Anderson-Darling test
Goodness of fit and normality · reference distribution: A² (tabulated)
When to use it
Test goodness of fit to a distribution, giving more weight to the tails than Kolmogorov-Smirnov.
Null hypothesis
The data follow the distribution F.
Assumptions
- Independent observations
Test statistic
A^2 = -n - \dfrac{1}{n} \sum_{i=1}^{n} (2i - 1)\left[\ln F(x_{(i)}) + \ln\left(1 - F(x_{(n+1-i)})\right)\right]How to report it
A² = 0.52, p = .18
In R and Python
R
library(nortest)
ad.test(x)Python
stats.anderson(x, dist="norm") # returns critical values, not the p-valueIn Python, stats is scipy.stats and np is numpy.
Where it sits in the catalog
Goodness of fit and normality. Goodness of fit: do the data follow the expected distribution? Normality tests are the most common case and check an assumption of parametric tests.
In the decision tree
- What do you want to do? Check an assumption or the distribution of the data
- What do you want to check? Whether the data follow another continuous distribution
- Are the parameters of the distribution known in advance? No, they are estimated from the data
It also appears alongside other tests:
- As an alternative to Shapiro-Wilk.