Anderson-Darling

The Anderson-Darling procedure (NIST, 2005; Press, et al, 1992) is a general test used to compare the fit of an observed cumulative distribution function to an expected cumulative distribution function. This test is applicable to complete data sets (without censored observations) and can be used as an alternative to the two-sample Kolmogorov-Smirnov (KS) test. While the KS statistic is primarily sensitive at the median (and therefore good for detecting shifts between the cumulative distributions), the AD statistic is sensitive over the entire range of the distribution and is more likely to detect differences in the spread of the cumulative distributions. Thus, the AD statistic is a more desirable indicator of whether the simulated data consistently model the observed data over its entire range.

The critical values for the Anderson-Darling statistic have been tabulated (see, for example, Dodson, 1994, Table 4.4) for sample sizes between 10 and 40; however, the critical values (and p-values) reported in Distributions and Simulation and PROCEED are calculated via an approximation method (see, Marsaglia, 2004).

Note on Process Analysis. When used in the Process Analysis module (via the Weibull and Reliability/Failure Time Analysis options), the statistic is only calculated for sample sizes between 10 and 40. Other tests used in the Process Analysis module include the Mann-Scheuer-Fertig Test and Hollander-Proschan Test.