kvotmått

Kvotmått is a term used in Swedish to refer to two related concepts in mathematics and statistics. In measurement theory it denotes ratio-level measurement, i.e., a measurement scale where zero means none and both differences and ratios between values are meaningful. Such data support arithmetic operations including multiplication and division. Examples include length, mass, time durations, income, and physical quantities measured with an absolute zero. By contrast, interval scales (where zero is arbitrary) do not support meaningful ratios.

In practice, kvotmått implies that it is legitimate to compare values by computing ratios (e.g., doubling a length) and to compute statistics appropriate for ratio data, such as the geometric mean or the coefficient of variation. When data are on a kvotmått, many standard parametric methods assume an approximately normal distribution on the log-scale or apply methods that respect multiplicative structure.

In measure theory, kvotmått can refer to a quotient measure. Given a measure space (X, Σ, μ) and an equivalence relation ~ partitioning X into classes, there is a natural projection π: X → X/~. The quotient measure μ* on the quotient space is defined by μ*(A) = μ(π^{-1}(A)) for measurable A. This measure is the pushforward of μ by the quotient map and is invariant under the equivalence relation.