The Anderson–Darling test is a statistical test of whether a given sample of data is drawn from a given probability distribution. In its basic form, the test assumes that there are no parameters to be estimated in the distribution being tested, in which case the test and its set of critical values is distribution-free. However, the test is most often used in contexts where a family of distributions is being tested, in which case the parameters of that family need to be estimated and account must be taken of this in adjusting either the test-statistic or its critical values. When applied to testing whether a normal distribution adequately describes a set of data, it is one of the most powerful statistical tools for detecting most departures from normality. K-sample Anderson–Darling tests are available for testing whether several collections of observations can be modelled as coming from a single population, where the distribution function does not have to be specified. In addition to its use as a test of fit for distributions, it can be used in parameter estimation as the basis for a form of minimum distance estimation procedure. The test is named after Theodore Wilbur Anderson (1918–2016) and Donald A. Darling (1915–2014), who invented it in 1952. The single-sample test The Anderson–Darling and Cramér–von Mises statistics belong to the class of quadratic EDF statistics (tests based on the empirical distribution function). If the hypothesized distribution is , and empirical (sample) cumulative distribution function is , then the quadratic EDF statistics measure the distance between and by where is the number of elements in the sample, and is a weighting function. When the weighting function is , the statistic is the Cramér–von Mises statistic. The Anderson–Darling (1954) test is based on the distance which is obtained when the weight function is . Thus, compared with the Cramér–von Mises distance, the Anderson–Darling distance places more weight on observations in the tails of the distribution. Basic test statistic The Anderson–Darling test assesses whether a sample comes from a specified distribution. It makes use of the fact that, when given a hypothesized underlying distribution and assuming the data does arise from this distribution, the cumulative distribution function (CDF) of the data can be assumed to follow a uniform distribution. The data can be then tested for uniformity with a distance test (Shapiro 1980). The formula for the test statistic to assess if data