Analysis of data with interval uncertainty: application of a combined sample consistency measure

The article considers one of the main problems of data analysis, i.e., estimation of parameters characterizing the data sample of a constant quantity. Data analysis is required in all areas of experimental physics to obtain reliable measurement results. To describe sample units under bilateral constraints on their error, the apparatus of interval analysis and statistics is used. In particular, data homogeneity in the sample is described using various consistency measures. A set of three consistency measures is presented that describe different relationships between sample units. On the basis of the considered set, a combined sample consistency measure is proposed that can simultaneously provide outer and inner estimates of the quantity under study. The specified estimates are important in solving a massive data processing problem (i.e., processing of a set of samples obtained under different measurement conditions). The article provides necessary information on interval analysis and various interval arithmetics. The relationships between the proposed combined measure and the results of computations with interval twins and fuzzy sets are considered. This combined measure can be used in solving the massive data processing problem typically addressed in theoretical and applied semiconductor physics. A practical example is presented of using the combined sample consistency measure in the testing of solar transducers against a reference transducer as part of the study of their spectral properties and quantum yield.