Parametric statistics | Statistical tests | Normality tests

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 interpretations of probability: * In descriptive statistics terms, one measures a goodness of fit of a normal model to the data – if the fit is poor then the data are not well modeled in that respect by a normal distribution, without making a judgment on any underlying variable. * In frequentist statistics statistical hypothesis testing, data are tested against the null hypothesis that it is normally distributed. * In Bayesian statistics, one does not "test normality" per se, but rather computes the likelihood that the data come from a normal distribution with given parameters μ,σ (for all μ,σ), and compares that with the likelihood that the data come from other distributions under consideration, most simply using a Bayes factor (giving the relative likelihood of seeing the data given different models), or more finely taking a prior distribution on possible models and parameters and computing a posterior distribution given the computed likelihoods. A normality test is used to determine whether sample data has been drawn from a normally distributed population (within some tolerance). A number of statistical tests, such as the Student's t-test and the one-way and two-way ANOVA, require a normally distributed sample population. (Wikipedia).

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Related pages

68–95–99.7 rule | Quantile | Shapiro–Wilk test | Skewness | Bayes factor | Statistics | Cramér–von Mises criterion | T-statistic | Null hypothesis | Differential entropy | Anderson–Darling test | Kolmogorov–Smirnov test | Kurtosis risk | Multivariate normal distribution | Seven-number summary | Bayesian statistics | Model selection | Empirical characteristic function | Randomness test | Pearson's chi-squared test | Power of a test | Standardized moment | D'Agostino's K-squared test | Kullback–Leibler divergence | Lilliefors test | Goodness of fit | Histogram | Linear regression | Sample maximum and minimum | Normal distribution | Statistical hypothesis testing | Descriptive statistics | Jarque–Bera test | Random variable | Normal probability plot | Kurtosis | Test statistic | Chi-squared test