Kolmogorov-Smirnov Goodness of Fit Test Calculator

Advanced statistical tool for goodness of fit analysis. Test data against theoretical distributions seamlessly now. Calculate critical values and probabilities with complete confidence today.

Calculator Options

Example: 1.2, 2.3, 1.9, 2.1, 2.5, 1.8, 2.0, 2.2, 1.7, 2.4

Formula Used

The Kolmogorov-Smirnov (K-S) goodness of fit test quantifies a distance between the empirical cumulative distribution function ($F_n(x)$) of the sample and the cumulative distribution function ($F_0(x)$) of the reference distribution.

Test Statistic ($D$):

$$D = \sup_x |F_n(x) - F_0(x)|$$

Critical Value Approximation (Two-Sided):

$$D_{\alpha} = \frac{c(\alpha)}{\sqrt{n}}$$

Where $c(0.05) \approx 1.358$, $c(0.01) \approx 1.628$, and $n$ is the sample size.

How to Use This Calculator

  1. Enter your continuous numerical sample data into the text box separated by commas, spaces, or newlines.
  2. Select the target theoretical distribution you wish to test against (e.g., Normal Distribution).
  3. Choose your desired significance level ($\alpha$) and alternative hypothesis direction.
  4. Click the Calculate K-S Test button to instantly view test statistics, empirical CDF comparisons, and statistical decisions.

Understanding the Kolmogorov-Smirnov Test in Statistics

The Kolmogorov-Smirnov test is a powerful non-parametric statistical test used to determine whether a given sample departs from a hypothesized probability distribution. Unlike the Chi-Square test, the K-S test does not require data binning, making it exceptionally useful for continuous datasets.

Key Advantages

One of the primary benefits of the K-S test is its distribution-free nature regarding the cumulative distribution function. It directly evaluates the maximum vertical deviation between empirical observations and theoretical expectations, providing robust diagnostic power even with moderate sample sizes.

Frequently Asked Questions

The null hypothesis ($H_0$) states that the sample data follows the specified theoretical distribution. The alternative hypothesis ($H_1$) states that it does not follow that distribution.

The standard Kolmogorov-Smirnov test is designed for continuous distributions. Applying it to discrete distributions can be conservative and lead to inaccurate critical boundaries.

Related Calculators

Paver Sand Bedding Calculator (depth-based)Paver Edge Restraint Length & Cost CalculatorPaver Sealer Quantity & Cost CalculatorExcavation Hauling Loads Calculator (truck loads)Soil Disposal Fee CalculatorSite Leveling Cost CalculatorCompaction Passes Time & Cost CalculatorPlate Compactor Rental Cost CalculatorGravel Volume Calculator (yards/tons)Gravel Weight Calculator (by material type)

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.