Quick Method for Choosing a Transf orrnation

The choice of non-linear transformations in the analysis of data can frequently be simplified by restricting the possible transformations to a particular family. Tukey has shown that the “simple family” has many desirable properties from this point of view. This family can be represented as the set of solutions to a third order differential equation and the constant of this equation provides a convenient index of the family. This index may be approximated by substituting the given data into the corresponding difference equation. The resulting approximation can then be used for rough solutions or as a starting value for the iterative solution of the maximum likelihood equations given by Turner. Two examples are provided to demonstrate the procedure.