writer
6,694
edits
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: − + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Manuals/calci/KSTESTCORE (view source)
Revision as of 19:50, 14 December 2016
, 19:50, 14 December 2016no edit summary
==Ks
<div style="font-size:30px">'''KSTESTCORE (XRange,ObservedFrequency,Test,someconfidence,NewTableFlag)'''</div><br/>
*<math>n_1,n_2,n_3...</math> are any real numbers.
==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 <math>x_i</math>, where i=1,...,n.
*2.Smallest empirical estimate of fraction of points falling below <math>x_i</math>, and computed as <math>\frac{(i-1)}{n}</math> for i=1,...,n.
*3.Largest empirical estimate of fraction of points falling below <math>x_i</math> and computed as <math>\frac{i}{n}</math> for i=1,...,n.
*4.Theoretical estimate of fraction of points falling below <math>x_i</math> and computed as <math>F(x_i)</math>, 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:<math> D_n=Sup_x|F_n(x)-F(x)|</math>where <math>sup_x</math> is the supremum of the set of distances.
*<math>F_n(x)</math> is the empirical distribution function for n,with the observations <math>X_i</math> is defined as:<math>F_n(x)= Refer Wikipedia I_{X_i\le x}</math>where <math>I_{X_i\le x}</math> is the indicator function, equal to 1 if <math>X_i\le x</math> and equal to 0 otherwise.
==Examples==