Kolmogorov-Smirnov-Test
Scientific explanation of the Kolmogorov-Smirnov-Test
The Kolmogorov-Smirnov-Test is a non-parameterized test for checking the goodness of fit between two distributions. This test checks whether an underlying probability distribution deviates from an assumed distribution. (Dodge, Y. (2008). Kolmogorov–Smirnov Test. In The Concise Encyclopedia of Statistics (pp. 283–287). New York, NY: Springer New York.)
It is often used to find out whether data are normally distributed, since many statistical procedures assume or have as a prerequisite that the data are normally distributed.
In this test, the distribution of the observed data is compared with the theoretical distribution and the null hypothesis is made that the observed data originate from the theoretical distribution. If the p-value of the test is less than a predetermined significance level, the null hypothesis is rejected and it can be assumed that the observed data do not originate from the theoretic distribution.
This value can be calculated using this formula:
A p-value of 0.0 means that the null hypothesis can be rejected, indicating that the distributions are not identical, whereas a p-value of one indicates that the hypothesis is accepted and the distributions are identical. (Steinskog, D. J., Tjøstheim…
