Where does rank collide?

A level in the nested classification of living things at which organisms are grouped, such as kingdom, class, order, genus, and species. Linnaeus's 1735 Systema Naturae arranged nature into these fixed, nested tiers, so that every organism sits at a named tier inside a larger one, and de Queiroz and Gauthier's 1992 Phylogenetic taxonomy later re-examined whether such tiers should be kept at all. Here a rank is a category in a classification held by a whole group of organisms, and it has nothing to do with the count of independent directions in a matrix, the ordered position of a number in a list, or a place in a social hierarchy.[1][2]

Unit

One tier in the classification hierarchy, held by a named group of organisms

Recovery means

Not applicable

Measured by

Assigned by taxonomists from shared characters and, in modern practice, evolutionary relationships, and codified by the nomenclatural codes

The number of linearly independent columns of a matrix, equal to the dimension of the space those columns span. Frobenius introduced the term (German Rang) in his 1879 paper Über homogene totale Differentialgleichungen, giving a single number for how many of a matrix's directions are genuinely distinct, so that a matrix whose columns are all multiples of one column has rank one. Here a rank is a count of independent dimensions carried by an array of numbers, and it is unrelated to a tier in biological classification, an ordered position in sorted data, or standing in a social group.[3]

Unit

A whole number from zero up to the smaller of the row and column counts

Recovery means

Not applicable

Measured by

Computed by row reduction, or as the count of non-zero pivots or non-zero singular values

The position of an observation once a set of values is sorted from smallest to largest, used so that a method depends only on order and not on the raw numbers. Spearman's 1904 The proof and measurement of association between two things replaced paired measurements by their ranks to gauge how closely two orderings agree, and Wilcoxon's 1945 Individual comparisons by ranking methods built hypothesis tests on the same ranking idea. Here a rank is an ordinal label attached to one data point relative to the others, and it differs from a tier in a classification, the count of independent directions in a matrix, or a person's place in a social order.[4][5]

Unit

An integer position, from 1 for the smallest value up to n for the largest, with ties averaged

Recovery means

Not applicable

Measured by

Obtained by sorting the observations and recording each value's position, then used in rank correlation and rank-based tests

An individual's standing in a hierarchy of status and dominance, from the top of the order down to the bottom. Schjelderup-Ebbe's 1922 Beiträge zur Sozialpsychologie des Haushuhns first described such a ranked order, the pecking order among domestic hens, as a stable pattern of who yields to whom, and social rank theory in human psychology, set out by Price, Sloman, Gardner, Gilbert, and Rohde in 1994 and by Gilbert and Allan in 1998, treated felt low rank as a factor in depression. Here a rank is a position held by a person or animal within a group, and it is not a tier in biological classification, a count of independent directions in a matrix, or the ordered position of a number in a dataset.[6][7][8]

Unit

A position within a group's dominance or status ordering

Recovery means

Rank can rise or fall as contests, alliances, and circumstances change

Measured by

Assessed from observed wins and losses in dominance interactions, or in people by self-report scales of perceived social rank and status