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For example, paired data can arise from measuring a single set of individuals at different points in time. [1] A clinical trial might record the blood pressure in a set of n patients before and after administering a medicine. In this case, the "before" and "after" data sets are paired, as each patient has a "before" measurement and an "after ...
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. [1] An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one.
A pairing can also be considered as an R-linear map: (,), which matches the first definition by setting ():= (,). A pairing is called perfect if the above map Φ {\displaystyle \Phi } is an isomorphism of R -modules and the other evaluation map Φ ′ : N → Hom R ( M , L ) {\displaystyle \Phi '\colon N\to \operatorname {Hom} _{R}(M,L ...
In mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number. Any pairing function can be used in set theory to prove that integers and rational numbers have the same cardinality as natural numbers.
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
The individual's pre-test probability was more than twice the one of the population sample, although the individual's post-test probability was less than twice the one of the population sample (which is estimated by the positive predictive value of the test of 10%), opposite to what would result by a less accurate method of simply multiplying ...
In mathematics, a dual system, dual pair or a duality over a field is a triple (,,) consisting of two vector spaces, and , over and a non-degenerate bilinear map:.. In mathematics, duality is the study of dual systems and is important in functional analysis.
A paired difference test, better known as a paired comparison, is a type of location test that is used when comparing two sets of paired measurements to assess whether their population means differ. A paired difference test is designed for situations where there is dependence between pairs of measurements (in which case a test designed for ...