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
Which is more powerful the K-S test or the refined test?
As these refined tests are generally considered to be more powerful than the original K-S test, many analysts prefer them. Also, the advantage for the K-S test of having the critical values be indpendendent of the underlying distribution is not as much of an advantage as first appears.
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.
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.
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.
How to calculate the significance of two sample KS?
KS2TEST(R1, R2, lab, alpha, b, iter, m) is an array function which outputs a column vector with the values D-stat, p-value, D-crit, n1, n2 from the two-sample KS test for the samples in ranges R1 and R2, where alpha is the significance level (default =.05) and b, iter and m are as in KSINV.