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A polygon is a generalization of a 3-sided triangle, a 4-sided quadrilateral, and so on to n sides. A hypercube is a generalization of a 2-dimensional square, a 3-dimensional cube, and so on to n dimensions. A quadric, such as a hypersphere, ellipsoid, paraboloid, or hyperboloid, is a generalization of a conic section to higher dimensions.
Generalizability theory, or G theory, is a statistical framework for conceptualizing, investigating, and designing reliable observations.It is used to determine the reliability (i.e., reproducibility) of measurements under specific conditions.
Therefore, generalization is a valuable and integral part of learning and everyday life. Generalization is shown to have implications on the use of the spacing effect in educational settings. [13] In the past, it was thought that the information forgotten between periods of learning when implementing spaced presentation inhibited generalization ...
The full generalization rule allows for hypotheses to the left of the turnstile, but with restrictions. Assume Γ {\displaystyle \Gamma } is a set of formulas, φ {\displaystyle \varphi } a formula, and Γ ⊢ φ ( y ) {\displaystyle \Gamma \vdash \varphi (y)} has been derived.
Multiple testing correction refers to making statistical tests more stringent in order to counteract the problem of multiple testing. The best known such adjustment is the Bonferroni correction, but other methods have been developed.
In statistics, the generalized Dirichlet distribution (GD) is a generalization of the Dirichlet distribution with a more general covariance structure and almost twice the number of parameters. Random vectors with a GD distribution are completely neutral .
Unlike Lebesgue's and Brouwer's generalization of the Jordan curve theorem, this statement becomes false in higher dimensions: while the exterior of the unit ball in R 3 is simply connected, because it retracts onto the unit sphere, the Alexander horned sphere is a subset of R 3 homeomorphic to a sphere, but so twisted in space that the ...
A generalization of the Sierpiński triangle can also be generated using Pascal's triangle if a different modulus is used. Iteration n {\displaystyle n} can be generated by taking a Pascal's triangle with P n {\displaystyle P^{n}} rows and coloring numbers by their value modulo P {\displaystyle P} .
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