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When to use the Kolmogorov-Smirnov test?
The Kolmogorov-Smirnov Test is a type of non-parametric test of the equality of discontinuous and continuous of a 1D probability distribution that is used to compare the sample with the reference probability test (known as one-sample K-S Test) or among two samples (known as two-sample K-S test).
How to do the K-S test in R?
The K-S test can be performed using the ks.test () function in R. y: numeric vector of data values or a character string which is used to name a cummulative distribution function. alternative: used to indicate the alternate hypothesis.
When does The K.S test reject normality?
So they don’t follow a normal distribution. Am I doing something wrong? Based on (Hair et al., 1998), when observations are above 1000 the K.S test becomes highly sensitive which means small deviations from normality will result in p values below .05 and thus rejecting the normality.
What does p < 0.05 mean in R-Cross?
However, here that would mean that the test says ( p<0.05 ): a. Cannot say that X = Y; b. Can say that X = Z; c. Cannot say that X = X (!) Besides appearing that x is different from itself (!), it is also quite strange to me that x=z, as the two distributions have zero overlapping support.
How to interpret p-value of K-S test?
The p-value returned by the k-s test has the same interpretation as other p-values. You reject the null hypothesis that the two samples were drawn from the same distribution if the p-value is less than your significance level. You can find tables online for the conversion of the D statistic into a p-value if you are interested in the procedure.
While the Kolmogorov–Smirnov test is usually used to test whether a given F(x) is the underlying probability distribution of Fn(x), the procedure may be inverted to give confidence limits on F(x) itself.
How to calculate the KINV of the Kolmogorov distribution?
where c(α) = the inverse of the Kolmogorov distribution at α, which can be calculated in Excel as Dm,n,α = KINV (α)*SQRT ((m+n)/ (m*n)) where KINV is defined in Kolmogorov Distribution. The values of c(α) are also the numerators of the last entries in the Kolmogorov-Smirnov Table.
Is there a non parametric K sample Anderson Darling test?
I also know of K-Sample Analogues of the Kolmogorov-Smirnov and Cramer-V. Mises Tests (but they have less power as far as I know). There is an R package kSamples that gives you, among other things, a non-parametric k-sample Anderson-Darling test.
How to determine if two samples come from the same distribution?
The values of c(α) are also the numerators of the last entries in the Kolmogorov-Smirnov Table. Example 1: Determine whether the two samples on the left side of Figure 1 come from the same distribution. The values in columns B and C are the frequencies of the values in column A.