The Box-Cox plot is a tool to help you determine the most appropriate power transformation to apply to response data. Most data transformations can be described by the power function,
As a reminder, here are the commonly used transformations:
λ = 1 no transformation
λ = 0.5 square root
λ = 0 natural log
λ = -0.5 inverse square root.
λ = -1 inverse
Power law transformations can only be performed on responses that are greater than zero, so you may need to add a constant, k, to all the responses.
The plot shows the minimum lambda values, as well as lambdas at the 95% confidence range. The plot also shows the current power transformation so you can see where that fits. It is possible that the 95% confidence interval will not be shown due to it being outside the +/- 3 lambda limits.
RECOMMENDED TRANSFORMATION: The software will recommend the standard transformation that falls closest to the best lambda value and is within the confidence interval. If there is no standard transformation within the confidence interval, then the Power transformation is recommended with the best lambda value. After implementing the recommended transformation, the Box-Cox will still provide a recommendation. Usually, it is the same as the transformation just applied. In that case, this plot is complete. If a different transformation is recommended (say a change from log to square root) then the new recommendation should be tried. This may happen when the effects/model chosen changes as a result of implementing the transformation. In all cases, the transformations should be improving the statistical analysis and/or the diagnostic plots.
ArcSin(Sqrt) and Logit transformations are non-power law, and will never be suggested by the Box-Cox plot. They are applied manually based on the type of data gathered.