# What does the Kolmogorov-Smirnov test show?

## What does the Kolmogorov-Smirnov test show?

The two sample Kolmogorov-Smirnov test is a nonparametric test that compares the cumulative distributions of two data sets(1,2). The KS test report the maximum difference between the two cumulative distributions, and calculates a P value from that and the sample sizes.

## How do you calculate KS in SAS?

First step is to split predicted probability into 10 parts (decile) and then compute the cumulative % of events and non-events in each decile and check the decile where difference is maximum (as shown in the image below.) In the image below, KS is 57.8% and it is at third decile. KS curve is shown below.

How do you interpret a KS statistic?

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.

What is D value in Kolmogorov-Smirnov test?

What is the Kolmogorov D statistic? The letter “D” stands for “distance.” Geometrically, D measures the maximum vertical distance between the empirical cumulative distribution function (ECDF) of the sample and the cumulative distribution function (CDF) of the reference distribution.

### How do you interpret the p-value in Kolmogorov-Smirnov test?

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.

### How do you interpret normality results?

If the Sig. value of the Shapiro-Wilk Test is greater than 0.05, the data is normal. If it is below 0.05, the data significantly deviate from a normal distribution.

How do you calculate KS test?

The critical value of D is found from the K-S table values for one sample test….

1. Fo(X) = Observed cumulative frequency distribution of a random sample of n observations.
2. and Fo(X)=kn = (No. of observations ≤ X)/(Total no. of observations).
3. Fr(X) = The theoretical frequency distribution.

How do you calculate KS value?

Graph the two distributions together. Measure the greatest vertical distance between the two graphs. Calculate the test statistic. Find the critical value in the KS table.

## What is the D statistic?

Cohen’s d statistic is a type of effect size. The calculation of Cohen’s d and its interpretation provide a way to estimate the actual size of observed differences between two groups, namely, whether the differences are small, medium, or large.

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