The critical value of correlation coefficient $|r{|}_{\mathrm{C}}$, which varies with the degree of windowed moving average k, freedom n and confidence ξ, 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 $|r{|}_{\mathrm{MC}}$ for these samples X, Y to establish the model parameters and then examine the model result $|r{|}_{\mathrm{MO}}$ for three different astronomical fields to calculate the confidence level ξ of sample correlation coefficient $|r|$, which is compared with MC result $|r{|}_{\mathrm{MC}}$. The results show that the MC results $|r{|}_{\mathrm{MC}}$ and model results $|r{|}_{\mathrm{MO}}$ are in exceptionally good agreement, and the applicability of the model to obtain the confidence level ξ is satisfactory when calculating the sample correlation coefficient $|r|$ for two independent samples X and Y.