Comparison of histograms in physical research

Abstract

The review of methods of histograms comparison is presented. Possible approaches for the comparative analysis of histogram are considered. The term "histogram" was coined by the famous statistician Karl Pearson to refer to a "common form of graphical representation" [1]. Histograms are very useful in their canonical visual representation, but today histograms are considered as purely mathematical objects. Histograms are used in different scientific fields. Besides physics data analyses, histograms play a very important role in databases, image processing and computer vision [1]. Correspondingly, goals and methods of treatment of histograms are varied in dependence to the area of application. In this paper histograms are considered in frame of tasks related to physical experiments. The paper presents some of the methods and results of the comparison of histograms. A comparison was made of three methods of the comparison of histograms: the Kolmogorov-Smirnov (KS) method, the Anderson-Darling (AD) method and the method for statistical comparison of histograms (SCH). The dependence of the mean error in hypotheses testing of distinguishability of the reference data set and test data set on the difference in position parameter of samples: the Anderson-Darling and Kolmogorov-Smirnov criteria give the better result than SCH method. The dependence on the width parameter of samples: the SCH criterion gives the better result than AD and KS criteria. Nevertheless, the SCH is a multidimensional method. It allows to include the any one-dimensional test statistic as an additional component of multidimensional test statistic in the frame of the method. For example, the including of the AD test statistic into SCH method as third component of the three dimensional test statistic will allow to reach the better coordinate resolution in the example which was considered above. Possible approaches for the comparative analysis of histogram are considered. As shown, there is no single best test for all applications. It means that before application any test must be checked with care. A good solution is a combined use of several tests.