Percentage point
Encyclopedia
Percentage points are the unit for the arithmetic difference of two percentage
s.
Consider the following hypothetical example: in 1980, 40 percent of the population smoked, and in 1990 only 30 percent smoked. We can thus say that from 1980 to 1990, the incidence of smoking decreased by 10 percentage points even though smoking did not decrease by 10 percent (actually it decreased by 25 percent, assuming the same total population in both years) — percentages indicate ratios, not differences.
Statements such as "between 1980 and 1990, the smoking rate decreased twice as much as the lung cancer rate" are ambiguous: it is not clear whether percentages or percentage points are being compared.
Percentage points are also used to express the difference of risks or probabilities
. Consider for instance a certain drug, which cures a given disease in 70 percent of all cases; without the drug, the disease heals spontaneously in only 50 percent of cases. The drug thus causes an absolute risk reduction of 20 percentage points. Here the reciprocal
is especially meaningful and is known as the number needed to treat
(NNT): 1/(20%) = 1/0.20 = 5; if you treat 5 patients with the drug, you can expect to heal one more case of the disease than you would have without using the drug.
For a 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.
There are two correct ways to talk about a rise from 50% to 60%:-
(1) a rise of 20%,
or,
(2) a rise of 10 Percentage Points
Percentage
In mathematics, a percentage is a way of expressing a number as a fraction of 100 . It is often denoted using the percent sign, “%”, or the abbreviation “pct”. For example, 45% is equal to 45/100, or 0.45.Percentages are used to express how large/small one quantity is, relative to another quantity...
s.
Consider the following hypothetical example: in 1980, 40 percent of the population smoked, and in 1990 only 30 percent smoked. We can thus say that from 1980 to 1990, the incidence of smoking decreased by 10 percentage points even though smoking did not decrease by 10 percent (actually it decreased by 25 percent, assuming the same total population in both years) — percentages indicate ratios, not differences.
Statements such as "between 1980 and 1990, the smoking rate decreased twice as much as the lung cancer rate" are ambiguous: it is not clear whether percentages or percentage points are being compared.
Percentage points are also used to express the difference of risks or probabilities
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
. Consider for instance a certain drug, which cures a given disease in 70 percent of all cases; without the drug, the disease heals spontaneously in only 50 percent of cases. The drug thus causes an absolute risk reduction of 20 percentage points. Here the reciprocal
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the...
is especially meaningful and is known as the number needed to treat
Number needed to treat
The number needed to treat is an epidemiological measure used in assessing the effectiveness of a health-care intervention, typically a treatment with medication. The NNT is the average number of patients who need to be treated to prevent one additional bad outcome...
(NNT): 1/(20%) = 1/0.20 = 5; if you treat 5 patients with the drug, you can expect to heal one more case of the disease than you would have without using the drug.
For a measurements with percentage as unit, like growth, yield
Yield (finance)
In finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return...
, or ejection fraction
Ejection fraction
In cardiovascular physiology, ejection fraction is the fraction of Blood pumped out of the Right Ventricle of the heart to the Pulmonary Circulation and Left Ventricle of the heart to the Systemic Circulation with each Heart beat or Cardiac cycle...
, the standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
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.
There are two correct ways to talk about a rise from 50% to 60%:-
(1) a rise of 20%,
or,
(2) a rise of 10 Percentage Points
Related units
- PercentagePercentageIn mathematics, a percentage is a way of expressing a number as a fraction of 100 . It is often denoted using the percent sign, “%”, or the abbreviation “pct”. For example, 45% is equal to 45/100, or 0.45.Percentages are used to express how large/small one quantity is, relative to another quantity...
- Per millePermilleA per mil or per mille is a tenth of a percent or one part per thousand. It is written with the sign ‰ , which looks like a percent sign with an extra zero at the end...
(‰) 1 part in 1,000 - Basis pointBasis pointA basis point is a unit equal to 1/100 of a percentage point or one part per ten thousand...
(‱) 1 part in 10,000 - Parts-per notationParts-per notationIn 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...
- Baker percentageBaker percentageBaker's percentage is a baker's notation method indicating the flour-relative proportion of ingredients used when making breads, cakes, muffins, and other pastries. It is also referred to as baker's math, or otherwise contextually indicated by a phrase such as based on flour weight...