Justification of the method of approximation of experimental data

Abstract

Goal. To carry out a comparison of linear and curvilinear methods of approximation of experimental data with the provision of recommendations for their use to ensure the reliability and adequacy of the obtained results. Methods. The analysis of linear and curvilinear methods of approximation of experimental data was carried out using the foundations of higher mathematics, the theory of mathematical statistics of random processes, regression and correlation analyses. Calculations were performed in the Microsoft Excel software environment version 2016. Results. The goal was achieved using the example of the analysis of the dependence of soil hardness on its density. For the used experimental data, the tightness of their linear connection was estimated by the correlation coefficient, and the curvilinear one by the correlation ratio. Further comparison of these statistical indicators using the F-criterion showed that the actual value of this criterion (1.52) was significantly lower than the table value (19.40). With this in mind, despite the lower value of the correlation coefficient (0.77) compared to the correlation ratio (0.84), the functional relationship between density and soil hardness at the statistical significance level of 0.05 was linear. Conclusions. Obtaining an adequate scientific result when processing experimental data depends on the correct choice of the correlation between the argument and the function of the studied stochastic process. The type of such a relationship (linear or curvilinear) at a given level of probability should be based on a comparison of the correlation coefficient and the correlation ratio of experimental data through such a statistical indicator as the F-criterion. For a smaller value of the latter compared to the table, the correlation between the argument and the function of the random process is assumed to be linear, in the opposite case — curvilinear.