Anderson-Darling test was developed in 1952 by Theodore Anderson and Donald Darling. To test whether or not a sample of data comes from a population that is normally distributed, we may use the Anderson-Darling test. This test gives more weight to the tails and is an alternative to the chi-square and Kolmogorov-Smirnov goodness-of-fit tests. The test involves calculating the Anderson-Darling statistic.

\[ AD = - N - \sum_{i=1}^N \frac{(2_i - 1)}{N} [ln F(Y_i) + ln(1-F(Y_{N+1-i})) ] \]

where n = sample size and F is the cumulative distribution function of the specified distribution.

Anderson-Darling statistic is then adjusted to calculate different p-values. The highest p-value is the basis for deciding whether or not to reject the null hypothesis, comparing it with a given alpha , e.g., 0.05.

We can formulate the following set of hypothesis.

**H**_{0}: The data follow the normal distribution VS H_{a} : The data do not follow the normal distribution

If we find that the calculated p-value is less extreme than alpha, we reject the null hypothesis.