Оценка значений выборочного коэффициента линейной парной корреляции, статистически неотличимых от единицы

Сергей Алексеевич Добротин; Ольга Николаевна Косырева

doi:10.17308/sait/1995-5499/2025/1/12-23

Authors

Sergey A. Dobrotin The Russian Presidential Academy of National Economy and Public Administration (The Presidential Academy, RANEPA), Dzerzhinsky branch
Olga N. Kosyreva The Russian Presidential Academy of National Economy and Public Administration (The Presidential Academy, RANEPA), Dzerzhinsky branch https://orcid.org/0000-0003-2126-3275 (unauthenticated)

DOI:

https://doi.org/10.17308/sait/1995-5499/2025/1/12-23

Keywords:

indirect measurements, standard uncertainty, sample, linear pair correlation coefficient, insignificant difference from unity, statistical hypothesis testing

Abstract

Uncertainty assessment of indirect measurement results ensures their reliability. The formula for calculating the standard uncertainty specified in GOST 34100.3-2017 uses the coefficient of linear pair correlation between the results of direct measurements. The literature notes the effect of bias of its sample value due to such reasons as sample limitations, the presence of errors in measurement results, etc. To use a special case of this formula, it is necessary to develop a methodology for testing the hypothesis about an insignificant difference of the sample coefficient of linear pair correlation from one. In the special case of a normal distribution of correlation-dependent random variables with the same parameters, this hypothesis can be replaced by an equivalent one about an insignificant difference of the absolute value of the free term of the linear regression equation from zero. Using the method of statistical modeling of correlation-dependent normal variables with subsequent testing of this hypothesis, the dependence of the sample correlation coefficient, indistinguishable from one, on the sample size was obtained. A block diagram of the implementation of the numerical experiment is given. The standard deviation of the obtained correlation coefficient is estimated and its dependence on the sample size is shown. Using the weighted least squares method according to the methodology specified in RMG 54-2002, a fractional-linear regression equation is obtained, describing the dependence of the sample correlation coefficient, indistinguishable from one, on the sample size.

Author Biographies

Sergey A. Dobrotin, The Russian Presidential Academy of National Economy and Public Administration (The Presidential Academy, RANEPA), Dzerzhinsky branch

Doctor of Technical Sciences, Professor, Head of the Department of Information, Natural Sciences and Humanities of The Russian Presidential Academy of National Economy and Public Administration (The Presidential Academy, RANEPA), Dzerzhinsky branch
Olga N. Kosyreva, The Russian Presidential Academy of National Economy and Public Administration (The Presidential Academy, RANEPA), Dzerzhinsky branch

Associate Professor of the Department of Information, Natural Sciences and Humanities of The Russian Presidential Academy of National Economy and Public Administration (The Presidential Academy, RANEPA), Dzerzhinsky branch

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