RESEARCH ON THE HOMOGENEITY OF PSEUDO-RANDOM SAMPLES USING ANDERSON'S CRITERION AND ITS ANALOGS

Abstract

The paper examines in detail the criteria for statistical homogeneity of samples of experimental measurements in cases where the probability distribution functions are a priori unknown. In particular, the Anderson criterion, which is widely used in practice to assess the homogeneity of data based on rank distributions, is analyzed. The Spearman criterion is also considered, which allows comparing two samples obtained using the same measuring device and identifying statistical differences between them. In addition, the combined Busch-Wind criterion is proposed, which is based on logistic random variables and is analogous to the well-known Van der Waerden and Klotz statistics in its properties. The corresponding mathematical models, algorithms for calculations, and critical values used to test statistical hypotheses regarding the homogeneity of samples are presented. Experimental studies have been conducted that included logistic and exponential samples, which confirmed the high efficiency of the criteria used in applied data analysis problems.