6.0 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Coefficient of variation | 2/3 | https://en.wikipedia.org/wiki/Coefficient_of_variation | reference | science, encyclopedia | 2026-05-05T07:23:32.496013+00:00 | kb-cron |
This term was intended to be analogous to the coefficient of variation, for describing multiplicative variation in log-normal data, but this definition of GCV has no theoretical basis as an estimate of
c
v
{\displaystyle c_{\rm {v}}\,}
itself. For many practical purposes (such as sample size determination and calculation of confidence intervals) it is
s
l
n
{\displaystyle s_{ln}\,}
which is of most use in the context of log-normally distributed data. If necessary, this can be derived from an estimate of
c
v
{\displaystyle c_{\rm {v}}\,}
or GCV by inverting the corresponding formula.
== Comparison to standard deviation ==
=== Advantages === The coefficient of variation is useful because the standard deviation of data must always be understood in the context of the mean of the data. In contrast, the actual value of the CV is independent of the unit in which the measurement has been taken, so it is a dimensionless number. For comparison between data sets with different units or widely different means, one should use the coefficient of variation instead of the standard deviation.
=== Disadvantages === When the mean value is close to zero, the coefficient of variation will approach infinity and is therefore sensitive to small changes in the mean. This is often the case if the values do not originate from a ratio scale. Unlike the standard deviation, it cannot be used directly to construct confidence intervals for the mean.
== Applications == The coefficient of variation is also common in applied probability fields such as renewal theory, queueing theory, and reliability theory. In these fields, the exponential distribution is often more important than the normal distribution. The standard deviation of an exponential distribution is equal to its mean, so its coefficient of variation is equal to 1. Distributions with CV < 1 (such as an Erlang distribution) are considered low-variance, while those with CV > 1 (such as a hyper-exponential distribution) are considered high-variance. Some formulas in these fields are expressed using the squared coefficient of variation, often abbreviated SCV. In modeling, a variation of the CV is the CV(RMSD). Essentially the CV(RMSD) replaces the standard deviation term with the Root Mean Square Deviation (RMSD). While many natural processes indeed show a correlation between the average value and the amount of variation around it, accurate sensor devices need to be designed in such a way that the coefficient of variation is close to zero, i.e., yielding a constant absolute error over their working range. In actuarial science, the CV is known as unitized risk. In industrial solids processing, CV is particularly important to measure the degree of homogeneity of a powder mixture. Comparing the calculated CV to a specification will allow to define if a sufficient degree of mixing has been reached.
=== Laboratory measures of intra-assay and inter-assay CVs === CV measures are often used as quality controls for quantitative laboratory assays. While intra-assay and inter-assay CVs might be assumed to be calculated by simply averaging CV values across CV values for multiple samples within one assay or by averaging multiple inter-assay CV estimates, it has been suggested that these practices are incorrect and that a more complex computational process is required. It has also been noted that CV values are not an ideal index of the certainty of a measurement when the number of replicates varies across samples − in this case standard error in percent is suggested to be superior. If measurements do not have a natural zero point then the CV is not a valid measurement and alternative measures such as the intraclass correlation coefficient are recommended.
=== As a measure of economic inequality === The coefficient of variation fulfills the requirements for a measure of economic inequality. If x (with entries xi) is a list of the values of an economic indicator (e.g. wealth), with xi being the wealth of agent i, then the following requirements are met:
Anonymity – cv is independent of the ordering of the list x. This follows from the fact that the variance and mean are independent of the ordering of x. Scale invariance: cv(x) = cv(αx) where α is a real number. Population independence – If {x,x} is the list x appended to itself, then cv({x,x}) = cv(x). This follows from the fact that the variance and mean both obey this principle. Pigou–Dalton transfer principle: when wealth is transferred from a wealthier agent i to a poorer agent j (i.e. xi > xj) without altering their rank, then cv decreases and vice versa. cv assumes its minimum value of zero for complete equality (all xi are equal). Its most notable drawback is that it is not bounded from above, so it cannot be normalized to be within a fixed range (e.g. like the Gini coefficient which is constrained to be between 0 and 1). It is, however, more mathematically tractable than the Gini coefficient.
=== As a measure of standardisation of archaeological artefacts === Archaeologists often use CV values to compare the degree of standardisation of ancient artefacts. Variation in CVs has been interpreted to indicate different cultural transmission contexts for the adoption of new technologies. Coefficients of variation have also been used to investigate pottery standardisation relating to changes in social organisation. Archaeologists also use several methods for comparing CV values, for example the modified signed-likelihood ratio (MSLR) test for equality of CVs.