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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 ).
Shapiro–Wilk test: interval: univariate: 1: Normality test: sample size between 3 and 5000 [16] Kolmogorov–Smirnov test: interval: 1: Normality test: distribution parameters known [16] Shapiro-Francia test: interval: univariate: 1: Normality test: Simpliplification of Shapiro–Wilk test Lilliefors test: interval: 1: Normality test
Kolmogorov–Smirnov test: this test only works if the mean and the variance of the normal distribution are assumed known under the null hypothesis, Lilliefors test: based on the Kolmogorov–Smirnov test, adjusted for when also estimating the mean and variance from the data, Shapiro–Wilk test, and; Pearson's chi-squared test.
More generally, Shapiro–Wilk test uses the expected values of the order statistics of the given distribution; the resulting plot and line yields the generalized least squares estimate for location and scale (from the intercept and slope of the fitted line). [9]
N = the sample size The resulting value can be compared with a chi-square distribution to determine the goodness of fit. The chi-square distribution has ( k − c ) degrees of freedom , where k is the number of non-empty bins and c is the number of estimated parameters (including location and scale parameters and shape parameters) for the ...
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.
In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods.
Equivalence T-Tests: Test the difference between two means with an interval-null hypothesis. JAGS: Implement Bayesian models with the JAGS program for Markov chain Monte Carlo. Learn Bayes: Learn Bayesian statistics with simple examples and supporting text. Learn Stats: Learn classical statistics with simple examples and supporting text.