Kolmogorov-Smirnov Test: A Nonparametric Statistical Test to Compare Two Samples
The Kolmogorov-Smirnov Test (K-S test) is a nonparametric statistical test used to compare two samples. It is a powerful tool for testing whether two samples originate from the same population based on their cumulative distribution functions (CDFs). The K-S test is used in a variety of fields, such as biostatistics, economics, engineering, and psychology.
The K-S test is a two-sided test, which means that it tests whether two samples come from the same population. It works by comparing the cumulative distributions of the two samples. The K-S test is based on the maximum absolute difference between the two cumulative distributions, called the Kolmogorov-Smirnov statistic (D). If D is small, then the two samples come from the same population.
The K-S test has several advantages compared to other statistical tests. First, it is a nonparametric test, meaning that it does not require any assumptions about the underlying distribution of the data. Second, it is a powerful test, meaning that it has high statistical power for detecting differences between two samples. Third, it is easy to calculate and interpret. Finally, it is robust to violations of the assumptions of other tests, such as normality.
Despite its advantages, the K-S test has some limitations. First, it does not provide information about the direction or magnitude of the difference between two samples. Second, it is sensitive to outliers, meaning that outliers can affect the results. Third, it is not suitable for testing the equality of more than two samples.
In conclusion, the K-S test is a powerful nonparametric statistical test for comparing two samples. It is easy to calculate, robust to violations of assumptions, and has high statistical power. However, it is not suitable for testing the equality of more than two samples, and it is sensitive to outliers.
References
Hirsch, B., Yakowitz, S.J., & Mendenhall, W. (2015). A First Course in Business Statistics. Cengage Learning.
Gibbons, J.D. & Chakraborti, S. (2011). Nonparametric Statistical Inference. CRC Press.
Nelson, S. (2011). Kolmogorov-Smirnov Test. Retrieved from http://www.itl.nist.gov/div898/handbook/eda/section3/eda35e.htm