Percentage point

Last updated

A percentage point or percent point is the unit for the arithmetic difference of two percentages. 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. [1] In literature, the unit is usually either written out, [2] 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 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. [ citation needed ] 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).

See also

Related Research Articles

<span class="mw-page-title-main">Standard deviation</span> In statistics, a measure of variation

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 of the set, while a high standard deviation indicates that the values are spread out over a wider range.

<span class="mw-page-title-main">Percentage</span> Number or ratio expressed as a fraction of 100

In mathematics, a percentage 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 used. A percentage is a dimensionless number ; it has no unit of measurement.

<span class="mw-page-title-main">Parts-per notation</span> Set of pseudo units to describe small values of miscellaneous dimensionless quantities

In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Commonly used are parts-per-million, parts-per-billion, parts-per-trillion and parts-per-quadrillion. This notation is not part of the International System of Units (SI) system and its meaning is ambiguous.

In economics, elasticity measures the percentage change of one economic variable in response to a percentage change in another. If a good's price elasticity of demand is -2, a 10% increase in price causes the quantity demanded to fall 20%.

<span class="mw-page-title-main">Standard score</span> How many standard deviations apart from the mean an observed datum is

In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.

<span class="mw-page-title-main">Per mille</span> Unit for parts per thousand (‰)

Per mille is an expression that means parts per thousand. Other recognised spellings include per mil, per mill, permil, permill, or permille.

In pharmacology, bioavailability is a subcategory of absorption and is the fraction (%) of an administered drug that reaches the systemic circulation.

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 a percentage, and is defined as the ratio of the standard deviation to the mean . The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, and in neuroscience.

A basis point 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 an interest rate of 10% increased by 1 bp, it changed to 10.01%.

One millionth is equal to 0.000 001, or 1 x 10−6 in scientific notation. It is the reciprocal of a million, and can be also written as 11,000,000. Units using this fraction can be indicated using the prefix "micro-" from Greek, meaning "small". Numbers of this quantity are expressed in terms of μ.

The percent sign% is the symbol used to indicate a percentage, a number or ratio as a fraction of 100. Related signs include the permille sign and the permyriad sign , which indicate that a number is divided by one thousand or ten thousand, respectively. Higher proportions use parts-per notation.

Cost per mille (CPM), also called cost per thousand (CPT), is a commonly-used measurement in advertising. It is the cost an advertiser pays for one thousand views or impressions of an advertisement. Radio, television, newspaper, magazine, out-of-home advertising, and online advertising can be purchased on the basis of exposing the ad to one thousand viewers or listeners. It is used in marketing as a benchmarking metric to calculate the relative cost of an advertising campaign or an ad message in a given medium.

In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared. The comparison is expressed as a ratio and is a unitless number. By multiplying these ratios by 100 they can be expressed as percentages so the terms percentage change, percent(age) difference, or relative percentage difference are also commonly used. The distinction between "change" and "difference" depends on whether or not one of the quantities being compared is considered a standard or reference or starting value. When this occurs, the term relative change is used and otherwise the term relative difference is preferred. Relative difference is often used as a quantitative indicator of quality assurance and quality control for repeated measurements where the outcomes are expected to be the same. A special case of percent change called percent error occurs in measuring situations where the reference value is the accepted or actual value and the value being compared to it is experimentally determined.

<span class="mw-page-title-main">Per cent mille</span> One-thousandth of a percent

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.

Health in Indonesia is affected by a number of factors. Indonesia has over 26,000 health care facilities; 2,000 hospitals, 9,000 community health centres and private clinics, 1,100 dentist clinics and 1,000 opticians. The country lacks doctors with only 0.4 doctors per 1,000 population. In 2018, Indonesia's healthcare spending was US$38.3 billion, 4.18% of their GDP, and is expected to rise to US$51 billion in 2020.

<span class="mw-page-title-main">Health in Thailand</span>

Thailand has had "a long and successful history of health development," according to the World Health Organization. Life expectancy is averaged at seventy years. Non-communicable diseases form the major burden of morbidity and mortality, while infectious diseases including malaria and tuberculosis, as well as traffic accidents, are also important public health issues.

In the post-Soviet era, the quality of Uzbekistan’s health care has declined. Between 1992 and 2003, spending on health care and the ratio of hospital beds to population both decreased by nearly 50 percent, and Russian emigration in that decade deprived the health system of many practitioners. In 2004 Uzbekistan had 53 hospital beds per 10,000 population. Basic medical supplies such as disposable needles, anesthetics, and antibiotics are in very short supply. Although all citizens nominally are entitled to free health care, in the post-Soviet era bribery has become a common way to bypass the slow and limited service of the state system. In the early 2000s, policy has focused on improving primary health care facilities and cutting the cost of inpatient facilities. The state budget for 2006 allotted 11.1 percent to health expenditures, compared with 10.9 percent in 2005.

Healthcare in Laos is provided by both the private and public sector. It is limited in comparison with other countries. Western medical care is available in some locations, but remote areas and ethnic groups are underserved. Public spending on healthcare is low compared with neighbouring countries. Still, progress has been made since Laos joined the World Health Organization in 1950: life expectancy at birth rose to 66 years by 2015; malaria deaths and tuberculosis prevalence have plunged; and the maternal mortality ratio (MMR) has declined by 75 percent.

In macroeconomics, the cost of business cycles is the decrease in social welfare, if any, caused by business cycle fluctuations.

<span class="mw-page-title-main">Health in Norway</span> Overview of health in Norway

Health in Norway, with its early history of poverty and infectious diseases along with famines and epidemics, was poor for most of the population at least into the 1800s. The country eventually changed from a peasant society to an industrial one and established a public health system in 1860. Due to the high life expectancy at birth, the low under five mortality rate and the fertility rate in Norway, it is fair to say that the overall health status in the country is generally good.


  1. Brechner, Robert (2008). Contemporary Mathematics for Business and Consumers, Brief Edition. Cengage Learning. p. 190. ISBN   9781111805500. Archived from the original on 18 May 2015. Retrieved 7 May 2015.
  2. Wickham, Kathleen (2003). Math Tools for Journalists. Cengage Learning. p. 30. ISBN   9780972993746. Archived from the original on 18 May 2015. Retrieved 7 May 2015.