From 4% to 5%, is that one point or 25%?

A service says cancellations rose from 4% to 5%. One headline calls that a one-point rise. Another says cancellations increased 25%. Those headlines can describe the same rates. To see why, start by asking what each writer is using as a denominator.

Calculate the gap first

Subtract 4% from 5% and you get an increase of one percentage point. The Office for National Statistics uses percentage points to describe the difference between two percentages. If the subscription base stayed at 1,000 and the periods were equal, cancellations would rise from 40 to 50. The one-point increase would amount to ten more cancellations in that example.

Now divide the one-point increase by the starting rate of four points and multiply by 100. The relative increase is 25%. It tells you that the new rate is one-quarter higher than the old rate. Writing only “rose 25%” leaves readers to guess whether you mean the count of cancellations or the cancellation rate.

Check what went into each rate

Change the subscriber totals and the same two rates can tell a different story. If the business had 2,000 subscribers in the first period, 4% would be 80 cancellations. If it had 1,000 in the second, 5% would be 50. The cancellation rate rose one point while the number of cancellations fell by 30. You can tell both changes accurately once you name the numerator, denominator and period.

Look at the population before doing the arithmetic. A rate among all active subscriptions can differ from a rate among subscriptions that came up for renewal. A change in the definition may make the two published rates hard to compare even when their labels look similar.

Compare in the right direction

Going from 5% back to 4% is also a one-point move. The relative decrease is 20%, because the starting rate is now five points. Percentage-point changes keep the same size when the direction reverses. Relative changes use a new starting value.

A move from exactly zero to a positive rate has a percentage-point change. Relative percentage change from zero is undefined because the calculation requires division by zero. If the source rounded a small figure to zero, seek the unrounded data before deciding whether a relative change can be computed.

• Write down both original rates and the group each covers.
• Check the counts when the headline describes people, payments or events.
• State which rate is the starting value if you calculate relative change.