# 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.