This advanced tool calculates the Kolmogorov-Smirnov test statistic in real-time to compare two empirical distributions or test goodness-of-fit. Enter your data manually, generate random samples, or upload CSV files to get instant results.
Data Input
Distribution 1 Data 0 points
Distribution 2 Data 0 points
Test Results
Distribution Comparison
Advanced Settings
How to Use the Kolmogorov-Smirnov Test Calculator
1. Input Your Data
Enter data for two distributions manually, generate random samples, or upload CSV files. You can use predefined distributions (normal, uniform, exponential) or enter custom values.
2. Calculate KS Statistic
Click "Calculate KS Test" to compute the Kolmogorov-Smirnov test statistic (D), which measures the maximum vertical distance between the two empirical distribution functions.
3. Interpret Results
Review the test statistic, p-value, and visual comparison. The tool automatically determines if distributions are significantly different based on your chosen significance level.
Understanding the Kolmogorov-Smirnov Test
The Kolmogorov-Smirnov (KS) test is a nonparametric statistical test used to compare two probability distributions. Unlike parametric tests that assume specific distribution forms, the KS test makes no assumptions about the distribution of data, making it versatile for various applications.
Key Applications:
- Goodness-of-fit testing: Determine if a sample comes from a specific distribution
- Two-sample comparison: Test whether two samples come from the same distribution
- Model validation: Compare empirical data with theoretical distributions
- Quality control: Monitor process consistency over time
Interpreting the Results:
| KS Statistic (D) | P-Value | Interpretation |
|---|---|---|
| Close to 0 | > 0.05 | No significant difference between distributions |
| Larger value | ≤ 0.05 | Significant difference between distributions |
| > Critical Value | < 0.01 | Strong evidence against null hypothesis |
Pro Tip
For small sample sizes (n < 50), consider using the exact KS test or Monte Carlo simulation for more accurate p-values. The KS test is most sensitive to differences near the center of the distribution rather than the tails.