Anderson-Darling (adj) statistics assess the fit of each distribution. Substantially smaller Anderson-Darling values generally indicate that the distribution fits the data better. However, slight differences may not be practically relevant. In addition, values calculated for different distributions may not be directly comparable. Therefore, you should also use the probability plot and other information to evaluate the distribution fit.
If you use the alternative estimation method—the least squares (LSXY) method—Minitab calculates a Pearson correlation coefficient in addition to the Anderson-Darling statistic. The correlation coefficient is a positive number that can be no greater than 1. Higher correlation coefficients generally indicate that the distribution provides a better fit to the data.
For the new muffler data, the Weibull distribution has an Anderson Darling statistic of 7.278, which is lower than the other distributions. However, this difference may not be practically relevant. Use the probability plots to further evaluate the distribution fit.