The denominator matters
Check a percentage by translating it into counts.
“It doubled” sounds impressive, but without a starting point it remains incomplete. A change from 1 to 2 and a change from 100 to 200 are both increases of 100%, with different absolute differences. Look for the denominator, time period, and population.
In a fictional example, 2 of 100 people finish a task in group A and 4 of 100 in group B. The rate rises from 2% to 4%: two percentage points, or a 100% relative increase. Percentage points subtract the rates; relative change divides the difference by the original rate.
Then ask whether the groups are comparable, how participants were selected, and what else differed. Correct arithmetic does not establish causation. Reconstruct the counts before interpreting what the comparison means.
Make your understanding visible
A proportion rises from 20% to 30%. What is the percentage-point change and the relative increase?
Compare with a reference response
Ten percentage points; the relative increase is (30−20)/20 = 50%. This is an original arithmetic example, not a real experiment or a health-risk estimate.
Sources & further reading
Original arithmetic exercise · worked calculation included