3.2 Testing differences, correlations and the equilibrium assumption
In order to analyse differences and correlations of the data, we performed several statistical tests. Each dataset was tested for normality using Shapiro-Wilk . If normally distributed, we performed simple t ‑statistics to test for significant differences. If data were skewed or non-normal, we performed non-parametric alternatives: Wilcoxon signed-rank test for two groups and Kruskal-Wallis test by ranks for more than two groups . To test correlations of non-linear data we applied Spearman’s rho statistic .
Due to the nature of the high-resolution dataset of δv, we could also test the equilibrium assumption of δv and precipitation for the sampling period using the following equation:
\(R_{\text{atm}}=\ R_{v}-R_{p}\)(3)
where Rv and Rp are the liquid Majoube-corrected isotope ratios of δv and liquid isotope ratios of precipitation and ΔRatm is the difference in isotope ratios of water vapour and precipitation in atmosphere. These laboratory standards are also relative to VSMOW. IfΔRatm = 0, a perfect equilibrium between precipitation and δv isotope ratios prevails. We used the daily mean of δv at 2 m height for the tree site and grassland site separately to compare both types of landcover.ΔRatm was calculated for days when precipitation occurred.