Analysis of Correlations between Variables Using Control Charts Developed Based on Kendall's Criterion

Abstract

The article expands the potential applications of Kendall’s criterion by using the control chart method to determine the correlation between two variables. This method of studying the correlation is particularly useful in longitudinal studies frequently encountered in pedagogical, psychological, medical, environmental research, statistical monitoring of natural phenomena, and forecasting.

The processing of experimental data and statistical conclusions in the control chart method are depicted in the diagram of this chart, which serves as a common language for various specialists. The hypothesis of independence or presence of correlation in diagrams is tested over time. The diagram not only assesses trends but also predicts changes in the process, which can be effective for data analysis. The diagram allows comparison of results from experiments on the same problem. Additionally, during the experiment, it is possible to adjust or refine the course of the experiment.

The control charts developed in this work take into account the sample size. For small samples, the binomial criterion is used, while for large samples, Kendall's criterion is applied. The characteristics of the new control chart are derived using Kendall's theorem. As an example, one problematic task from seismology was investigated, and the iterative process of drawing conclusions for this task is demonstrated using a control chart diagram.