Interpreting Anderson-Darling (A-D) Test Values

Q: What do A-D test values like 1.67895 (Inverse Gauss) vs 6.78744 (Loglogistic) mean?

A: The A-D value measures the average squared difference between the empirical and fitted cumulative distributions, with extra weighting on the tails. A value of 6.79 indicates roughly four times the deviation of 1.68, so lower values indicate a better fit.

Q: Does the A-D test have a unique distribution like χ²?

A: No. Unlike χ², the A-D test does not have a standard test distribution, so p-values and critical values are generally unavailable. Comparisons are made directly between A-D values rather than against a reference distribution.

References:

• Law & Kelton, Simulation Modeling and Analysis

• D’Agostino & Stephens, Goodness-of-Fit Techniques