paarweisen

Paarweise is a German term meaning “in pairs” or “two at a time.” It is formed from the noun Paar (pair) and the suffix -weise, indicating a manner or method. The standard form is paarweise, used as an adverb in most contexts; the corresponding noun form is less common but may appear in some technical writings.

In mathematics, statistics and related fields, paarweise describes operations or properties that involve all two-element combinations from a set. Common usages include pairwise distinct (paarweise verschieden), where no two elements are equal, and pairwise independence (paarweise unabhängig), where any two variables are independent. The concept also appears in pairwise comparisons, where items are evaluated two at a time rather than all at once.

In data analysis and computer science, paarweise processing refers to tasks performed on every unordered pair of observations or items. This includes computing pairwise distances or similarities, creating pairwise distance matrices, or conducting pairwise correlation analyses. In handling missing data, pairwise deletion describes a method where only the data available for a given pair are used, rather than discarding an entire observation.

Usage notes and variations: while the adjective/adverb form paarweise is standard, some texts may also use related phrases such as “in Paaren” to stress physical grouping into couples. The term is common in academic writing but less frequent in everyday language, where clearer phrases like “in zwei aufeinanderfolgenden Schritten” or “zwei auf einmal” may be preferred depending on context.

See also: Paar, Paarung, Pairwise distance, Pairwise comparison.