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Which is the statistic of the Kolmogorov-Smirnov test?
The test statistic in the Kolmogorov-Smirnov test is very easy, it is just the maximum vertical distance between the empirical cumulative distribution functions of the two samples. The empirical cumulative distribution of a sample is the proportion of the sample values that are less than or equal to a given value.
Can you use Shapiro Wilk or Kolmogorov Smirnov?
A better choice is to use a test where the parameters aren’t assumed known, such as a Shapiro Wilk. If you’re wedded to a Kolmogorov-Smirnov type of test, you can take the approach of Lilliefors’ test.
How is the KS test used to detect variance?
KS Test can detect the variance. In this case the red distribution has a slightly binomial distribution which KS detect. In other words: Student’s T-Test says that there is 79.3% chances the two samples come from the same distribution.
What are chances of two samples coming from the same distribution?
Student’s T-Test says that there is 79.3% chances the two samples come from the same distribution. KS Test says that there are 1.6% chances the two samples come from the same distribution. There are many other Test and algorithms to do that type of work.
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
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.
Which is better KS test or ml test?
If we need to decide for Student-T data with df = 2 via KS test whether the data could be normal or not, then a ML estimate based on H 0 (data is normal, so using the standard deviation for scale) would give much larger KS distance, than a fit with minimum KS.