Stop getting fooled by this common statistics trick
- Travis M.
- 58 minutes ago
- 7 min read
Short of time? Click here to read the key takeaways!
🎯 A 71% increase can sound alarming, but without context, it can mislead. In the aspirin example, the relative increase is 71%, yet the absolute risk only rises from 0.18% to 0.31%. Both figures are correct, but they create very different impressions of the underlying risk.
🔍 Relative and absolute percentages answer different questions. Absolute change measures the direct difference between starting and ending values, while relative change measures how large that difference is compared to the starting point. Both are mathematically valid, but each can distort understanding when used without proper context.
📰 Relative percentages often grab attention, which is why they appear frequently in headlines and marketing. A large relative increase applied to a tiny starting number can sound dramatic while hiding how small the real-world change is. But absolute changes can also mislead when they obscure meaningful proportional shifts.
📊 Natural frequencies are often clearer than percentages. Saying “18 in 10,000 people have major bleeds without aspirin, and 31 in 10,000 with aspirin” makes the situation easier to understand. Research finds that natural frequencies reduce common reasoning errors and help people interpret statistical information more accurately.
Did you know that aspirin can increase your chances of major bleeding by 71%? But, wait, before you throw out your stash, let us tell you why you shouldn’t worry (except in very special circumstances). Once you know the reason, you’ll be able to spot a particular kind of misleading statistic that's all over the place.
The problem with the “71% increase” statistic is not that it’s false. In fact, the evidence for it comes from a systematic review and meta-analysis, which is often a very robust kind of evidence. The problem is that it's misleading - at least, without other context. To their credit, the authors of that meta-analysis do provide the necessary context, but the news media often doesn’t. So, let’s talk about how this sort of statistic can be used to mislead.
An increase of 71% sounds scary because it sounds like a massive change in your chances, but you’d probably be a lot less worried if we told you that the chances of having a major bleed without taking aspirin are only 0.18%, which means that the 71% increase only actually raises your chances to 0.31%. That’s still less than a third of one percent! Of course, if you had an injury that was prone to bleeding, or you're practicing juggling with knives for the first time, that's another matter - but for most people, the 71% is not something to be concerned about!
This illustrates a common way people mislead with statistics: by exploiting the difference between ‘relative’ and ‘absolute’ percentages. That’s what we’re going to talk about in this article. We’ll explain the difference between the two kinds of percentages, how they can each be misleading in some situations, and then tell you about a third way of presenting the same information, which is typically much clearer. All of this will equip you to spot this kind of misleading reporting in the wild and call it out when you see it. Once you start to notice it, you’ll feel like you can’t escape it.
What Are Relative and Absolute Percentages?
Imagine you’ve bought a ticket for a raffle. There are 1000 tickets in total, so with only one ticket, you have a 1 in 1000 (that’s a 0.1%) chance of winning. Now, here’s a question: By what percentage do your chances of winning increase if you buy a second ticket? There are two very different answers, both of which are correct.
Correct answer #1 (The Absolute Percentage)
If you said your chances increase by 0.1% when you buy that extra ticket, you’d be correct. Each ticket gives you a 1 in 1000 chance of winning, so going from one ticket to two tickets increases your chances from 0.1% to 0.2%. That’s an increase of 0.1%. This is the absolute percentage increase. Sometimes the phrase "percentage points" rather than "percent" is used to make it clear that absolute percentages are being talked about.
Correct answer #2 (The Relative Percentage)
If you said your chances increase by 100%, you’d also be correct. To see why, ask the question: “What percentage of my starting number do I need to add (or subtract), to get to the final number?” To go from 0.1 to 0.2, you need to add 100% of your starting number (0.1). So your chances of winning have increased by 100% (of your starting chances). This is the relative percentage increase.
To put it simply:
The absolute percentage change is the difference between your starting percentage and your final percentage. Going from 5% to 20% is a 15% absolute change - or an increase of 15 percentage points.
The relative percentage change is the percentage of your starting percentage you need to add or subtract to get to your final percentage. Going from 5% to 20% is a 300% relative change.
How Do People Mislead You With Percentages?
Obviously, it’s scarier and more dramatic to tell people that aspirin increases their chances of major bleeds by 71% (the relative percentage change) than by 0.13% (the absolute percentage change). They’re both technically correct, but one is going to get a lot more interest than the other. That’s probably a big part of the reason why relative percentages are so common in things like the news and marketing; people who want your attention will grab it by using the most dramatic-sounding claims they think they can get away with. This becomes misleading when it is used to convey a false impression (e.g., that the absolute risk is very high), even without saying anything false. Imagine the headline: "Aspirin increases your risk by 0.31%" - that's not going to get a lot of clicks!
So, if someone is telling you that something has increased by a certain percentage, you can think more carefully by asking the question: Is this an absolute or a relative percentage increase? If it’s a large relative increase of something that started very small, you might be being misled (even if you’re not being told something false).
However, absolute percentage changes can also mislead in some cases. For example, if all you were told about a company was that, last year, it reduced its percentage of products that failed to make it to market by 2% (in absolute terms), you might think that sounds insignificant. However, if you learn that they started the year with 2.3% of products failing to make it to market, you might think that their achievement (nearly eliminating all such failures) is much more impressive. In cases like this, the relative percentage change (87%) might seem a fairer way to represent the change and will probably lead to more accurate impressions of the company’s achievement.
The choices that are made about how to present data affect what people conclude. One of those choices is between presenting percentage change as either relative or absolute. To be on your guard against subtle misinformation, you can keep this distinction in mind whenever you encounter a percentage.
There is a Clearer Way of Thinking
There are alternatives to expressing change in terms of absolute or relative percentages. A particularly important alternative is called ‘natural frequency’. Instead of using percentages, natural frequencies present information as one whole number out of another (usually larger and often a ‘round’ number). For example, we could present the findings of that study about aspirin and major bleeds like this:
18 in 10,000 people not taking aspirin experience major bleeds
31 in 10,000 people taking aspirin (for at least a year) experience major bleeds
That’s 13 additional major bleeds for every 10,000 people.
Studies find that people who see data presented as natural frequencies are much less likely to commit statistical fallacies like the base rate fallacy, and are much more able to perform Bayesian calculations. And that’s not surprising: As the authors of that famous study (Gerd Gigerenzer and Ulrich Hoffrage) argue, percentages and probabilities are human inventions that significantly abstract away from reality, and only became common with the advent of the metric system during the French Revolution. Natural frequencies, however, correspond more directly to what’s happening in the world and are (Gigerenzer and Hoffrage argue) the best explanation for how our evolutionary ancestors would have made statistical judgments.
Natural frequencies let us talk more directly about the reality behind the percentages. Instead of saying ‘a 71% increase,’ they show you what’s actually happening in a group of people. That makes them much harder to spin.
When natural frequencies aren't available, or in scientific contexts, an alternative approach is to simply look at both absolute and relative percentages. Together they give a more complete picture.
What To Keep In Mind
In his popular book, Bad Science, the British physician and academic Ben Goldacre offers a useful list of details he wants to see reported “to help me make decisions about my health”, instead of just relative percentage changes:
|
If you’re being presented with data about things like change or risk (which involve reasoning about probability) and you don’t have this kind of information, you might be missing something important.
But the simplest insight we want to leave you with is this: people regularly exploit or ignore the difference between absolute and relative percentages when talking about important issues. You can increase your odds of having true beliefs and not getting misled if you keep the distinction in mind and regularly question whether the data you’re seeing is in a misleading format.
The next time you see a story about some medicine increasing your risk of X, or some food reducing your chances of Y, you could try asking: What kind of percentage is that? And what are the natural frequencies?
Do you want to test your skills at spotting other misconceptions? Then why not try our Common Misconceptions Quiz. See whether you can separate fact from B.S. in this quiz that asks you to identify the misconceptions among 30 common beliefs.