Fig. 4. Yields without fertiliser N

Fig. 4. Yields without fertiliser N application (YIELDN0) in winter wheat (a) and spring barley (c), respectively as a function of SOC, and residual plots from the full model (excluding SOC) for winter wheat yields (b) and spring barley yields (d) without fertiliser N application as a function of SOC (note the axes are transformed). The solid line is the estimated regression line, whilst the dotted lines demonstrate the 95% confidence interval.coefficients are measures in scales of standard deviations, which allow for comparison of the coefficients across the effects. The full models for each response variable and crop type were validated by quintile plots and residual plots. The residual plots for the full models are presented for each crop type and response variable indicating the residual effect of SOC on the response variable when all other effects are removed. On these plots, the axes weretransformedsothatSOCandtheresponsevariablecanberead directly on the graph. The effect of SOC on the three response variables (YIELDPot, YIELDN0, and NUE) was tested in the full model by removing SOC fromthemodelandtestingifthisdecreasedtheabilityofthemodel toexplainthevarianceintheresponsevariables.ThenullhypothesisforthistestwasthattherewasnoeffectofSOContheresponse variable.IfSOCiscorrelatedwithothervariables,apotentialcausal effect of SOC could be explained by these variables and we would acceptthenullhypothesisofnoeffectofSOC.Thisapproachisconservative in the sense that if an effect is identified, this effect can only be explained by SOC and none of the other variables. However, it is inefficient if we want to show that there is an effect of SOC.