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The name of this formula stems from the fact that is the twentieth formula discussed in Kuder and Richardson's seminal paper on test reliability. [1] It is a special case of Cronbach's α, computed for dichotomous scores. [2] [3] It is often claimed that a high KR-20 coefficient (e.g., > 0.90) indicates a homogeneous test. However, like ...
Consider a linear non-homogeneous ordinary differential equation of the form = + (+) = where () denotes the i-th derivative of , and denotes a function of .. The method of undetermined coefficients provides a straightforward method of obtaining the solution to this ODE when two criteria are met: [2]
In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets.They relate to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part.
In mathematics, the annihilator method is a procedure used to find a particular solution to certain types of non-homogeneous ordinary differential equations (ODEs). [1] It is similar to the method of undetermined coefficients, but instead of guessing the particular solution in the method of undetermined coefficients, the particular solution is determined systematically in this technique.
Ordinary least squares regression of Okun's law.Since the regression line does not miss any of the points by very much, the R 2 of the regression is relatively high.. In statistics, the coefficient of determination, denoted R 2 or r 2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).
The undetermined coefficients method is a method of appropriately selecting a solution type according to the form of the non-homogeneous term and determining the undetermined constant, so that it satisfies the non-homogeneous equation. [4] On the other hand, the ERF method obtains a special solution based on differential operator. [2]
In this situation, one can often replace the equation above with an equation of the form ∇ ⋅ ( A ∗ ∇ u ) = f {\displaystyle \nabla \cdot \left(A^{*}\nabla u\right)=f} where A ∗ {\displaystyle A^{*}} is a constant tensor coefficient and is known as the effective property associated with the material in question.
For processes that produce homogeneous batches (e.g., chemical) where repeat measurements vary primarily because of measurement error; The "chart" actually consists of a pair of charts: one, the individuals chart, displays the individual measured values; the other, the moving range chart, displays the difference from one point to the next.