The Numbers Don’t Lie (Except When They Do)

They say the numbers don’t lie, but there are all kinds of ways to distort the truth using numbers that might even be technically correct. 

Several Republican governors have recently tried to claim that healthcare costs will go up in their states due to the passage of the Affordable Care Act. Take, for example, the announcement that new individual health plans in Indiana would cost on average about $570, an increase by 72% over current rates. While that number is, in fact, the average of the price of the different tiers of coverage that were offered by the state’s insurance companies, it ignores the fact that very few people choose the expensive “Gold” and “Platinum” plans that skew the average. In Massachusetts, which implemented an Obamacare-like system years ago, 84% of enrollees chose plans from the “Bronze” and “Silver” tiers, while only 8% chose the most expensive plans. Sy Mukherjee at Think Progress came up with an apt example of the faulty math at play here:

That’s like saying the average cost of a car in an Indiana dealership is $100,000 because it sells $20,000 Fords, $60,000 BMWs, and $220,000 Lamborghinis – technically true, but highly misleading.

It’s obvious in the above analogy that most people visiting the dealership are buying the $20,000 Fords, with a much smaller percentage choosing BMWs and only a few people shelling out for the Lamborghini. Even if we apply the above percentages to this and assume 84% of customers buy Fords while a full 8% each buy the more expensive cars, the average price is $39,200 per customer, not $100,000–and it’s still irrelevant because people aren’t paying the average, they’re paying what they choose to pay for the car they want.

More than a month after the initial misleading announcement, Indiana still hasn’t released the full set of numbers each insurance provider quoted for the various tiers, so it’s impossible to say what the actual averages will be for each tier, or what the overall average per person will likely be. Suffice to say, however, that most people in Indiana will pay much less than $570 for an individual plan, especially since low-income individuals and families are eligible for subsidies to help pay for their insurance. Unfortunately, Gov. Mike Pence is still touting that $570 number as though it’s an accurate representation of what people will pay.

Of course, politicians aren’t the only ones who present numbers without context in order to support a desired narrative; people who hate or mistrust the government are just as likely to exaggerate claims to “prove” that there’s some sort of conspiracy going on. Take the recent story that went viral about arsenic in chicken (I’m not linking to any of the particularly fearmongering versions because I don’t want to give them the pageviews or make y’all’s heads hurt as much as mine does after slogging through a couple). Yes, a study did find that some supermarket chicken samples had an average of three times higher levels of inorganic arsenic than others. The varying levels depended on whether or not there were detectible levels of Roxarsone, a drug widely used to prevent parasitic infections. Samples that contained Roxarsone contained 2.3 parts per billion (ppb) of arsenic, while samples without any trace of the drug had a level of 0.8 ppb. Yes, the first group’s levels were three times higher, which sounds scary! But it ignores that the FDA’s threshold for dangerous levels of arsenic are 500 ppb, more than 200 times higher than was found in the chicken, and that the EPA limits arsenic in drinking water to 10 ppb, more than 4 times higher. Some people have suggested that people should stick to organic chicken because they think the study says that it contains no arsenic, but that’s due to a misunderstanding of the study’s findings–none of the organic chicken samples showed signs of Roxarsone, but they were still in the group that had 0.8 pbb of inorganic arsenic. Another misunderstanding arises from the study’s testing of raw vs. cooked chicken. The concentration was slightly higher in cooked chicken, but cooking doesn’t add arsenic to the samples; cooking removes some of the moisture and therefore alters the ratios somewhat.

The study estimated that if the average person weighs 175 lbs and eats 2.9 oz of conventional chicken every single day of their life, this could result in approximately 124 more cases of lung or bladder cancer per year over 70 years than if the chicken consumed had the lower levels (this is out of over 300 million Americans, 75% of whom were estimated to eat chicken). The lifetime risk of getting cancer from the arsenic in Roxarsone-treated chicken was estimated at 3.7 per 100,000. Of course, if you’re one of the 124 people in the entire country who might get cancer from eating chicken, it sucks. Does it mean everyone should be terrified of eating conventionally raised chicken? No, especially since the chicken tested was purchased between December 2010 and June 2011; Roxarsone was voluntarily pulled from the market in the U.S. in 2011, so it’s not in any of the chicken you buy today.

There are countless other examples of math being used to distort reality, especially if the distorted view feeds into some sort of agenda. We saw it with the McDonald’s proposed household budget, most stories about why the post office and Social Security are broke, and a lot of the rhetoric around parenting choices such as whether to breastfeed or put your kids in daycare. The takeaway here? Be skeptical if a news story or viral post quotes percentages or averages without any context. Sure, X activity may double your risk of Y adverse outcome, but if the risk was infinitesimally small to begin with, there’s no need to panic!

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[E] Hillary

Hillary is a giant nerd and former Mathlete. She once read large swaths of "Why Evolution is True" and a geology book aloud to her infant daughter, in the hopes of a) instilling a love of science in her from a very young age and b) boring her to sleep. After escaping the wilds of Waco, Texas and spending the next decade in NYC, she currently lives in upstate New York, where she misses being able to get decent pizza and Chinese takeout delivered to her house. She lost on Jeopardy.

2 thoughts on “The Numbers Don’t Lie (Except When They Do)”

  1. And this happens SO MUCH. People who don’t add the necessary word ‘percentage’ to something, think that a quarter is always 25 (DON’T GET ME STARTED) and plenty of other mistakes.
    That’s why the ‘Oops This Really Isn’t What It Looks Like’ coverage so addictive to me.

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