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Geodetski list, Vol. 76 (99) No. 2, 2022.

Review article

New Formula for Finding the Correlation Coefficient in Geodetic Measurements for a Small Number of Observations

Valeriy Gladilin orcid id orcid.org/0000-0002-0492-3510 ; Department of Geodesy, Cartography and Land Management, Bila Tserkva National Agrarian University, Bila Tserkva, Kyivska oblast, Ukraine
Vadym Belenok orcid id orcid.org/0000-0001-5357-7493 ; Department of Aerospace Geodesy and Land Management, National Aviation University, Kyiv, Ukraine
Sergiy Kryachok orcid id orcid.org/0000-0001-5633-1501 ; Department of Geodesy, Cartography and Land Management, Chernihiv Polytechnic National University, Chernihiv, Ukraine
Tetiana Siroshtan ; Department of Geodesy, Cartography and Land Management, Bila Tserkva National Agrarian University, Bila Tserkva, Kyivska oblast, Ukraine
Iryna Hamalii ; Department of Geodesy, Cartography and Land Management, Bila Tserkva National Agrarian University, Bila Tserkva, Kyivska oblast, Ukraine

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Abstract

When performing geodetic surveys, the number of measurements is usually small, which in the case of dependent series of measurements leads to an underestimation of the correlation coefficient calculated by the standard formula. A new formula for determining the correlation coefficient is proposed. The values of correlation coefficients calculated by the new formula and by the known ones were compared for the number of measurements . It was found that the correlation coefficient values calculated by the new formula will have higher values as compared to the values calculated by the known formulas, i.e. these values will be less biased with respect to the true values of the correlation coefficients. The correlation coefficients obtained by the new formula will be maximal at an appropriate level of significance and number of degrees of freedom. With a large number of measurements, the values of correlation coefficients obtained by the new formula and by the formulas that are widely used in geodesy and photogrammetry will not differ significantly.

Keywords

correlation coefficient; unbiased and biased estimator of correlation coefficient; calculating the correlation coefficient in geodesy; new method for calculating the correlation coefficient; regression equation

Hrčak ID:

281105

URI

https://hrcak.srce.hr/281105

Publication date:

29.6.2022.

Article data in other languages: croatian

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