Normality and Assumption Tests
Kolmogorov-Smirnov Normality Test Calculator
Kolmogorov-Smirnov Normality Test Calculator test normality using KS method.
Normality and Assumption Tests
Kolmogorov-Smirnov Normality Test Calculator
Test normality using KS method.
Formula
The Lilliefors normality test computes the maximum empirical-CDF difference after estimating the normal mean and sample standard deviation, then applies the Lilliefors p-value correction.
About the Kolmogorov-Smirnov Normality Test Calculator
Test normality using KS method. Assumption tests evaluate a named aspect of distribution shape, variance equality, or repeated-measures covariance structure.
How the Kolmogorov-Smirnov Normality Test Calculator Works
The Lilliefors normality test computes the maximum empirical-CDF difference after estimating the normal mean and sample standard deviation, then applies the Lilliefors p-value correction.
The calculation runs in your browser. Submitted values are validated for the required numeric range, data shape, units, and method-specific restrictions before a result is shown.
Required Inputs
- Raw numeric data (required)
- Alpha (required)
Results Reported
The result panel shows the final answer together with the intermediate quantities needed to audit the calculation. Depending on this method, reported values include:
methodnfitted_meanfitted_sample_sdd_plusd_minusd_statisticp_valuealphadecision
Kolmogorov-Smirnov Normality Test Calculator Example
Use the example data button to load a known sample, then calculate and review the statistic, p-value or estimate, and interpretation.
| Input | Example value |
|---|---|
| Raw numeric data | 1.2,2.1,2.8,3.4,4.0,4.7,5.3,5.9,6.4,7.1,7.8,8.2 |
| Alpha | 0.05 |
How to Use the Calculator
- Confirm that the calculator title and method match the quantity, test, conversion, or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date, or option format.
- Select Example Data to inspect a valid input layout, or enter your own values and select Calculate.
- Review the result table, formula, worked substitutions, warnings, and interpretation rather than using only the headline number.
- Use Copy Result or Download CSV when you need a reusable record of the displayed calculation.
Understanding the Result
Use plots and subject-matter judgment with p-values because assumption tests can have low power in small samples and excessive sensitivity in large samples.
Keep the entered values, units, selected options, and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size, and decision. For an estimate or conversion, report the formula convention and final unit.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods, or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the Kolmogorov-Smirnov Normality Test Calculator calculate?
Test normality using KS method.
Which formula does the Kolmogorov-Smirnov Normality Test Calculator use?
The Lilliefors normality test computes the maximum empirical-CDF difference after estimating the normal mean and sample standard deviation, then applies the Lilliefors p-value correction.
What input does this calculator need?
The calculator form shows the required values and validates them before calculating.
Are the formulas visible?
Yes. Each calculator displays its method, assumptions, and interpretation unless disabled by the site administrator.