|This article does not cite any references or sources. (June 2009)|
Consider the following hypothetical example: In 1980, 40 percent of the population smoked, and in 1990 only 30 percent smoked. One can thus say that from 1980 to 1990, the incidence of smoking decreased by 10 percentage points even though smoking did not decrease by 10 percent (actually it decreased by 25 percent) – percentages indicate ratios, not differences.
Percentage points are also used to express the difference of risks or probabilities. Consider for instance a certain drug, which cures a given disease in 70 percent of all cases; without the drug, the disease heals spontaneously in only 50 percent of cases. The drug thus causes an absolute risk reduction of 20 percentage points. Here the reciprocal is especially meaningful and is known as the number needed to treat (NNT): 1/(20%) = 1/0.20 = 5; if you treat 5 patients with the drug, you can expect to heal one more case of the disease than you would have without using the drug.
For measurements with percentage as unit, like growth, yield, or ejection fraction, the standard deviation will have percentage points as unit. Mistakenly using percentage as the unit for the standard deviation is confusing since percentage is also used as a unit for the relative standard deviation, i.e., the standard deviation divided by the average value (Coefficient of Variation).
- Percentage (%) 1 part in 100
- Per mille (‰) 1 part in 1,000
- Basis point (‱) 1 part in 10,000
- Parts-per notation
- Baker percentage
- Percent point function