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The Shapiro–Wilk test tests the null hypothesis that a sample x1, ..., xn came from a normally distributed population. The test statistic is. where. with parentheses enclosing the subscript index i is the i th order statistic, i.e., the i th-smallest number in the sample (not to be confused with ). is the sample mean.
Normality test. In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed. More precisely, the tests are a form of model selection, and can be interpreted several ways, depending on one's ...
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. [1]
Empirical testing has found [5] that the Anderson–Darling test is not quite as good as the Shapiro–Wilk test, but is better than other tests. Stephens [1] found to be one of the best empirical distribution function statistics for detecting most departures from normality.
Various studies have found that, even in this corrected form, the test is less powerful for testing normality than the Shapiro–Wilk test or Anderson–Darling test. [2] However, these other tests have their own disadvantages. For instance the Shapiro–Wilk test is known not to work well in samples with many identical values.
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
The data cover the period 1893–2001. In statistics, a Q–Q plot (quantile–quantile plot) is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other. [1] A point (x, y) on the plot corresponds to one of the quantiles of the second distribution (y -coordinate) plotted ...
A confidence band is used in statistical analysis to represent the uncertainty in an estimate of a curve or function based on limited or noisy data. Similarly, a prediction band is used to represent the uncertainty about the value of a new data-point on the curve, but subject to noise. Confidence and prediction bands are often used as part of ...