Understand the hypothesis test
Treat model checks as evidence, not proof
Anderson–Darling Normality Test. A diagnostic test compresses one kind of departure into a statistic. Different checks emphasize tails, shape, cumulative gaps, or ordering.
1Specify the reference pattern2Measure the chosen discrepancy3Combine the result with plots and context
Test statistic and reference model
A²=−n−(1/n)Σ(2i−1)[ln F(xi)+ln(1−F(xn+1−i))].
The test weights tail discrepancies strongly and should accompany graphical and process-based assessment.
Responsible interpretation
Failure to reject is not proof that the data are normal, random, independent, or well modeled. Small samples may have little power and huge samples may flag minor departures.
Required assumption: Mean and SD are estimated from the entered data; the displayed p-value uses Stephens’ finite-sample approximation.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the anderson–darling normality test calculator works
A²=−n−(1/n)Σ(2i−1)[ln F(xi)+ln(1−F(xn+1−i))].
The test weights tail discrepancies strongly and should accompany graphical and process-based assessment.
Worked example
Anderson–Darling Normality Test example
Ordered standardized observations are compared with their fitted-normal cumulative probabilities.
A²=−n−(1/n)Σ(2i−1)[ln F(xi)+ln(1−F(xn+1−i))].
Supported inputs
Precision and limits
Model and design
Mean and SD are estimated from the entered data; the displayed p-value uses Stephens’ finite-sample approximation.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
The test weights tail discrepancies strongly and should accompany graphical and process-based assessment.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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