The test provides a measure that indicates the fit of the distribution of your data to some known distribution. To illustrate how it works we start by generating 1000 pseudo-random data points with a Gaussian distribution:
Although it is not necessary for the purpose of the test, we compute the cumulative distribution function for this data set using the following commands:
Here W_Hist is the PDF shown above and W_INT is the CDF shown below.
To compare this to a normal CDF we can use the built-in StatsNormalCDF in the following user function:
To run the KS test execute the command:
Note that the operation's input are the raw data and a user defined continuous distribution function. The results are shown in the Kolmogorov-Smirnov Test table:
Since the test statistic D is smaller than the critical value we can't reject the null hypothesis that the two distributions are the same.
To illustrate a difference between distributions, suppose your data have a Poisson distribution as in:
Here the PDF is shown in the graph above and the CDF below.
To test this data set against the same normal distribution as above you can execute the command:
which yields the following table:
alpha 0.05 N 1000 D 0.286538 Critical 0.0427766 PValue 1.80085e-73
In this case the test statistic D is clearly larger than the critical value and the hypothesis that data2 is taken from a normal distribution is rejected.