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Equivalence relations are a ready source of examples or counterexamples. For example, an equivalence relation with exactly two infinite equivalence classes is an easy example of a theory which is ω-categorical, but not categorical for any larger cardinal number.
In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.Notionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations, where the test statistic used is the ratio of two sample variances. [1]
Equivalence tests are a variety of hypothesis tests used to draw statistical inferences from observed data. In these tests, the null hypothesis is defined as an effect large enough to be deemed interesting, specified by an equivalence bound. The alternative hypothesis is any effect that is less extreme than said equivalence bound.
In mathematics, given a category C, a quotient of an object X by an equivalence relation: is a coequalizer for the pair of maps , =,, where R is an object in C and "f is an equivalence relation" means that, for any object T in C, the image (which is a set) of : = (,) () is an equivalence relation; that is, a reflexive, symmetric and transitive relation.
An example is the relation "is equal to", because if a = b is true then b = a is also true. If R T represents the converse of R, then R is symmetric if and only if R = R T. [2] Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation. [1]
Measurement invariance or measurement equivalence is a statistical property of measurement that indicates that the same construct is being measured across some specified groups. [1] For example, measurement invariance can be used to study whether a given measure is interpreted in a conceptually similar manner by respondents representing ...
Graph of an example equivalence with 7 classes An equivalence relation is a mathematical relation that generalizes the idea of similarity or sameness. It is defined on a set X {\displaystyle X} as a binary relation ∼ {\displaystyle \sim } that satisfies the three properties: reflexivity , symmetry , and transitivity .
Let Z * (X) := Z[X] be the free abelian group on the algebraic cycles of X. Then an adequate equivalence relation is a family of equivalence relations, ~ X on Z * (X), one for each smooth projective variety X, satisfying the following three conditions: (Linearity) The equivalence relation is compatible with addition of cycles.