Member-only story
Percentages and points
What differs between a percent and a percentage point?
A percent is a number or ratio, expressed as a fraction of 100.
Percentages often describe shares or changes.
- Say 15% of shirts are blue. That means: for every 100 shirts, 15 are blue.
- An increase of £1 on a price of £4 is: 1/4, equal to 0.25. As a percentage, that is a 25% increase.
In one use, a percentage change is about the relative change between two values. Sometimes, we need to show changes in percentages themselves.
One pertinent example is vaccine efficacy estimates from clinical trials. A trial has 43,000 participants, split into two even arms. There are eight disease cases in the vaccine arm, and 162 among those who got the placebo.
First, we calculate the ‘attack rate’ in both arms:
- Attack rate in the vaccinated group: Eight divided by 21,500, or 0.04%.
- Attack rate in the unvaccinated arm: 162 divided by 21,500, or 0.75%.
The relative reduction from 0.75% to 0.04% is 95%. That is the central estimate of vaccine efficacy during the study period.
Instead, we could calculate the reduction in arithmetic terms. When discussing risks, this is the ‘absolute risk reduction’. The decrease from 0.75% to 0.04% is about 0.71 percentage points.
The reason to specify percentage points is because percentages describe a relative change. Here, we intend to convey an arithmetic or absolute difference. Whilst it can sound like pointless pedantry, this term avoids ambiguity and confusion. Clarity in statistical communication helps your audience.
In financial services, there is a need to describe smaller changes in interest rates. For that purpose, you may hear people talk about basis points or ‘bips’. Here, 100 basis points is the same as one percentage point.
Why do people get this wrong? My view is: it sounds right. Most of the time, people express arithmetic differences in the same unit: prices, scores, and so on. For those same differences in percentages, we need to say ‘percentage points’ or ‘points’.
