A percentage point or percent point is the

unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * ''Unit'' (alb ...

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 Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

. 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 Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another pol ...

, also known as the

number needed to treat The number needed to treat (NNT) or number needed to treat for an additional beneficial outcome (NNTB) is an epidemiological measure used in communicating the effectiveness of a health-care intervention, typically a treatment with medication. The ...

(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 An ejection fraction (EF) is the volumetric fraction (or portion of the total) of fluid (usually blood) ejected from a chamber (usually the heart) with each contraction (or heartbeat). It can refer to the cardiac atrium, ventricle, gall bladder, ...

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 A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and an ...

, 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 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 ...

, 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 Per mille (from Latin , "in each thousand") is an expression that means parts per thousand. Other recognised spellings include per mil, per mill, permil, permill, or permille. The associated sign is written , which looks like a percent sig ...

(‰) 1 part in 1,000 *

Basis point A basis point (often abbreviated as bp, often pronounced as "bip" or "beep") is one hundredth of 1 percentage point. The related term ''permyriad'' means one hundredth of 1 percent. Changes of interest rates are often stated in basis points. If ...

(bp) difference of 1 part in 10,000 *

Permyriad A basis point (often abbreviated as bp, often pronounced as "bip" or "beep") is one hundredth of 1 percentage point. The related term ''permyriad'' means one hundredth of 1 percent. Changes of interest rates are often stated in basis points. If ...

(‱) 1 part in 10,000 *

Per cent mille A per cent mille or pcm is one one-thousandth of a percent. It can be thought of as a "milli-percent". It is commonly used in epidemiology, and in nuclear reactor engineering as a unit of reactivity. Epidemiology Statistics of crime rates, mortal ...

(pcm) 1 part in 100,000 *

Baker percentage Baker's percentage is a notation method indicating the proportion of an ingredient relative to the flour used in a recipe when making breads, cakes, muffins, and other baked goods. It is also referred to as baker's math, and may be indicated by a ph ...

References

{{Reflist Mathematical terminology Probability assessment Units of measurement ru:Процент#Процентный пункт

Differences between percentages and percentage points

Related units

See also

References