Measures how well the data follow a particular distribution. The better the distribution fits the data, the smaller this statistic will be. Use the Anderson-Darling statistic to compare the fit of several distributions to see which one is best or to test whether a sample of data comes from a population with a specified distribution. For example, you can use the Anderson-Darling statistic to choose between the Weibull and lognormal distributions for a reliability data analysis or to test whether data meets the assumption of normality for a t-test.
The hypotheses for the Anderson-Darling test are:
H0: The data follow a specified distribution
H1: The data do not follow a specified distribution
If the p-value (when available) for the Anderson-Darling test is lower than the chosen significance level (usually 0.05 or 0.10), conclude that the data do not follow the specified distribution. Minitab does not always display a p-value for the Anderson-Darling test because it does not mathematically exist for certain cases.
If you are trying to determine which distribution the data follow and you have multiple Anderson-Darling statistics, it is generally correct to compare them. The distribution with the smallest Anderson-Darling statistic has the closest fit to the data. If distributions have similar Anderson-Darling statistics, choose one based on practical knowledge.
Some commands generate an adjusted Anderson-Darling, or AD*, statistic. The non-adjusted Anderson-Darling statistic uses the nonparametric step function based on the Kaplan-Meier method of calculating plot points, while the adjusted Anderson-Darling statistic uses other methods to calculate the plot points.