Anderson-Darling Normality Test

Introduction: Anderson-Darling Normality Test

The Anderson-Darling Normality Test is a statistical method used to check whether a dataset follows a normal distribution. Since many statistical tests assume normality, this test helps researchers confirm whether their data meet that requirement.

Background

The test was developed in the 1950s by Theodore W. Anderson and Donald A. Darling. It is an improvement over earlier normality tests because it gives more weight to the tails of the distribution, where deviations from normality often occur.

Key Elements / Features

• Empirical vs theoretical distribution: The test compares the actual data distribution with a perfect normal distribution.
• Test statistic: Measures how far the data deviate from the expected normal curve.
• A value close to 0 = data fit normal distribution well.
• Higher values = stronger evidence against normality.
• Interpretation: If the test statistic and p-value indicate non-normality, researchers may choose different statistical methods.

Applications / Examples

• Medical research: Testing whether blood pressure readings are normally distributed before applying ANOVA.
• Manufacturing: Checking if product dimensions follow a normal curve before using process control methods.
• Finance: Assessing whether stock returns follow normality before risk modelling.

For example, if a dataset of exam scores produces a high Anderson-Darling value with p < 0.05, researchers conclude the scores are not normally distributed and may use non-parametric methods like the Mann-Whitney U test instead.

Relevance / Impact

The Anderson-Darling test is crucial for validating assumptions in statistics. By confirming normality (or showing deviations), it ensures researchers select appropriate tools, avoid errors, and strengthen the reliability of their conclusions.

See also

• Normal Distribution
• Shapiro-Wilk Test
• Kolmogorov-Smirnov Test
• Non-Parametric Tests