For observations from a known distribution, the variance-stabilizing transformationTransformation yields approximately normally distributed transformed variables. For data, the Box–Cox family of power transformationsTransformation, indexed by a parameter \(\lambda \) , provides a widely applicable method for transformationTransformation of positive response data to approximate normality. The chapter describes procedures for making the transformationTransformation robust and extending the robustnessRobustness to more general problems. An approximate score test for the null value \(\lambda _0\) is developed in Sect. 6.1.2. A significant value leads to rejection of the value \(\lambda _0\) . Using the FSFS to monitor the score test for a set of values of \(\lambda _0\) leads in Sect. 6.1.3 to the “Fan PlotFan plot”. This reveals the effect of outliersOutlier on the estimated transformationTransformation and so to the deletion of outliersOutlier and selection of a value of \(\lambda \) for further data analysis. Section 6.2 develops related procedures (the extended Yeo–Johnson transformationTransformation) for data which can be positive or negative. The approach is visual, being based on the interpretation of fan plotsFan plot. Section 6.3 provides an automatic procedure for estimating these transformationsTransformation using quantities calculated from fan plotsFan plot. TransformationTransformation procedures when the responses are proportions or percentages follow, as well as transformationsTransformation of both sides of a statistical model.