What is the difference between the Kolmogorov-Smirnov test and the chi squared test?
The Chi Square Goodness of fit test is used to test whether the distribution of nominal variables is same or not as well as for other distribution matches and on the other hand the Kolmogorov Smirnov test is only used to test to the goodness of fit for a continuous data.
What is KS approach SAS?
In predictive modeling, it is very important to check whether the model is able to distinguish between events and non-events. There is a performance statistics called “Kolmogorov-Smirnov” (KS) statistics which measures the discriminatory power of a model.
How is the Kolmogorov-Smirnov test used to compare distributions?
The test statistic developed by Kolmogorov and Smirnov to compare distributions was simply the maximum vertical distance between the two functions. Kolmogorov-Smirnov tests have the advantages that (a) the distribution of statistic does not depend on cumulative distribution function being tested and (b) the test is exact.
Why did Kolmogorov-Smirnov test give the wrong p value?
We give a well known example where a Kolmogorov-Smirnov test of final digits of P-values (a discrete variable) suggested that they deviated from the expected (continuous) uniform distribution. The test, however, gave the wrong P-value because with many ties, the test is far too liberal.
How to compare a sample with a distribution?
When we compare a sample with a theoretical distribution, we can use a Monte Carlo simulation to create a test statistics distribution. For instance, if we want to test whether a p-value distribution is uniformly distributed (i.e. p-value uniformity test) or not, we can simulate uniform random variables and compute the KS test statistic.
When did Lilliefors introduce the Kolmogorov Smirnov test?
Sprent (1998) covers both the one- and two-sample tests in Chapter 6. Siegel (1956) introduces the Kolmogorov-Smirnov tests, but does not of course consider the (later) tests by Lilliefors and Anderson-Darling. Khamis et al. (2000) (1992) propose a modification of the test which improves its power for small to moderate size samples.