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.