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BoxCox transformationThe BoxCox transformation is a procedure for obtaining the optimal transformation to normalize data within the following family of power transformations:
The required value of λ is given by that value which maximizes the following log likelihood function
This equation is solved iteratively using a series of values of λ. Values of the log likelihood function are then plotted against λ to obtain the maximum. Where the data includes zeros, a constant is added to each value of Y  usually either 1 or 0.5. As with other transformations, if there are many zeros this can result in bias. Detransformation is achieved using the following:
Although you can use the precise value of λ in the transformation, it is more common to use the (common) transformation closest to that suggested by the BoxCox transformation, providing it still lies within the 95% confidence interval of λ. This is known as a 'convenient estimator' (although this model can be impossible to interpret in biological terms).
