Where does deviation collide?

A measure of how far the values in a set spread from their average: each value's deviation is its signed distance from the mean, and the standard deviation is the root mean square of those distances, a single number summarising the dispersion of the whole set. Pearson's 1894 Contributions to the mathematical theory of evolution introduced the term standard deviation for this quantity and placed it at the centre of the emerging theory of statistical variation. The referent is a computed property of a distribution, expressed in the units of the data, and it has nothing to do with a broken social rule, a compass error, or a bent ray of light.[1]

Unit

A distance from the mean, in the units of the measured variable (or its square, for the variance)

Recovery means

Not applicable

Measured by

Computed over a sample or population as the root mean square of each value's departure from the mean

Behaviour that departs from the norms a social group treats as binding, together with the group's response to it: what counts as deviance is not fixed by the act alone but set by the rules a society makes and the way it applies them. Becker's 1963 Outsiders argued that deviance is created when social groups make rules and label those who break them as outsiders, so the label, and not only the conduct, is part of the phenomenon. Merton's earlier account traced it instead to the strain between the goals a culture prizes and the means it makes available. The referent is a relation between conduct and social rules, studied through fieldwork and official records, and it is unrelated to a number summarising a distribution, a magnetic compass error, or the bending of light.[2][3]

Unit

An act or person judged against a group's norms, described by the rule broken and the reaction

Recovery means

Not applicable

Measured by

Studied through ethnography, interviews, self-report surveys, and recorded rates of rule-breaking and sanction

The error of a magnetic compass caused by the magnetism of the vessel that carries it: the ship's own iron and electrical fields pull the needle away from magnetic north, and this deviation changes with the vessel's heading, so it has to be tabulated heading by heading. As The American Practical Navigator sets out, deviation is kept strictly apart from variation, the difference between magnetic and true north that belongs to the Earth's own field and depends only on location. The referent is a heading-dependent instrument error read in degrees east or west, and it is not a statistic, a broken social rule, or the bending of a light ray.[4]

Unit

An angular error of the compass needle, in degrees east or west, varying with heading

Recovery means

Reduced by compensating magnets and soft-iron correctors, with any residual recorded on a deviation card

Measured by

Found by swinging the ship through known headings and comparing each compass reading with the known magnetic bearing

The change in direction of a ray of light as it passes through a refracting element such as a prism: the angle of deviation is the angle between the incoming ray and the emerging ray, and for a prism it reaches a minimum at a particular symmetric orientation from which the material's refractive index can be found. As Hecht's Optics describes, the deviation depends on the prism angle, the wavelength, and the refractive index, which is why a prism spreads white light into a spectrum. The referent is a geometric angle set by refraction, measured in degrees, and it shares nothing with a measure of statistical spread, a violated social norm, or a compass's magnetic error.[5]

Unit

An angle between an incident ray and the emerging ray, in degrees

Recovery means

Not applicable

Measured by

Read on a spectrometer table from the angle of the emerging ray, often at the minimum-deviation position