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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 ).
An example of Pearson's test is a comparison of two coins to determine whether they have the same probability of coming up heads. The observations can be put into a contingency table with rows corresponding to the coin and columns corresponding to heads or tails. The elements of the contingency table will be the number of times each coin came ...
Samuel Shapiro may refer to: Samuel Shapiro (Illinois politician) (1907–1987), governor of Illinois; Samuel Shapiro (Maine politician) (born 1927), Maine politician; Shmuel Shapiro (born 1974), French Jewish rabbi, hazzan, and singer; Samuel Sanford Shapiro (1930–2023), statistician who developed the Shapiro–Wilk test
The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.
Samuel Sanford Shapiro (July 13, 1930 – November 5, 2023) was an American statistician and engineer. He was a professor emeritus of statistics at Florida International University . He was known for his co-authorship of the Shapiro–Wilk test and the Shapiro–Francia test .
The elements of a dispersion fan diagram [1] are: . a circular line as scale; a diameter which indicates the median; a fan (a segment of a circle) which indicates the quartiles; two feathers which indicate the extreme values.
A normal quantile plot for a simulated set of test statistics that have been standardized to be Z-scores under the null hypothesis. The departure of the upper tail of the distribution from the expected trend along the diagonal is due to the presence of substantially more large test statistic values than would be expected if all null hypotheses were true.
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 .