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Normality Test Calculator

Evaluate skewness, kurtosis, Jarque-Bera statistic, p-value, and distribution visual.

Input

Configure inputs first. Final results, visuals, downloads, and copy summary remain hidden until Calculate Normality succeeds.

Input mode

Manual inputLocal CSV input

Values

Variance conventionHistogram binsAlpha

What This Tool Does

The Normality Test Calculator reports Jarque-Bera diagnostics only after Calculate Normality is clicked and never states that data are proven normal.

Method

Jarque-Bera compares sample skewness and kurtosis to the normal-distribution expectations.

Worked Example

Symmetric values tend to produce smaller skewness than strongly right-tailed values, but sample size affects the p-value.

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.

References

NIST e-Handbook: Distributional Adequacy: NIST/SEMATECH e-Handbook of Statistical Methods, distributional adequacy and normality diagnostics.

What does Jarque-Bera test?

It checks whether skewness and kurtosis depart from normal-distribution expectations.

Does p > 0.05 prove normality?

No. It only means insufficient evidence to reject the normality null under this test.

Why does sample size matter?

Large samples can detect small departures, while small samples may miss meaningful non-normality.

What is a Q-Q plot?

It compares ordered data values to expected quantiles from a target distribution.

Does the Normality Test Calculator calculate automatically while I type?

No. Inputs and CSV previews never produce final statistics until the explicit calculate button is clicked.

Are CSV files uploaded?

No. Selected CSV files are processed locally in the browser. ScholarTool does not upload the file to a third-party calculation or data-analysis API.

Can a p-value prove a hypothesis?

No. A p-value is evaluated against the selected alpha level under stated assumptions; it does not prove the null or alternative hypothesis.

Engineering disclaimer

This statistics tool is intended for education, planning, and preliminary analysis. Review assumptions, study design, and professional statistical judgement before using results in research, engineering, safety, regulatory, or compliance decisions. ScholarTool does not prove hypotheses or replace qualified analysis.

Need Professional Support?

ScholarTool is powered by ScholarEase Consultancy Services LLP. Professional engineering, simulation, research, and technical documentation support is available through the connected services website.

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Last reviewed: 2026-07-07

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Engineering disclaimer

Normality Test Calculator

Input

What This Tool Does

Method

Worked Example

Common Mistakes

Limitations

References

Related Tools

Engineering disclaimer

Need Professional Support?

Normality Test Calculator

Input

What This Tool Does

Method

Worked Example

Common Mistakes

Limitations

References

Related Tools

Engineering disclaimer

Need Professional Support?