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 use ...

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 is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...

. 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 (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 deviations and related descriptive statistics, including the standard deviation and root-mean-square error, 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 ...

, 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 a ...

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 use ...

(%) 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 ...

(‰) 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, morta ...

(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