What Kolmogorov-smirnov test is
The Kolmogorov-Smirnov test (K-S test) is a nonparametric test used to evaluate whether two samples come from the same population. It is used to compare a sample to a reference probability distribution (one-sample K-S test), or to compare two samples (two-sample K-S test).
Steps for Kolmogorov-Smirnov Test:
- Define the null and alternative hypothesis:
Null Hypothesis: The two samples come from the same population.
Alternative Hypothesis: The two samples come from different populations.
- Calculate the K-S statistic:
The K-S statistic is calculated by comparing the cumulative distribution functions (CDFs) of the two samples.
- Calculate the p-value:
The p-value is calculated using a table of critical values for the K-S statistic for different sample sizes.
- Make a decision:
If the p-value is less than the significance level (α), then the null hypothesis is rejected and the alternative hypothesis is accepted. If the p-value is greater than the significance level (α), then the null hypothesis is not rejected.
Examples
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The Kolmogorov-Smirnov test is often used to compare two samples to determine if they come from the same underlying distribution.
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It is also used as a goodness-of-fit test to determine whether a given sample follows a specified probability distribution, such as the normal distribution.
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The Kolmogorov-Smirnov test can also be used to compare two data sets to determine whether they are significantly different from each other.
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It can be used as a test for normality to determine whether a given sample is normally distributed.
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The Kolmogorov-Smirnov test can also be used to test the hypothesis that two data sets have the same distribution.