You will be able to convert relative changes into absolute ones and ask for the base rate.
Priya's manager forwards a news headline to the team chat with one word: "Worrying." The headline says the risk of a particular side effect from a common medicine has risen by 50 percent. Two colleagues reply that they are stopping the medicine. Priya opens the article, scrolls to the eighth paragraph and finds the actual numbers. The answer to "should I worry" was there all along, just not in the headline.
This lesson covers four ways percentages mislead, all of which you can check with arithmetic you already know. The figures in the examples are made up, and every calculation has been checked.
A percentage change on its own tells you nothing about size. "Complaints up 50 percent" could mean they rose from 4 to 6 or from 4,000 to 6,000. Both are 50 percent rises. One is a rounding error in a busy month and the other is a crisis.
So when you see a percentage change, ask for the starting number and the ending number. If a small base produces a large percentage, the story is probably smaller than it sounds. If the article or report does not give you the base at all, that is worth noting, because the writer had it and chose not to show you.
The medicine headline is a case of relative risk. Relative risk tells you how much more likely something is in one group compared with another. Absolute risk tells you how likely it is in the first place.
Suppose that, in this made-up example, the side effect used to affect 2 people in every 10,000 who took the medicine, and a new study suggests the figure is 3 in every 10,000. Going from 2 to 3 is a 50 percent rise, so the headline is accurate. But in absolute terms, it is one extra case for every 10,000 people. For most people taking the medicine for a good reason, that changes very little. That decision belongs with their doctor anyway.
Headlines prefer relative risk because it makes a bigger number. So do advertisements, in the other direction: "cuts your risk by half" sounds better than "cuts your risk from 2 in 1,000 to 1 in 1,000." Whenever you see relative risk, convert it. Ask: out of how many people, how many before, how many after?
When a rate is already a percentage, a change in it can be described in two ways, and people mix them up constantly.
Say an unemployment rate in some made-up sector rises from 2 percent to 3 percent. That is a rise of one percentage point, because 3 minus 2 is 1. It is also a rise of 50 percent, because the new rate is half as large again as the old one. Both statements are true. They sound very different.
The same applies to interest rates, survey results and conversion rates. If a loan rate goes from 4 percent to 5 percent, a writer can say it "rose 1 point" or "jumped 25 percent". When you see a change in a rate, check which one is being used. When you write one, say "percentage points" for the difference between two percentages, so nobody has to guess.
The last trap is the one that catches even careful people. Base rate neglect means judging a case by its details while ignoring how common the thing is in the first place.
Here is a made-up example. A bank's system flags transactions as possibly fraudulent. Suppose 1 in every 1,000 transactions is actually fraud. The system catches 99 percent of real fraud, and it wrongly flags 2 percent of honest transactions. Your card gets flagged. How likely is it that the transaction really was fraud?
Most people say something close to 99 percent. Work it through with 100,000 transactions instead. One in 1,000 is fraud, so 100 transactions are fraudulent. The system catches 99 of them. The other 99,900 are honest, and 2 percent of those get flagged by mistake, which is 1,998 false alarms. So of the 2,097 flagged transactions, only 99 are real fraud. That is under 5 percent. More than 95 percent of the flags are false alarms.
The detail, a system that is 99 percent accurate at catching fraud, made the flag feel decisive. The base rate, fraud being rare, is what decides the answer. When the thing you are looking for is rare, even a good test produces mostly false alarms.
The same logic applies to a job applicant with a polished CV, a startup that "looks like" a past success, or a customer whose behaviour "fits the profile" of someone about to leave. Before you judge the case, ask how common the outcome is in general. Lesson 7.4, Update your beliefs with new evidence, shows how to start from that base rate and adjust it.
Priya replies to the team chat with three lines: the old risk was 2 in 10,000, the new estimate is 3 in 10,000, and that is one extra case per 10,000 people. One colleague says, "Oh, that's nothing like what I thought." Nobody needs to stop anything without asking a doctor first.
That conversion is the habit to build: from a relative change to the absolute numbers, from percent to percentage points, from a vivid case to how common it is. Any news site will give you material to practise on this week, and the activity below asks you to do the conversion on three real headlines.
Rewrite three headline statistics from recent news as absolute numbers, and note where the article did not give you enough to do so.
Junxiong-WFG Organisation is an authorised representative of AIA Financial Advisers Private Limited (Reg. No. 201715016G).