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The Shapiro–Wilk test tests the null hypothesis that a sample x 1, ..., x n came from a normally distributed population. The test statistic is = (= ()) = (¯), where with parentheses enclosing the subscript index i is the ith order statistic, i.e., the ith-smallest number in the sample (not to be confused with ).
The Shapiro–Francia test is a statistical test for the normality of a population, based on sample data. It was introduced by S. S. Shapiro and R. S. Francia in 1972 as a simplification of the Shapiro–Wilk test .
A graphical tool for assessing normality is the normal probability plot, a quantile-quantile plot (QQ plot) of the standardized data against the standard normal distribution. Here the correlation between the sample data and normal quantiles (a measure of the goodness of fit) measures how well the data are modeled by a normal distribution. For ...
In assessing whether a given distribution is suited to a data-set, the following tests and their underlying measures of fit can be used: Bayesian information criterion; Kolmogorov–Smirnov test; Cramér–von Mises criterion; Anderson–Darling test; Berk-Jones tests [1] [2] Shapiro–Wilk test; Chi-squared test; Akaike information criterion ...
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
Normal probability plots are made of raw data, residuals from model fits, and estimated parameters. A normal probability plot. In a normal probability plot (also called a "normal plot"), the sorted data are plotted vs. values selected to make the resulting image look close to a straight line if the data are approximately normally distributed.
Martin Bradbury Wilk, OC (18 December 1922 – 19 February 2013) [1] [2] was a Canadian statistician, academic, and the former chief statistician of Canada. In 1965, together with Samuel Shapiro , he developed the Shapiro–Wilk test , which can indicate whether a sample of numbers would be unusual if it came from a Gaussian distribution .
This requires that the data be on an ordered metric scale, a type of scale that carries more information than an ordinal scale but may have less than an interval scale. [6] The data for a one-sample test is a sample in which each observation is a real number: , …,. Assume for simplicity that the observations in the sample have distinct ...