ABSTRACT
The inverse process of a transformation. The inverse of logarithmic transformation is exponentiation or anti-logging. In the case of power transformations, the transformed variable, x*, is calculated as x* = x q (where q is the power to which the values of variable x are raised), and the inverse transformation is given by x* raised to power 1/q, i.e. x = (x*)1/q (HAMILTON, 1990). For example, the inverse transformation to the square power transformation [x* = x 2] is the square root transformation [x = √x*, i.e. x = (x*)1/2]. When transformations are applied, data analyses are performed using the transformed variable(s), and back-transformation is applied to the summaries resulting from these analyses. A drawback of performing data analyses on transformed variables is the lack of meaning of back-transformed confidence intervals for differences between means, the exception being the logarithmic transformation and anti-logged confidence limits (see BLAND & ALTMAN, 1996b). See BLAND (2015) for an illustrative example and interpretation. See also delta method.
