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Two-Sample Kolmogorov-Smirnov Test and Mann-Whitney Test

The two-sample Kolmogorov-Smirnov test (KS-test) and Mann-Whitney test (MW-test) are two of the useful and general alternative nonparametric methods of two-sample t-test. They can be used to test whether two samples come from the same distribution.

The two-sample Kolmogorov-Smirnov test uses the maximal distance between cumulative frequency distributions of these two samples as the statistic. However, the Mann-Whitney test takes the difference between mean ranks of these two samples as the statistic.

As an example, researchers would like to know whether the handgrip of diabetics and healthy individuals come from the same distribution. Fifty subjects were observed. Half of them are diabetic, the other half are healthy men. Both two-sample Kolmogorov-Smirnov and Mann-Whitney tests were used:

At first, we use two-sample Kolmogorov-Smirnov test.

Two-Sample Kolmogorov-Smirnov Test interface

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  An illustration of Two-Sample Kolmogorov-Smirnov Test results being displayed in Origin

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Here we use Mann-Whitney test.

Mann-Whitney Test interface

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  An illustration of Mann-Whitney Test results being displayed in Origin

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