A method for statistical comparison of data sets and its uses in analysis of nuclear physics data

UDC: 
УДК 53.088, 519.23

Issue of journal:

Abstract: 

We propose a method for statistical comparison of two data sets. The method is
based on the method of statistical comparison of histograms. Usually a one
dimensional test statistic is used as a measure of distinction of data sets. This test
statistic depends on the shape of distributions in data sets. Using the two
dimensional test statistics which is determined via the statistical moments of
distribution produced by the calculation of “the significance of deviations” for the
corresponding points with observed values is proposed in the paper as a distinction
measure between data sets. The significance of deviation in the corresponding
points can be considered as a realization of the random variable which is close to
a standard normal random variable if we observe the same random value in both
data sets. It helps to avoid the dependence of the result on the shape of
distributions. The accuracy of the estimator for the measure of distinction is
determined by the MonteCarlo experiment which, by analogy with the construction
of repeated samples (resampling) in the bootstrap method, it is possible to call
construction of repeated data set (redatasetting). As an estimator of quality of the
decision made, it is proposed to use the value which it is possible to call the
probability that the decision ‘’data sets are various’’ is correct.

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