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What is the maximum deviation of the KS test?
The KS-test uses the maximum vertical deviation between the two curves as the statistic D. In this case the maximum deviation occurs near x =1 and has D =.45. (The fraction of the treatment group that is less then one is 0.2 (4 out of the 20 values); the fraction of the control group that is less than one is 0.65 (13 out of the 20 values).
When to use Kolmogorov’s d statistic in statistics?
Have you ever run a statistical test to determine whether data are normally distributed? If so, you have probably used Kolmogorov’s D statistic. Kolmogorov’s D statistic (also called the Kolmogorov-Smirnov statistic) enables you to test whether the empirical distribution of data is different than a reference distribution.
Which is the maximal value of D +?
The maximal value of D + will always occur at a left-hand endpoint of the ECDF. The D statistic is simply the maximum of D – and D + . You can compare the statistic D to critical values of the D distribution, which appear in tables.
Is the d statistic greater than the critical value?
The D statistic is simply the maximum of D – and D + . You can compare the statistic D to critical values of the D distribution, which appear in tables. If the statistic is greater than the critical value, you reject the null hypothesis that the sample came from the reference distribution.
How is the KS test used to compare two distributions?
As a non-parametric test, the KS test can be applied to compare any two distributions regardless of whether you assume normal or uniform. In practice, the KS test is extremely useful because it is efficient and effective at distinguishing a sample from another sample, or a theoretical distribution such as a normal or uniform distribution.
How is the KS test used in statistics?
How the KS Test Works 1 Descriptive Statistics. Thus descriptive statistics were developed to reduce the list of all the data items to a few simpler numbers. 2 Cumulative Fraction Function 3 Empirical Distribution Function. 4 Percentile Plot 5 Estimated Distribution Function Ogive. 6 A Final Example.
How to find the maximum distance between ecdfs?
To achieve this, the KS test finds the maximum distance between the ECDFs. More importantly, the test requires evaluating whether the distance is large enough to claim that the two samples do not belong to each other. In the diagram below, the maximum distance between the income ECDFs is indicated by the red arrow.