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.
In statistics, normalitytests 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...
Khan, Rehan Ahmad (8 September 2015). "A power comparison of various normalitytests". Pakistan Journal of Statistics and Operation Research. 11 (3): 331–345...
Look up normality or normalities in Wiktionary, the free dictionary. Normality may refer to: Asymptotic normality, in mathematics and statistics Complete...
a mathematical discipline, the fundamental normalitytest gives sufficient conditions to test the normality of a family of analytic functions. It is another...
In statistics, the Lilliefors test is a normalitytest based on the Kolmogorov–Smirnov test. It is used to test the null hypothesis that data come from...
non-normal data. Multivariate normalitytests include the Cox–Small test and Smith and Jain's adaptation of the Friedman–Rafsky test created by Larry Rafsky...
additional information. The sample extrema can be used for a simple normalitytest, specifically of kurtosis: one computes the t-statistic of the sample...
(1901) There are statistical methods to empirically test that assumption; see the above Normalitytests section. In biology, the logarithm of various variables...
the basis for robust measures of skewness and kurtosis, and even a normalitytest. Summary statistics Socio-economic decile (for New Zealand schools)...
hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see Kolmogorov–Smirnov test),...
such terms as feeble-mindedness, border-line intelligence, dullness, normality, superior intelligence, genius, etc.? When we use these terms two facts...
plot is a graphical technique to identify substantive departures from normality. This includes identifying outliers, skewness, kurtosis, a need for transformations...
going to be positive or negative. D'Agostino's K-squared test is a goodness-of-fit normalitytest based on sample skewness and sample kurtosis. Other measures...
Global Information