Kolmogorov-Smirnov (K-S) Test Calculator | AAT Bioquest (2024)

FAQs

How to use Kolmogorov-Smirnov test calculator? ›

The p-value for the KS test is calculated by comparing the observed value of the KS statistic to the critical value of the KS statistic under the null hypothesis that the two samples come from the same distribution. The critical value of the KS statistic depends on the sample sizes.

The Shapiro–Wilk test is more appropriate method for small sample sizes (<50 samples) although it can also be handling on larger sample size while Kolmogorov–Smirnov test is used for n ≥50.

How do you interpret KS test p value? If the p-value is below the chosen significance level (commonly 0.05), we would reject the null hypothesis. It indicates significant difference; large p-value (i.e.below the chosen significance level ) suggests no significant difference.

K-S should be a high value (Max =1.0) when the fit is good and a low value (Min = 0.0) when the fit is not good. When the K-S value goes below 0.05, you will be informed that the Lack of fit is significant.

To calculate this value, the KS statistic is taken into account along with the sample size of both distributions. Typical thresholds for rejecting the null hypothesis are 1% and 5%, implying that any p-value less than or equal to these values would lead to the rejection of the null hypothesis.

The p-value is the probability of obtaining a test statistic (such as the Kolmogorov-Smirnov statistic) that is at least as extreme as the value that is calculated from the sample, when the data are normal. Larger values for the Kolmogorov-Smirnov statistic indicate that the data do not follow the normal distribution.

21.1 Kolmogorov-Smirnov Two-Sample Test

The null hypothesis (H_o) is that the two dataset values are from the same continuous distribution. The alternative hypothesis (H_a) is that these two datasets are from different continuous distributions.

The KS test can not be applied in two or more dimensions.

One can construct a statistic based on some ordering procedure, and then compute the supremum distances between two datasets (or one dataset and a curve). But the critical values of the resulting statistic are not distribution-free.

What is the formula for the Kolmogorov Smirnov test? ›

1 The Kolmogorov–Smirnov Test. (5.3) H 0 : F ( x ) = G ( x ) , all x , versus H 1 : F ( x ) ≠ G ( x ) for at least one x, where F and G are the distributions associated with two independent groups (cf. Li et al., 1996).

The KS metric is calculated by finding the maximum absolute difference between the empirical CDF of the predicted classes and the theoretical CDF of the true classes. This maximum difference is then used as the KS statistic. The higher the KS statistic, the better the performance of the classifier.

The Kolmogorov-Smirnov test (Chakravart, Laha, and Roy, 1967) is used to decide if a sample comes from a population with a specific distribution. where n(i) is the number of points less than Y_i and the Y_i are ordered from smallest to largest value.

You have to use D*Sqrt(samplesize) and refer the p-value as (1-table value) - that is to emphasize the reverse distribution which you can understand intuitively - a difference of zero (D=0) would imply that p-value would be 1, implies 100% of samples would have D value zero or more.

The KS metric is calculated by finding the maximum absolute difference between the empirical CDF of the predicted classes and the theoretical CDF of the true classes. This maximum difference is then used as the KS statistic. The higher the KS statistic, the better the performance of the classifier.

To run the test, go to XLSTAT / Nonparametric tests / Distribution fitting. In the General tab, select the brand A data, the normal distribution, activate the Enter option and enter the following parameters: µ = 21.5 and sigma = 2.3. In the Charts tab, activate the Cumulative histograms option. Click on the OK button.

The Kolmogorov Smirnov test (KS test or K-S test) is used to compare two distributions to determine if they are pulling from the same underlying distribution. In the typical ML use case, there are two distributions (A & B) that you are trying to compare.