Computation of probability associated with Anderson-Darling statistic

Abstract

The correct application of a statistical test is directly connected with information related to the distribution of data. Anderson-Darling is one alternative used to test if the distribution of experimental data follows a theoretical distribution. The conclusion of the Anderson-Darling test is usually drawn by comparing the obtained statistic with the available critical value, which did not give any weight to the same size. This study aimed to provide a formula for calculation of p-value associated with the Anderson-Darling statistic considering the size of the sample. A Monte Carlo simulation study was conducted for sample sizes starting from 2 to 61, and based on the obtained results, a formula able to give reliable probabilities associated to the Anderson-Darling statistic is reported.