Kolmogorov-Smirnov Test (Two-Sample)
Computes the two-sample Kolmogorov-Smirnov test, which checks whether two samples come from the same distribution — without assuming what that distribution is. It compares the empirical cumulative distribution functions of the two samples and takes the largest vertical distance between them, the D statistic. Unlike the t-test, which only compares means, the KS test is sensitive to any difference in shape, spread or location. Enter the two samples of values.
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Kolmogorov-Smirnov Test (Two-Sample)
Computes the two-sample Kolmogorov-Smirnov test, which checks whether two samples come from the same distribution — without assuming what that distribution is. It compares the empirical cumulative distribution functions of the two samples and takes the largest vertical distance between them, the D statistic. Unlike the t-test, which only compares means, the KS test is sensitive to any difference in shape, spread or location. Enter the two samples of values.
Do two samples come from the same distribution?
Comparing two groups by their mean is the most common reflex, but the mean hides a lot. Two samples can have the same mean and completely different distributions in shape and spread. The two-sample Kolmogorov-Smirnov test goes further: it asks whether the two come from the same distribution, whatever it may be.
The idea is to build the empirical cumulative distribution function of each sample — the step curve showing, for each value, the fraction of data below it — and measure the largest vertical distance between the two curves. That maximum distance is the D statistic. If the samples come from the same distribution, the curves track each other closely and D is small; any divergence in location, scale or shape pulls the curves apart and increases D.
Enter the two samples of values. The tool returns the D statistic and an asymptotic p-value, based on the limiting Kolmogorov distribution. Being non-parametric and sensitive to the entire distribution, the test is a valuable safety net when you don't want to bet everything on a comparison of means alone.
Related Tools
Kolmogorov-Smirnov Test (vs Normal)
Computes the one-sample Kolmogorov-Smirnov test against a normal distribution with specified mean and standard deviation. It measures the largest vertical distance between your data's empirical cumulative distribution and the theoretical normal curve — the D statistic. Unlike tests that look only at skewness or kurtosis, the KS compares the entire distributions, point by point. Enter the sample and the normal parameters (mean and standard deviation) to test.
Mann-Kendall Trend Test
Computes the Mann-Kendall test, used to detect a monotonic trend (upward or downward) in a time series without assuming the data are normal or the trend is linear. It sums the signs of all pairwise comparisons between values: if the series tends to rise over time, positive signs prevail. It's widely used in hydrology, climatology and environmental science to assess trends in long series. The S statistic becomes a z via the normal approximation, with a tie correction. Enter the series in chronological order.
Mann-Whitney U Test
Computes the Mann-Whitney U test, the non-parametric alternative to the t-test for comparing two independent groups. Instead of comparing means, it compares the ranks of the combined data, which makes it valid even when the data don't follow a normal distribution or are ordinal. The tool computes the U statistic and the normal approximation z, with a tie correction. Enter the two groups of observations, separated by commas.
Runs Test (Wald-Wolfowitz)
Computes the Wald-Wolfowitz runs test, which checks whether a sequence of two values is random or has a pattern. A run is a stretch of consecutive equal values; too few runs indicate clustering (a trend), and too many indicate systematic alternation. By comparing the observed number of runs with the number expected under randomness, the z statistic reveals whether the order of the data is compatible with pure chance. It's useful for checking residuals, time series and number generators. Enter the sequence with two distinct symbols.
Mood's Median Test
Computes Mood's median test, a non-parametric test that checks whether several groups share the same median. The idea is simple and robust: you compute the grand median of all the data together and count, in each group, how many values fall above it. If the groups had the same median, those counts would be proportional to the sizes; an imbalance produces a large chi-square statistic. It's quite resistant to outliers, working only with counts. Enter the groups separated by semicolons.
Friedman Test
Computes the Friedman test, the non-parametric version of repeated-measures ANOVA. It's used when the same subjects (or blocks) go through three or more conditions and you want to know whether the conditions differ, without assuming normality. Within each block, the treatments are ranked; if one treatment is consistently better, it accumulates low ranks across all blocks, and the Friedman chi-square statistic grows. Enter the blocks: treatments separated by commas, blocks by semicolons.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.