For any value of A as described in One-sample Anderson Darling Test we can estimate the p-value to within 5 decimal places (6 places if A ≥ 2) using the following formulas:
For 0 < A < 2, the p-value can be estimated by
For A ≥ 2, the p-value can be estimated by
Real Statistics Functions: The Real Statistics Pack supplies the following functions.
AD_DIST(x) = the p-value of the AD test for the Anderson-Darling statistics x for large samples when the distribution parameters are known
AD_INV(p) = the critical value of the AD test at the significance level p for large samples when the distribution parameters are known
Reference:
Marsaglia, G. (2014) Evaluating the Anderson-Darling distribution. Journal of Statistical Software.
https://www.jstatsoft.org/article/view/v009i02