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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 although smoking did not decrease by 10 percent (actually it decreased by 25 percent) – percentages indicate ratios, not differences.
Percentage point differences are one way to express a risk or probability. Consider a drug that cures a given disease in 70 percent of all cases, while without the drug, the disease heals spontaneously in only 50 percent of cases. The drug reduces absolute risk by 20 percentage points. Alternatives may be more meaningful to consumers of statistics. The such as the reciprocal (also known as the number needed to treat (NNT)). In this case, the reciprocal transform of the percentage point difference would be 1 / (20%) = 1 / 0.20 = 5, i.e., if 5 patients are treated with the drug, one could expect to heal one more case of the disease than would have occurred in the absence of 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