Test for different histograms
Purpose
Description
Macro Synopsis
Modules
Related Functions
References
Purpose
Chi-square based significance test
Description
"Test for different histograms" performs a significance test for differences
between 'binned distributions' of two data sets, either two signals
or a signal and a model. In both cases the two input data sequences must be of the same length.
This function takes one parameter,
- sigtype, denoting whether the second input signal is
- a "model" (0), i.e. a cumulative distribution function increasing monotonously or
- a "second data set" (1).
It returns two parameters:
- chisq, which is the statistics (see below), and
- signif, which is the significance, i.e. the probability
[0..1] of randomly equal distributions, where small values
indicate significantly different distributions.
If the second signal is a model, the chi-square statistics is
where is the number of events observed in the ith bin and the number expected according to some known distribution.
Otherwise, (if the histograms of two data sets are to be compared), the chi-square statistics is
where are the number of occurences in
bin i for the first data set and the number of occurences in the same bin for the second data set and
Macro Synopsis
TestHistograms([xA,xB],sigtype,&chisq,&signif);
signal xA,xB;
option sigtype;
float chisq, signif;
Modules
Statistics
Related Functions
BDS test, Kolmogorov-Smirnov test,
Test for different means, Test for different variances,
Test for non-normal-distributed data,
Test for non-white-noise,
Test for the mean of a Gaussian, Test for the variance of a Gaussian,
Wilcoxon test
References
Hollander/Wolfe [13], Lehmann [36]