Normality Test Calculator

When to use

• Use it as one diagnostic for the distribution of a numeric sample or model residuals.
• Use it alongside a histogram, quantile assessment, sample size, and the assumptions of the planned method.
• Do not use a normality p-value as an automatic rule for choosing all subsequent analyses.

How to use

1. Enter the relevant sample or residual values, not unrelated variables combined together.
2. Calculate skewness, kurtosis, the Jarque-Bera statistic, and p-value.
3. Inspect the distribution visual and possible outliers.
4. Decide whether departures matter for the intended model rather than reading the threshold alone.

Inputs

Numeric sample

Finite observations from one variable or residual series.

Residuals

Observed minus fitted values when the assumption concerns model errors.

Alpha

The threshold for evidence against the normal-distribution null.

Sample size

Power to detect departures changes substantially with n.

Notation

Interpretation

• A small p-value indicates evidence against normality for this diagnostic.
• A large p-value does not prove that the population is normal.
• Jarque-Bera focuses on skewness and kurtosis and can miss other distribution departures.

Effect-size guidance

• Inspect the magnitude and direction of skewness and excess kurtosis.
• Judge whether the planned estimator is robust at the actual sample size.
• Separate harmless tail variation from data errors or distinct subgroups.

Worked examples

Assumptions

• Inputs are finite numeric values after parsing, with missing or invalid values handled according to the selected workflow.
• The tested values are the values relevant to the assumption, often residuals rather than raw outcomes.
• The sample size is adequate for the diagnostic to be informative.

Practical guidance

• Test model residuals when the model assumes normal errors.
• Use plots and domain context alongside the statistic.
• Consider robust or distribution-appropriate methods when departures are material.

Common mistakes

• Saying p > alpha proves normality.
• Testing raw data when model residuals are the relevant assumption.

Limitations

• Jarque-Bera can have low power in small samples.
• Shapiro-Wilk and Anderson-Darling implementations are out of scope.

Related workflow links