Where does dispersion collide?

In optics, dispersion is the dependence of a material's refractive index on the wavelength of light, so that colors bend by different amounts and separate as they pass through a medium. Newton's 1672 letter A new theory about light and colors reported that a glass prism spreads white sunlight into a band of colors, and argued that white light is a mixture of rays that the prism refracts unequally. The thing referred to here is a physical property of a medium, measured by how much the refractive index changes across wavelengths, and it has nothing to do with the spread of a data set, the scatter of prices in a market, or how evenly a word appears across texts.[1]

Unit

One material's change in refractive index across a band of wavelengths

Recovery means

Not applicable

Measured by

Measured by refractometry across wavelengths, and summarized by the Abbe number or a dispersion curve

In statistics, dispersion is the degree to which the values in a distribution are spread out around a central value rather than clustered tightly. Wilhelm Lexis introduced the term into statistical theory in his 1877 Zur Theorie der Massenerscheinungen in der menschlichen Gesellschaft, comparing the observed variability of statistical series against a chance standard, and Pearson's 1894 Contributions to the mathematical theory of evolution later supplied the standard deviation as a principal measure of it. The thing referred to here is the width of a set of numbers, quantified by range, variance, standard deviation, or the interquartile distance, and it is unrelated to light splitting in a prism, the gap between prices, or how a word is scattered through a body of texts.[2][3]

Unit

A single number summarizing how widely the values in a data set are spread

Recovery means

Not applicable

Measured by

Computed as the range, variance, standard deviation, or interquartile range of a sample

In economics, price dispersion is the observation that identical goods sell at different prices across sellers at the same time, rather than converging to a single market price. Stigler's 1961 The Economics of Information explained this as a result of costly search: because buyers must spend time and effort to learn prices, sellers can sustain a spread of prices, and Stigler modeled how much searching a buyer should do. The thing referred to here is variation in the money price of one product across a market, measured in currency or as a coefficient of variation of quoted prices, and it is distinct from color separation in glass, the spread of a data set in general, or how a word is distributed across texts.[4]

Unit

The spread of quoted money prices for one identical good across sellers

Recovery means

Not applicable

Measured by

Measured as the range, variance, or coefficient of variation of prices collected for the same item

In corpus linguistics, dispersion is how evenly a word or feature is distributed across the parts of a corpus, as distinct from how often it occurs overall. Juilland and Chang-Rodriguez introduced a dispersion coefficient, later called Juilland's D, in their 1964 Frequency dictionary of Spanish words to separate words that appear steadily everywhere from words that cluster in a few texts, and Gries's 2008 Dispersions and adjusted frequencies in corpora reviewed and extended the family of such measures. The thing referred to here is the evenness of a term's spread through a body of texts, scored on an index between concentrated and uniform, and it does not describe light through a prism, the scatter of numeric data, or the gap between market prices.[5][6]

Unit

An index of how evenly one word is spread across the sections of a corpus

Recovery means

Not applicable

Measured by

Scored by dispersion measures such as Juilland's D, computed from a word's frequencies across corpus parts