How should crop water-use efficiency be analyzed? A warning about spurious correlations

Water-use efficiency (WUE) is a common concept in the agronomy literature. Although definitions of WUE vary, the most common relates the ratio of grain yield (GY) to evapotranspiration (ET) e.g. WUEo=oGY/ET or WUEo=oET/GY. But using this metric has issues, as it is a ratio and is often analyzed relative to one of its components. Here it is shown that plotting WUE versus GY or ET causes spurious correlations, leading to artificial elevation of the proportion of variance explained. This may lead to higher confidence in WUE data than is warranted by the raw data. When WUE is regressed on GY, fitted slopes can be biased leading to predictions of high GY gain for little change in water use. A survey found (similar to)23% of WUE focused literature presented spurious correlations. To avoid these issues, future analyses could focus on interpretation of raw GY versus ET data and infer WUE changes from this plot. Treatments and site variation are shown to have effects on the interpretation of the GY to ET relationship. Statistical methods are reviewed to evaluate the mean/median response of GY to ET, and thus allow interpretation of patterns of WUE. Isolines of constant WUE are introduced as a general tool and illustrated relative to contrasting datasets. Other statistical methods are illustrated for evaluating the benchmark WUE, or boundary lines. Although no one statistical method will work for all datasets, the following conclusion is general across agronomy: spurious correlations can be avoided by not relating variables that share measured data.