Contents
What do you need to know about the Kolmogorov Smirnov test?
Summary. The Kolmogorov-Smirnov test (KS-test) tries to determine if two datasets differ significantly. The KS-test has the advantage of making no assumption about the distribution of data. (Technically speaking it is non-parametric and distribution free.) Note however, that this generality comes at some cost: other tests
How are critical values of K-S test determined?
This is due to limitation 3 above (i.e., the distribution parameters are typically not known and have to be estimated from the data). So in practice, the critical values for the K-S test have to be determined by simulation just as for the Anderson-Darling and Cramer Von-Mises (and related) tests.
Is the K-S test based on the maximum distance?
The graph below is a plot of the empirical distribution function with a normal cumulative distribution function for 100 normal random numbers. The K-S test is based on the maximum distance between these two curves. Characteristics and Limitations of the K-S Test
When is the hypothesis regarding the distributional form rejected?
The hypothesis regarding the distributional form is rejected if the test statistic, D, is greater than the critical value obtained from a table. There are several variations of these tables in the literature that use somewhat different scalings for the K-S test statistic and critical regions.
Which is the cumulative function of the Kolmogorov distribution?
The Kolmogorov distribution is the distribution of the random variable where B ( t) is the Brownian bridge. The cumulative distribution function of K is given by .
When to use K’s table in Smirnov test?
The critical value of D for samples where and is ≤ 40, the K-S table for two sample case is used. When and/or > 40 then the K-S table for large samples of two sample test should be used. The null hypothesis is accepted if the calculated value is less than the table value and vice-versa.
When to use logarithm transformation in Kolmogorov test?
The logarithm transformation may help to overcome cases where the Kolmogorov test data does not seem to fit the assumption that it came from the normal distribution. Using estimated parameters, the questions arises which estimation method should be used.