Critical value model of sample correlation coefficient after windowed moving average

The critical value of correlation coefficient vertical bar r vertical bar(C), which varies with the degree of windowed moving average k, freedom n and confidence xi, is widely accepted to judge the linear relationship between two independent samples X and Y. In order to avoid referring to inconvenient critical value tables or using time-consuming Monte Carlo (MC) simulation, this paper presents a mathematically unified model for calculating the critical value. In this paper, both independent samples X and Y follow the standard normal distribution. We analyse MC result vertical bar r vertical bar(MC) for these samples X, Y to establish the model parameters and then examine the model result vertical bar r vertical bar(MO) for three different astronomical fields to calculate the confidence level xi of sample correlation coefficient vertical bar r vertical bar, which is compared with MC result vertical bar r vertical bar(MC). The results show that the MC results vertical bar r vertical bar(MC) and model results vertical bar r vertical bar(MO) are in exceptionally good agreement, and the applicability of the model to obtain the confidence level xi is satisfactory when calculating the sample correlation coefficient vertical bar r vertical bar for two independent samples X and Y.