This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate? Excessive Violence Sexual Content Political / Social
Email Address:
Article Id: WHEBN0002690983 Reproduction Date:
The Shapiro–Wilk test is a test of normality in frequentist statistics. It was published in 1965 by Samuel Sanford Shapiro and Martin Wilk.^{[1]}
The Shapiro–Wilk test utilizes the null hypothesis principle to check whether a sample x_{1}, ..., x_{n} came from a normally distributed population. The test statistic is:
where
The user may reject the null hypothesis if W is below a predetermined threshold.
The null-hypothesis of this test is that the population is normally distributed. Thus if the p-value is less than the chosen alpha level, then the null hypothesis is rejected and there is evidence that the data tested are not from a normally distributed population. In other words, the data are not normal. On the contrary, if the p-value is greater than the chosen alpha level, then the null hypothesis that the data came from a normally distributed population cannot be rejected. E.g. for an alpha level of 0.05, a data set with a p-value of 0.02 rejects the null hypothesis that the data are from a normally distributed population.^{[2]} However, since the test is biased by sample size,^{[3]} the test may be statistically significant from a normal distribution in any large samples. Thus a Q–Q plot is required for verification in addition to the test.
Monte Carlo simulation has found that Shapiro–Wilk has the best power for a given significance, followed closely by Anderson–Darling when comparing the Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors, and Anderson–Darling tests.^{[4]}
Royston proposed an alternative method of calculating the coefficients vector by providing an algorithm for calculating values, which extended the sample size to 2000.^{[5]} This technique is used in several software packages including R,^{[6]} Stata,^{[7]}^{[8]} SPSS and SAS.^{[9]}
Probability theory, Regression analysis, Mathematics, Observational study, Calculus
Statistics, Nonparametric regression, Robust regression, Least squares, Ordinary least squares
Statistics, Canada, English language, French language, Peer review
Statistics, Regression analysis, Probability distribution, Statistical inference, Analysis of variance
Statistics, Regression analysis, Sociology, Economics, Demography
Statistics, Multivariate statistics, Regression analysis, Empirical distribution function, Cumulative distribution function
Statistics, Regression analysis, Data, Statistical dispersion, Survey methodology
Statistics, Python (programming language), Regression analysis, Normal distribution, Data
Statistics, Regression analysis, Survey methodology, Bioinformatics, Biostatistics