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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 ).
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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 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 .
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
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Each of the two competing models, the null model and the alternative model, is separately fitted to the data and the log-likelihood recorded. The test statistic (often denoted by D) is twice the log of the likelihoods ratio, i.e., it is twice the difference in the log-likelihoods:
Pa. Gov. Josh Shapiro wants to wipe out $400 million in medical debt with an infusion of $4 million in state funding. Medical debt saddles 1 in 10 York County residents. Gov.