An integrated excel workflow for significance testing of the Pearson correlation coefficient in hydrological analysis

For practitioners, educators, and students who rely on Excel for hydrological data analysis, assessing the significance of a Pearson correlation often ends at the coefficient of determination obtained from a scatterplot trendline. The formal significance test is frequently omitted, as Excel provides no built-in, one-step procedure for this inference. This paper presents an integrated Excel workflow that addresses this gap. The workflow consolidates regression modeling and exact significance testing into a single, automated procedure using only native Excel functions. It employs the LINEST array function to simultaneously extract R2, the F-statistic, and residual degrees of freedom; the sign of the correlation is recovered from the regression slope. It then computes the exact critical correlation coefficient via Excel's F.INV.RT function using a derived conversion formula. Built-in diagnostic steps enable screening of the classical regression assumptions before applying the test. Validation against R at three significance levels (α = 0.01, 0.05, and 0.10) confirms accuracy. Illustrative cases – including a strong-correlation dataset and a borderline case showing how sample size affects the significance decision – demonstrate how the workflow supports the transition from subjective R2-based assessment into a streamlined, statistically rigorous procedure suitable for both practice and teaching.