# Manuals/calci/KSTESTCORE

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KSTESTCORE (XRange,ObservedFrequency,Confidence,NewTableFlag,Test,DoMidPointOfIntervals)

• is the set of values.

## Description

• This function gives the test statistic of the K-S test.
• K-S test is indicating the Kolmogorov-Smirnov test.
• It is one of the non parametric test.
• This test is the equality of continuous one dimensional probability distribution.
• It can be used to compare sample with a reference probability distribution or to compare two samples.
• This test statistic measures a distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions of two samples.
• The two-sample KS test is one of the most useful and general nonparametric methods for comparing two samples.
• It is sensitive to differences in both location and shape of the empirical cumulative distribution functions of the two samples.
• This test can be modified to serve as a goodness of fit test.
• The assumption of the KS test is:
• Null Hypothesis(H0):The sampled population is normally distributed.
• Alternative hypothesis(Ha):The sampled population is not normally distributed.
• The Kolmogorov-Smirnov test to compare a data set to a given theoretical distribution is as follows:
• 1.Data set sorted into increasing order and denoted as , where i=1,...,n.
• 2.Smallest empirical estimate of fraction of points falling below , and computed as for i=1,...,n.
• 3.Largest empirical estimate of fraction of points falling below and computed as for i=1,...,n.
• 4.Theoretical estimate of fraction of points falling below and computed as , where F(x) is the theoretical distribution function being tested.
• 5.Find the absolute value of difference of Smallest and largest empirical value with the theoretical estimation of points.
• This is a measure of "error" for this data point.
• 6.From the largest error, we can compute the test statistic.
• The Kolmogorov-Smirnov test statistic for the cumulative distribution F(x) is:where is the supremum of the set of distances.
• is the empirical distribution function for n,with the observations is defined as:where is the indicator function, equal to 1 if and equal to 0 otherwise.
• Using this function we can identify the following deatils:
Are the data from the Normal distribution or Weibull distribution or Exponential distribution or a logistic distribution.


## Related Videos

Kolmogorov-Smirnov Test