Manuals/calci/KSTESTNORMAL

KSTESTNORMAL (XRange,ObservedFrequency,Confidence,DoMidPointOfIntervals,NewTableFlag)


  • is the array of x values.
  • is the frequency of values to test.
  • is the mean Value.
  • is the standard deviation of the set of values.
  • is either TRUE or FALSE.

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.

Example

Spreadsheet
A B
1 15 20
2 17 14
3 19 16
4 21 25
5 23 27
  • =KSTESTNORMAL(A1:A5,B1:B5,19,3.16)
KOLMOGOROV-SMIRNOV TEST
DATA OBSERVED FREQUENCY CUMULATIVE OBSERVED FREQUENCY SN Z-SCORE F(X) DIFFERENCE
15 20 20 0.19608 -0.74915 0.22688 0.03081
17 14 34 0.33333 -0.07293 0.47093 0.1376
19 16 50 0.4902 0.6033 0.72684 0.23665
21 25 75 0.73529 1.27952 0.89964 0.16435
23 27 102 1 1.95574 0.97475 0.02525
TEST STATISTICS
ANALYSIS
MEAN 17.21569
STANDARDDEVIATION 2.95761
COUNT 5
D 0.23665
D-CRITICAL #ERROR

KS TEST TYPE NORMALDIST

  • CONCLUSION - THE DATA IS NOT A GOOD FIT WITH THE DISTRIBUTION.

Related Videos

K-S Test

See Also

References