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Function Reference: adtest

statistics: h = adtest (x)
statistics: h = adtest (x, Name, Value)
statistics: [h, pval] = adtest (…)
statistics: [h, pval, adstat, cv] = adtest (…)

Anderson-Darling goodness-of-fit hypothesis test.

h = adtest (x) returns a test decision for the null hypothesis that the data in vector x is from a population with a normal distribution, using the Anderson-Darling test. The alternative hypothesis is that x is not from a population with a normal distribution. The result h is 1 if the test rejects the null hypothesis at the 5% significance level, or 0 otherwise.

h = adtest (x, Name, Value) returns a test decision for the Anderson-Darling test with additional options specified by one or more Name-Value pair arguments. For example, you can specify a null distribution other than normal, or select an alternative method for calculating the p-value, such as a Monte Carlo simulation.

The following parameters can be parsed as Name-Value pair arguments.

NameDescription
"Distribution"The distribution being tested for. It tests whether x could have come from the specified distribution. There are two choices available for parsing distribution parameters:

Source Code: adtest

  • One of the following char strings: "norm", "exp", "ev", "logn", "weibull", for defining either the ’normal’, ’exponential’, ’extreme value’, lognormal, or ’Weibull’ distribution family, respectively. In this case, x is tested against a composite hypothesis for the specified distribution family and the required distribution parameters are estimated from the data in x. The default is "norm".
  • A cell array defining a distribution in which the first cell contains a char string with the distribution name, as mentioned above, and the consecutive cells containing all specified parameters of the null distribution. In this case, x is tested against a simple hypothesis.
NameValue
"Alpha"Significance level alpha for the test. Any scalar numeric value between 0 and 1. The default is 0.05 corresponding to the 5% significance level.
"MCTol"Monte-Carlo standard error for the p-value, pval, value. which must be a positive scalar value. In this case, an approximation for the p-value is computed directly, using Monte-Carlo simulations.
"Asymptotic"Method for calculating the p-value of the Anderson-Darling test, which can be either true or false logical value. If you specify ’true’, adtest estimates the p-value using the limiting distribution of the Anderson-Darling test statistic. If you specify ’false’, adtest calculates the p-value based on an analytical formula. For sample sizes greater than 120, the limiting distribution estimate is likely to be more accurate than the small sample size approximation method.

Source Code: adtest

  • If you specify a distribution family with unknown parameters for the distribution Name-Value pair (i.e. composite distribution hypothesis test), the "Asymptotic" option must be false.
  • If you use MCTol to calculate the p-value using a Monte Carlo simulation, the "Asymptotic" option must be false.

[h, pval] = adtest (…) also returns the p-value, pval, of the Anderson-Darling test, using any of the input arguments from the previous syntaxes.

[h, pval, adstat, cv] = adtest (…) also returns the test statistic, adstat, and the critical value, cv, for the Anderson-Darling test.

The Anderson-Darling test statistic belongs to the family of Quadratic Empirical Distribution Function statistics, which are based on the weighted sum of the difference [Fn(x)-F(x)]^2 over the ordered sample values X1 < X2 < ... < Xn, where F is the hypothesized continuous distribution and Fn is the empirical CDF based on the data sample with n sample points.

See also: kstest

Source Code: adtest