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The Anderson–Darling test is a statistical test of whether a given sample of data is drawn from a given probability distribution.In its basic form, the test assumes that there are no parameters to be estimated in the distribution being tested, in which case the test and its set of critical values is distribution-free.
Computations or tables of the Wilks' distribution for higher dimensions are not readily available and one usually resorts to approximations. One approximation is attributed to M. S. Bartlett and works for large m [2] allows Wilks' lambda to be approximated with a chi-squared distribution
Assuming H 0 is true, there is a fundamental result by Samuel S. Wilks: As the sample size approaches , and if the null hypothesis lies strictly within the interior of the parameter space, the test statistic defined above will be asymptotically chi-squared distributed with degrees of freedom equal to the difference in dimensionality of and . [14]
where n is the total sample size, X_ i is the sum of items correct for the ith respondent and ¯ is the mean of X_ i values. If it is important to use unbiased operators then the sum of squares should be divided by degrees of freedom ( n − 1) and the probabilities are multiplied by n / ( n − 1 ) . {\textstyle n/(n-1).}
Suppose that we take a sample of size n from each of k populations with the same normal distribution N(μ, σ 2) and suppose that ¯ is the smallest of these sample means and ¯ is the largest of these sample means, and suppose S 2 is the pooled sample variance from these samples. Then the following random variable has a Studentized range ...
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
Size of a pixel on a 17-inch monitor with a resolution of 1024×768 560 μm Thickness of the central area of a human cornea [26] 750 μm Maximum diameter of Thiomargarita namibiensis, the second largest bacterium ever discovered 10 −3: 1 millimeter ~5 mm Length of an average flea is 1–10 mm (usually <5 mm) [27] 2.54 mm
In fluid dynamics, Sauter mean diameter (SMD) is an average measure of particle size. It was originally developed by German scientist Josef Sauter in the late 1920s. [1] [2] It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. Several methods have been devised to obtain a good estimate ...