What is the Anderson-Darling test?
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. See also our Fisher's Exact Test Calculator.
What is a normality test and why does it matter?
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.
How do I interpret the Anderson-Darling test result?
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.
What is the null hypothesis for the Anderson-Darling test?
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. You might also find our use the Hypothesis Testing Calculator useful.
What is the adjusted A* statistic?
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.
How many data points do I need for the Anderson-Darling test?
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.
How does the Anderson-Darling test compare to Shapiro-Wilk?
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.
What significance level (α) should I use?
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.