Stability to environmental variation in traits such as yield and grain quality is becoming increasingly important with climate change. The slope of regression in a reaction norm model, where the performance of a genotype is regressed over an environmental covariable, is often used as a measure of stability. This approach fails to account for the potential bias introduced by heterogeneity in the scale of genetic variance across environments, which is a form of genotype by environment interaction (G×E) known as scale-type G×E. These reaction norms are also limited to a linear function, which could be too restrictive for describing the interaction between genotypes and the environment. The aim of this paper was to demonstrate two methods which attempt to address these shortcomings in reaction norms and apply them to a multi-environment trial in Barley (Hordeum vulgare) that contains a large amount of scale-type G×E. Stability estimated from factor analytic models, which explicitly disentangle scale-type G×E, were used for comparison. The two methods substantially increased the correlation with stability measures estimated from the factor-analytic models, indicating that they removed variation in stability that originated from scale-type G×E. After accounting for scale-type GxE, breeding values for overall performance and stability were highly correlated between the linear reaction norms and factor analytic models. Analyses which use reaction norms to rank genotypes on stability should consider implementing the scale-corrections outlined in this study.