Anderson Darling Test Interpretation. Their results showed that the Shapiro-Wilk test is the most powerful normality test followed by Anderson-Darling test. A paper by Razali and Wah 2011 tested all these formal normality tests with 10000 Monte Carlo simulation of sample data generated from alternative distributions that follow symmetric and asymmetric distributions.
The A-D test value is simply the average squared difference between the empirical cumulative function and the fitted cumulative function with a special weighting designed to accentuate the tails of the distribution. The Anderson-Darling test for normality is one of three general normality tests designed to detect all departures from normality. Their results showed that the Shapiro-Wilk test is the most powerful normality test followed by Anderson-Darling test.
The Anderson-Darling statistic is a squared distance that is weighted more heavily in the tails of the distribution.
It is a modification of the Kolmogorov-Smirnov K-S test and gives more weight to the tails than does the K-S test. Precisely the Anderson-Darling adjusted statistic is a squared distance that is. It is a modification of theKolmogorov-SmirnovK-S testand gives more weight to the tails of the distribution thandoes the K-S test. To determine whether the data do not follow a normal distribution compare the p-value to the significance level.
