Anderson-Darling Test Calculator

The Anderson-Darling (AD) test is a statistical goodness-of-fit test used to determine whether a sample of data comes from a specified distribution — most commonly the normal distribution. It computes a test statistic A² that measures how well the data match the theoretical distribution, placing greater weight on the tails than other tests like Cramér–von Mises.

A normality test checks whether your data was plausibly drawn from a normally distributed population. Many statistical methods — such as t-tests, ANOVA, and linear regression — assume normally distributed data or residuals. If that assumption is violated, results may be unreliable, so testing normality is an important diagnostic step.

If the p-value is less than your chosen significance level (α), you reject the null hypothesis and conclude the data does not follow a normal distribution. If the p-value is greater than α, you fail to reject the null hypothesis, meaning there is insufficient evidence to say the data is non-normal. A smaller A² value generally indicates a better fit to the normal distribution.

The null hypothesis (H₀) states that the sample data comes from a normally distributed population. The alternative hypothesis (Hₐ) states that the data does not come from a normal distribution. If the test statistic exceeds the critical value for your chosen α, you reject H₀.

The adjusted statistic A* applies a small-sample correction to A² using the formula A* = A² × (1 + 0.75/n + 2.25/n²). This correction makes the test more accurate for smaller sample sizes (typically n < 25). The p-value is then derived from A* using interpolation of critical value tables.

The test requires a minimum of 7 to 8 data points to be meaningful. With very small samples (n < 7), the test has low power and may not reliably detect non-normality. For larger samples (n > 50), even minor deviations from normality may be detected, so practical significance should be considered alongside statistical significance.

Both tests assess normality, but they differ in approach. Shapiro-Wilk is generally considered the most powerful test for small to medium samples (n < 50). Anderson-Darling is more sensitive to deviations in the tails of the distribution and works well for moderate to large samples. For very small samples, Shapiro-Wilk is often preferred.

The most common significance level is α = 0.05 (5%), which means you accept a 5% chance of incorrectly rejecting the null hypothesis. In fields requiring stricter standards — such as medical or quality control applications — α = 0.01 is often used. For exploratory data analysis, α = 0.10 may be acceptable.