Why Percentages Can Be Deceptive
You know when you go to a doctor and they try to push specific medications onto you?
I remember going to a specialist doctor a few years ago (I’ll call him Dr. P), and he really, really wanted me to buy this medication, which I’ll just call Dolusol. He told me that Dolusol would not only help me with my problem, it would also increase my quality of life and decrease anxiety. He proclaimed that people on Dolusol “reported 20% more happiness! They reported 35% more calmness!” Then he gave me a snazzy bar graph and like 30 pages of promotional material on Dolusol. He also gave me a snowstorm of handouts on 5 or 6 other medications he wanted me to take.
I don’t have the graph anymore, but it looked something like the graph below. It certainly showed what Dr. P claimed, that patients who took Dolusol reported “20% more happiness” and “35% more calmness” and whatever:
Do you notice anything missing from this graph? Because rather than making me ecstatic to stuff my face with Dolusol pills, the graph made me confused, and a little suspicious.
The problem is that this graph only gives percentages¹. Because without context, these percentages are next to useless.
Percentages are a great thing. As Charles Wheelan notes in Naked Statistics, a percentage helps us make sense of change. It’s easier to understand me if I tell you a potato chip has “20 percent less sodium” than if I tell you that the potato chip has “5 fewer milligrams of sodium,” even though both of those statements may be true. Unless you’re an expert, it’s tough to tell if a change in 5 milligrams of sodium is a notable change at all. Percentages help bridge that gap in understanding, because a percentage tells us the change in a number relative to some other number.
But even though percentages are useful, we still need to know the starting point and the ending point of whatever we’re measuring. Wheelan recalls that he once invested in a business his college roommate started. He forgot about it, then years later received a letter that the company’s profits were 46% higher than the previous year. But the letter didn’t say how much the company made last year, so Wheelan “still had absolutely no idea how my investment was performing.”
For example, if the company’s profits were $1.00 in 2020, then $1.46 in 2021, that would technically be a 46% increase, but those profits are less than the price of a McChicken; they’re nothing to get excited over. If I have a failing restaurant with only 2 customers (my best friend and my mom) and then I get 3 more customers (my grandpa, my uncle, and the shifty-eyed radiologist Dave from across the street who always orders the lobster bisque) then I just increased my customer base by a stunning 150%. For a company like Nike or Amazon, increasing your customer base by 150% in one year would be mind-boggling, easily front-page news. But for my business, it’s a change of a mere 3 people.
This is important to keep in mind when looking at any statistic that involves percentages: a big percentage of a small number still makes a small number. By the way, the converse is also true: A small percentage of a big number still makes a big number. Saying that Amazon increased its annual revenue by 1% doesn’t seem like a lot, until you realize how much revenue they actually make. In 2020, they made 386 billion dollars in revenue. Increasing that by a mere 1% would still be an increase of almost 4 billion dollars (although Amazon certainly wouldn’t be happy about a 1% increase, considering their revenue increase from 2019 to 2020 was more like 38%).
Decisions have consequences. Even though statistics can help us make those decisions, we must still be careful. Wheelan states that “while the main point of statistics is to present a meaningful picture of things we care about, in many cases we also seek to act on the numbers.” And I should add, we also often seek for other people to act on the numbers, whether that’s investing in a company or buying an expensive medication. Truthfully, I’m not a pharmacist, and for all I know “Dolusol’’ might’ve been legit. Or maybe the doctor is shady and got a huge paycheck from a pharma company to push that medication. Maybe the doctor simply didn’t realize why the ubiquity of “%” symbols made me wary of his bar graphs. At the least, I can accurately say that I see that doctor 0% of the time now.
¹: Also, the graph doesn’t tell us how long the patients took Dolusol for, but it’s possible the original graph had that and I just forgot. If we wanted, we could probably find 1,000 things wrong with this mockup graph that I made in MS Paint.