The Chi-square test is used to test differences between binned distributions.
The selected Y-values in grid 1 and grid 2 are compared.
In the first test the Y-values in grid 1 are assumed to represent a theoretical
distribution. Chi-squared is defined as
where Ni is the number in the i-th bin and ni is the number expectred according to some known distribution. Both distributions should contain the same total number of events. The probablity (0<P<1) that the numbers Ni are drawn from the expected distribution is calculated. It is an incomplete Gamma function of Chi-squared. In the second test two measured data sets (in grid 1 and grid 2) are compared. Chi-squared is then defined as
where Ni and Mi are the numbers in the i-th bin of the distributions calculated in grid 1 and grid 2. The total numbers should be the same. The probablity P that the two distributions are drawn from the same underlying distribution is calculated. A small value of P indicates that the two distributions are probably different.
Kolmogorov-Smirnov test - 1 and 2
The KS-test is used to test differences between unbinned distributions of a single continuous variable. The largest vertical difference D between the cumulative distributions is determined. This yields the probability that the two distributions are drawn from the same underlying distribution. The first test compares the data in grid 2 with a theoretical (normalized) distribution function defined in the Function panel. The second test compares (observed) data in grid 1 and grid 2.