt, "Teen accused of killing Uber driver with machete in one hand, knife in the other", The Washington Post, 6/1/2017
  2. See Amphiboly.
  3. See Robert J. Gula, Precision: A Reference Handbook for Writers (1980), sections 10B & 10C

Solution to Your Mileage May Differ: Surprisingly enough, the family should replace the SUV. It looks as though they ought to trade in the compact car, since the replacement will get 10 MPG better mileage, whereas the new SUV will only get 5 MPG more. Since they drive the two cars about the same distance, it seems as though they would save more gas with the new compact car rather than the SUV.

Here's why they should select the SUV: suppose that they drive each vehicle 10,000 miles a year. Then, since the SUV gets 20 MPG, it uses 500 gallons of gas a year, and because the compact car gets 40 MPG, it uses half as much gas, namely, 250 gallons per year. An SUV that gets 25 MPG will use only 400 gallons a year, thus saving the family 100 gallons; whereas a compact car that gets 50 MPG, will use 200 gallons of gas in a year, for a savings of 50 gallons. They can save twice as much gas by trading in the SUV!

Why is this counter-intuitive result correct? Clearly, if both cars got the same MPG to start with, then the one to replace would be the one that most improves that MPG. However, there is a big difference in the MPGs of the two cars, with the compact getting twice the mileage on a tank of gas that the SUV gets.

Instead of looking at the absolute difference in MPGs, consider the percentage improvement: from 20 to 25 is a 25% improvement, and from 40 to 50 is also a 25% improvement. So, they're the same percentage improvement! However, because the SUV uses twice as much gas as the compact, a 25% improvement in mileage will actually save twice as much gas.

Source: Derrick Niederman & David Boyum, What the Numbers Say: A Field Guide to Mastering Our Numerical World (2003), pp. 65-66.

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