Percentage points and relative change

Two different comparisons can both be correct

A participation rate rises from 40% to 50%. The difference is 10 percentage points: 50 − 40. The relative percentage increase in the rate is (50 − 40)/40 × 100% = 25%. They use different reference quantities.

Calling the change “10%” without saying which comparison is intended can be misleading. The final rate 50% is 125% of the original rate 40%, so the increase is 25% of that original rate.

A rate does not give the underlying count

If the first population has 100 people and the second 200, the participating counts are 40 and 100. Their count increase is 150%, different from the rate increase. Know both population totals before inferring a change in people from a change in proportions.

Check your understanding 1 Name the reference whole

A proportion falls from 60% to 45%. Give the decrease in percentage points and the relative percentage decrease in the proportion.

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The drop is 15 percentage points. Relative to the original 60%, it is 15/60 × 100% = 25%. The denominator for relative change is the original proportion, not the final one.

Label the result

Report “percentage points” for the subtraction of two percentage rates and “percent” for the relative comparison. A number without that label does not say which change was calculated.