More about Anderson-Darling statistics

The Anderson-Darling (adj) statistic measures the area between the fitted line (based on chosen distribution) and the nonparametric step function (based on the plot points). More precisely, the Anderson-Darling statistic is a squared distance that is weighted more heavily in the tails of the distribution. Minitab uses an adjusted Anderson-Darling statistic, because the statistic changes when a different plot point method is chosen.

Goodness of Fit

              Anderson-Darling

Distribution             (adj)

Weibull                  6.056

Lognormal                6.109

Exponential              8.121

Normal                   6.057

For the iron cord data above, the Weibull distribution has the lowest Anderson-Darling statistic of 6.056. Because the Weibull has the lowest Anderson-Darling value, you can conclude that the Weibull distribution fits the data better than the other three distributions.

If you were to look at a probability plot and picture the area between the step function and the fitted line, you would see that the Weibull, lognormal, and normal distributions have similar areas whereas the exponential has a much larger area.

Therefore, for the iron cord data, the difference between AD values for the lognormal and Weibull (6.109 - 6.056 = 0.053) probably is not a practical difference while the difference between the exponential and Weibull AD values (8.121 - 6.056 = 2.065) is a practical difference.