A percentage point or percent point is the
unit for the
arithmetic difference between two
percentage
In mathematics, a percentage (from la, per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also us ...
s. For example, moving up from 40 percent to 44 percent is an increase of 4 percentage points, but a 10-percent increase in the quantity being measured. In literature, the unit is usually either written out,
or abbreviated as ''pp'' or ''p.p.'' to avoid ambiguity. After the first occurrence, some writers abbreviate by using just "point" or "points".
Differences between percentages and percentage points
Consider the following hypothetical example: In 1980, 50 percent of the population smoked, and in 1990 only 40 percent of the population smoked. One can thus say that from 1980 to 1990, the prevalence of smoking decreased by 10 ''percentage points'' (or by 10 percent of the population) or by ''20 percent'' when talking about smokers only - percentages indicate proportionate part of a total.
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, 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/(20pp) = 1/0.20 = 5. Thus 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 involving percentages as a unit, such as, growth,
yield, or
ejection fraction,
statistical deviation In mathematics and statistics, deviation is a measure of difference between the observed value of a variable and some other value, often that variable's mean. The sign of the deviation reports the direction of that difference (the deviation is po ...
s and related
descriptive statistics, including the
standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
and
root-mean-square error
The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed. The RMSD represents ...
, the result should be expressed in units of percentage points instead of percentage. 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. standard deviation divided by average value (
coefficient of variation
In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as ...
).
Related units
*
Percentage
In mathematics, a percentage (from la, per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also us ...
(%) 1 part in 100
*
Per mille (‰) 1 part in 1,000
*
Basis point (bp) difference of 1 part in 10,000
*
Permyriad (‱) 1 part in 10,000
*
Per cent mille (pcm) 1 part in 100,000
*
Baker percentage
See also
*
Parts-per notation
*
Per-unit system
*
Percent point function
*
Relative change and difference
References
{{Reflist
Mathematical terminology
Probability assessment
Units of measurement
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